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with radius R is called the osculating circle to the curve γ at the point P. If C is a regular space curve then the osculating circle is defined in a similar...

"kiss". An osculating orbit and the object's position upon it can be fully described by the six standard Kepler orbital elements (osculating elements)...

osculant, an invariant of hypersurfaces osculating circle osculating curve osculating plane osculating orbit osculating sphere The obsolete Quinarian system...

point. The word osculate is from Latin osculari 'to kiss'; an osculating plane is thus a plane which "kisses" a submanifold. The osculating plane in the...

first-order contact with C. The osculating circle to C at p, the osculating curve from the family of circles. The osculating circle shares both its first...

the center of the osculating circle. The curvature vector and the tangent vector are perpendicular vectors that span the osculating plane, the plane containing...

points, respectively, of a body's direct orbit around the Sun. Comparing osculating elements at a specific epoch to those at a different epoch will generate...

approximation to the ellipsoid in the vicinity of a given point is the Earth's osculating sphere. Its radius equals Earth's Gaussian radius of curvature, and its...

line is an osculating curve from the family of lines, and has first-order contact with the given curve; an osculating circle is an osculating curve from...

Usually, these instantaneous orbits are chosen to be osculating. This means that they osculate ("kiss" or touch) the real trajectory. The evolution of...

but a set of osculating elements for a particular epoch may only be (approximately) valid for a rather limited time, because osculating elements such...

available, one can draw an ellipse using an approximation by the four osculating circles at the vertices. For any method described below, knowledge of...

function, and for the osculating conics to a given smooth curve. Ghys, Étienne; Tabachnikov, Sergei; Timorin, Vladlen (2013), "Osculating curves: around the...

(now unchanging) conic section indefinitely; this conic is known as the osculating orbit and its orbital elements at any particular time are what are sought...

designated 109P/Swift–Tuttle) is a large periodic comet with a 1995 (osculating) orbital period of 133 years that is in a 1:11 orbital resonance with...

celestial bodies. The parameters of the osculating Kepler orbit will then only slowly change and the osculating Kepler orbit is a good approximation to...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

"Barycentric Osculating Orbital Elements for Comet Hyakutake (C/1996 B2)". Retrieved 2011-01-30. (Horizons) Horizons output. "Barycentric Osculating Orbital...

University of Minnesota Press, pp. 63–82, ISBN 9780816657971. P. 69: "Osculating curves don't kiss for long, and quickly revert to a more prosaic mathematical...

curvature at 0 is equal to κ(0). The osculating plane has the special property that the distance from the curve to the osculating plane is O(s3), while the distance...

time standard is called Barycentric Coordinate Time (TCB). Barycentric osculating orbital elements for some objects in the Solar System are as follows:...

normal), and r is its instantaneous radius of curvature based upon the osculating circle at time t. The components a t = d v d t u t and a c = v 2 r u n...

proper inclination (ip). The proper elements can be contrasted with the osculating Keplerian orbital elements observed at a particular time or epoch, such...

at the point of tangency with its defining circle, which is also its osculating circle at that point. It also has two finite inflection points and one...

of an orbit Nautical almanac – Publication on celestial body positions Osculating orbit – Orbital perturbations Ptolemy's table of chords – 2nd century...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

R_{\text{eq}}={\sqrt {\frac {6L^{2}}{4\pi }}}\approx 0.6910L} The osculating circle and osculating sphere define curvature-equivalent radii at a particular point...

fact leads to an easy proof of the Tait–Kneser theorem on nesting of osculating circles. The normals of the given curve at points of nonzero curvature...

toward the center of the circle in which the object is moving, or the osculating circle (the circle that best fits the local path of the object, if the...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Propulsion Laboratory: for the above reasons, they may strongly differ from osculating orbital elements provided by other sources. Otherwise, recently discovered...

at 01:30 local time A Sun-synchronous orbit is achieved by having the osculating orbital plane precess (rotate) approximately one degree eastward each...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

singular point of a curve. It is defined as a point where two (or more) osculating circles to the curve at that point are tangent. This means that two branches...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

graphs. He is also one of the namesakes of the Tait–Kneser theorem on osculating circles. Tait was born in Dalkeith on 28 April 1831 the only son of Mary...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

near a multiple root Newton's method Normal (geometry) Osculating circle Osculating curve Osculating plane Perpendicular Subtangent Supporting line Tangent...

with the osculating circle at that point. In contrast, generic points on a curve typically only have 3-point contact with their osculating circle. The...

February 2021. Retrieved 10 February 2021. Horizons output. "Barycentric Osculating Orbital Elements for 90377 Sedna (2003 VB12)". Retrieved 18 September...

often to determine a valid object state. Such element sets are known as osculating elements because they coincide with the actual orbit only at that moment...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Center. Retrieved 1 August 2026. Horizons. "JPL Horizons: Barycentric Osculating Orbital Elements for 2014 FE72". Retrieved 6 June 2022. "JPL Horizons...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

elements lie in the approximate ranges At the present epoch, the range of osculating orbital elements of the members (by comparison to the MPCORB database...

the torsion of a curve measures how sharply it is twisting out of the osculating plane. Taken together, the curvature and the torsion of a space curve...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

.K..110Y. doi:10.48377/MPEC/2025-K110. Horizons output. "Barycentric Osculating Orbital Elements for Comet ATLAS (C/2025 K1)". Retrieved 23 March 2026...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

and "Center: Sun" should be defaulted to.) Results are instantaneous osculating values at the precise J2000 epoch. Williams, David R. (November 25, 2020)...

UT on 15 November passed the first periselene of its lunar orbit. The osculating orbit on that date was 6,704 × 53,208 km, with an orbital period of 129...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

motion of a small orbiting body relative to a larger orbiting body. The osculating (instantaneous) orbital period of the smaller body remains very near that...

Osculating circles of the Archimedean spiral, tangent to the spiral and having the same curvature at the tangent point. The spiral itself is not drawn...

normal vector. It is the point at infinity if the curvature is zero. The osculating circle to the curve is centered at the centre of curvature. Cauchy defined...

tangent line at p also have the same normal curvature at p and their osculating circles form a sphere. The theorem was first announced by Jean Baptiste...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

origin in the positive x direction and gradually turns anticlockwise to osculate the circle. The spiral is a small segment of the above double-end Euler...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

original on September 2, 2010. Retrieved January 18, 2016. "Barycentric Osculating Orbital Elements for 90482 Orcus". Retrieved August 28, 2023. (PR= 8.986E+04...

Laboratory. Retrieved 11 November 2024. Horizons output. "Barycentric Osculating Orbital Elements for Comet Zhu-Balam (C/1997 L1)". ssd.jpl.nasa.gov. Jet...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

divisors (bundles of principal parts can be used to study the osculating (as in osculating plane) behaviors of a linear system.) Jet (mathematics) (a closely...

not a vertex of the curve, then at least four points of the curve have osculating planes passing through o {\displaystyle o} . In particular, for a curve...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

million km and at an inclination of about 165°. Horizons output. "Jovian Osculating Orbital Elements for Eukelade (547)". Retrieved 2025-12-20. "Apojove on...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

DES defines centaurs as nonresonant objects whose osculating perihelia are less than the osculating semimajor axis of Neptune at any time during the integration...

flexible production of highly accurate ephemerides for Solar System objects. Osculating elements at a given epoch (such as produced by the JPL Small-Body Database)...

minimal surface. Earth normal section Normal bundle Normal curvature Osculating plane Principal curvature Tangent plane (geometry) Ruane, Irving Adler...

central body and the perturbing bodies. Encke's method begins with the osculating orbit as a reference and integrates numerically to solve for the variation...

identified by analysing the proper orbital elements rather than the current osculating orbital elements, which regularly fluctuate on timescales of tens of thousands...

Neptune barycentre and Solar System barycentre. These are the instantaneous osculating values at the precise J2000 epoch. Barycentre quantities are given because...

approximate boundaries of the family. At the present epoch, the range of osculating orbital elements of these core members is: The Zappala 1995 analysis found...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

nephroid and its evolute magenta: point with osculating circle and center of curvature...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

In algebraic geometry, a complete algebraic curve is an algebraic curve that is complete as an algebraic variety. A projective curve, a dimension-one projective...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Base curve radius Bend radius Degree of curvature (civil engineering) Osculating circle Track transition curve Weisstien, Eric. "Radius of Curvature"....

elements lie in the approximate ranges At the present epoch, the range of osculating orbital elements of these core members is The Zappalà 1995 analysis found...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

function if and only if the osculating circle at that point has fourth-order contact with the curve; in general the osculating circle has only third-order...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

It currently has a magnitude of 24.12. Horizons output. "Barycentric Osculating Orbital Elements for 2014 SR349". Retrieved 8 February 2017. (Ephemeris...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

occurs at periapsis. origin of longitude orphan planet See rogue planet. osculating orbit The hypothetical, idealized Kepler orbit that an orbiting object...

43832 ly). But the orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

Exoplanet Survey Satellite) in 2018. Geocentric orbits Orbital spaceflight Osculating orbit Kessler syndrome Orbital periods and speeds are calculated using...

as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously as opposed to the eccentricity...

oscillating. He is also one of the namesakes of the Tait–Kneser theorem on osculating circles. Über einige fundamentalsätze aus der theorie der algebraischen...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

work consists of a globe cut in half and painted with concentric circles osculating in a spiral, mounted on velvet in a copper and plexiglass dome, and fitted...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

11 2001 January 15 (discovery and ephemeris) Horizons output. "Jovian Osculating Orbital Elements for Megaclite (519)". Retrieved 18 December 2025. "Planetary...

Archived from the original on July 30, 2021. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1995 O1 (Hale–Bopp)". Retrieved September...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

depicting evolution of a Cornu spiral with the tangential circle with the same radius of curvature as at its tip, also known as an osculating circle....

(2000 CR105)". 13 April 2021. Retrieved 27 September 2025. "Barycentric Osculating Orbital Elements for 2000 CR105". Retrieved 25 January 2016. (Ephemeris...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

centaurs as non-resonant objects whose instantaneous (osculating) perihelia are less than the osculating semi-major axis of Neptune at any time during the...

into his pan-Native American alliance. Horizons output. "Barycentric Osculating Orbital Elements for C/1811 F1 (Great comet)". Retrieved 2019-05-30. (Solution...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

on the radii of a ring of tangent circles surrounding a central circle Osculating circle Weisstein, Eric W. "Tangent Circles". mathworld.wolfram.com. Retrieved...

Sun at a distance of 1.1–4.0 AU with a period of around 4 years. The osculating orbit as of 2017 has a period just over 4 years, but the period varies...

Archived 2010-03-25 at the Wayback Machine Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2009 R1 (McNaught)". ssd.jpl.nasa.gov. Retrieved...

elements lie in the approximate ranges At the present epoch, the range of osculating orbital elements of these core members is Zappalà, Vincenzo; Bendjoya...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

blogspot.com. Retrieved 18 September 2014. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2011 J2 (LINEAR)". ssd.jpl.nasa.gov. Retrieved...

respect to Earth's orbit (the ecliptic). The period, considered as an osculating element, dips slightly at the approach in December 2028 and then slowly...

the original on 10 July 2011. Retrieved 19 July 2023. Horizons output. "Osculating Orbital Elements for 16P/Brooks (90000258)". Retrieved 20 July 2023. 16P/Brooks...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Quarterly. Retrieved 15 December 2024. Horizons output. "Barycentric Osculating Orbital Elements for Comet Ikeya-Seki (C/1965 S1-A)". Retrieved 26 August...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

"Pasiphae". Dictionary.com Unabridged (Online). n.d. Horizons output. "Jovian Osculating Orbital Elements for Callirrhoe (517)". Retrieved 18 December 2025. Grav...

minorplanetcenter.net. Retrieved 1 March 2023. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2023 A3 (Tsuchinshan–ATLAS)". Retrieved 9...

2013-V48. Bibcode:2013MPEC....V...48K. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2013 R1 (Lovejoy)". Retrieved 30 August 2023...

torsion is zero, the curve lies completely in the same osculating plane (there is only one osculating plane for every point t). It is defined as τ ( t ) =...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Propulsion Laboratory. Retrieved 2011-03-13. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2007 F1 (LONEOS)". Retrieved 2011-03-12....

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

Retrieved 3 February 2023. Horizons output (31 January 2023). "Barycentric Osculating Orbital Elements for Comet C/2022 E3 (ZTF) BEFORE perihelion (2021-10-25...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

 37. ISBN 981-256-182-X. A circle about the axis of rotation is not the osculating circle of the walker's trajectory, so "centrifugal" and "Coriolis" are...

January 2021. Retrieved 29 February 2020. Horizons output. "Barycentric Osculating Orbital Elements for 90377 Sedna (2003 VB12)". Archived from the original...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Jet Propulsion Laboratory. These may sometimes strongly differ from the osculating orbital elements orbital elements provided by other sources. Otherwise...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

8 April 2025. Retrieved 9 April 2025. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2025 F2 (SWAN)". ssd.jpl.nasa.gov. Retrieved...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

object of the dynamic geometry, but also: The center of curvature and osculating circle of a curve; Dilation, generic affinity, inversion, projective application...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

number Homoeoid Focaloid Circular symmetry Magic circle (mathematics) Osculating circle Spiral Circles: Alexander, Daniel C.; Koeberlein, Geralyn M. (2009)...

family extends at least to e=0.175 At the present epoch, the range of osculating orbital elements of these core members is The analysis by Zappalà found...

intersection point of multiplicity at least 3, the two curves are said to be osculating. If there is only one intersection point, which has multiplicity 4, the...

(1680 V1) ... 0.00622200 ... 16801218.48760 Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1680 V1 (C/1680 V1)". Solution using the...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

the solar wind. Comet C/2006 M4 is in a hyperbolic trajectory (with an osculating eccentricity larger than 1) during its passage through the inner Solar...

September 2014. Retrieved 15 September 2014. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2013 US10 (Catalina)". Solution using the...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

of the Tisserand invariant uses a value of 5.203363 AU for Jupiter's osculating semi-major axis (aJ). Also, the degrees of the objects inclination need...

Osculating elements as of January 1 Year 1600 1700 1800 1900 2000 2100 2200 2300 2400 2500 Periapsis (au) 0.34 0.27 0.23 0.17 0.12 0.09 0.07 0.04 0.03...

14:15 mean-motion resonance with the much larger Mimas. This causes its osculating orbital elements to vary with an amplitude of about 20 km (12 mi) in semi-major...

where the radius is greater than that of the sphere, corresponds to an osculating circle outside the light bulb, and is tangent to both the neck and the...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Sheppard et al. (2024) give the mean, minimum, and maximum values for Neso's osculating orbital elements in Table 6: semi-major axis 47646600+2522400 −1983400 km...

mean-longitude resonance with the much larger Mimas. This causes its osculating orbital elements to vary with an amplitude of about 20 km in semi-major...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

orbits. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

and "Center: Sun" should be set to default.) Results are instantaneous osculating values at the precise J2000 epoch. Simon, J.L.; Bretagnon, P.; Chapront...

model of the relevant celestial body, i.e., a small circle of the local osculating sphere. With respect to Earth, the center of the true horizon is below...

C 3), cyanogens (CN), and amides (NH 2) within the coma. "Barycentric Osculating Orbital Elements for Comet C/2013 X1 (PanSTARRS) in epoch 1800 and 2200"...

2003. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

{\displaystyle \mathbf {h} } vector is always perpendicular to the instantaneous osculating orbital plane, which coincides with the instantaneous perturbed orbit...

of theatrical trailer, it was revealed that the filming of ten second osculating scene between lead actors took four hours to complete after several re-takes...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

22 (9): 113. Bibcode:1963MNSSA..22..113. Horizons output. "Barycentric Osculating Orbital Elements for Comet Pereyra (C/1963 R1)". Retrieved 2 September...

participating institution membership required.) Horizons output. "Jovian Osculating Orbital Elements for Cyllene (548)". Retrieved 2025-12-19. S.S. Sheppard...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

here as their 2-wise intersection). If any two of the circles happen to osculate, they only have H as a common point, and it will then be considered that...

(2021) Comment on U+26B7 CHIRON L2/21-225, UTC Document Registry "Chiron's Osculating Elements 700AD generated with Solex 11, and data of close approach in...

5291: 1. Bibcode:2023CBET.5291....1W. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2023 P1 (Nishimura)". Retrieved 3 October...

the act. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

stable for objects that take thousands of years to orbit the Sun. Read osculating orbit for more details about heliocentric unperturbed two-body solutions...

barycentric semi-major axis of −62.44. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1980 E1 (Bowell)". Solution using the Solar...

1365-2966.2004.08240.x. S2CID 16002759. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1999 F1 (Catalina)". Archived from the original...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

belt's second-largest and second-most-massive body after Ceres. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Stuart (1876) Ben Nebo, and Other Poems, p. 22 Horizons output. "Jovian Osculating Orbital Elements for Sinope (509)". Retrieved 18 December 2025. Grav,...

2026. (JPL#102/Soln.date: 2026-Mar-13) Horizons output. "Barycentric Osculating Orbital Elements for Eris (20136199)". Retrieved November 1, 2025. (Solution...

tangent lines of a spatial curve. This is the envelope surface of the osculating planes of the curve. The curve itself is called the edge of regression...

Bibcode:2008ApJ...687.1415S. doi:10.1086/592081. Horizons output. "Barycentric Osculating Orbital Elements for Great March comet (C/1843 D1) at epoch 1900". Retrieved...

variants of the Black Moon include replacing the mean orbit with a "true" osculating orbit or with an interpolated orbit; charting the empty focus of the Moon's...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

2026. (JPL #58 / Soln.date: 2012-Jun-04) Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2011 W3 (Lovejoy)". Retrieved 7 August 2012...

directly from the Oort cloud. It follows a hyperbolic trajectory (with an osculating eccentricity larger than 1) during its passage through the inner Solar...

family are, however, very indistinct. At the present epoch, the range of osculating orbital elements of these core members is Zappalà's 1995 analysis found...

particle's frame of reference commonly are referred to the instantaneous osculating circle of its motion, not to a fixed center of polar coordinates. For...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

detailed positional information on each of the major planets including osculating orbital elements, heliocentric ecliptic and geocentric equatorial coordinates...

Cambridge. Retrieved 22 December 2024. Horizons output. "Barycentric Osculating Orbital Elements for Comet Wierzchos (C/2024 E1)". Archived from the original...

a Taylor series and using the first non-zero term to characterize an osculating parabola. The Taylor microscale is proportional to Re − 1 / 2 {\displaystyle...

Astronomy Now. Retrieved 17 January 2026. Horizons output. "Barycentric Osculating Orbital Elements for C/2026 A1 (MAPS)". Archived from the original on...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Bibcode:2024MPEC....H...22T. doi:10.48377/MPEC/2024-H22. "Barycentric Osculating Orbital Elements for Comet C/2024 G3 (ATLAS) in epoch 1800 and 2200"....

Archived from the original on 15 September 2020. Retrieved 11 May 2016. "Osculating elements from astorb-database for 309 Fraternitas". The Centaur Research...

greatest aphelion ^ Solution using the Solar System Barycenter ^ Read osculating orbit for more details about heliocentric unperturbed two-body solutions...

Gallery of curves Index of the curve List of curves topics List of curves Osculating circle Parametric surface Path (topology) Polygonal curve Position vector...

degree cannot be planar. We say that two circles drawn in a plane kiss (or osculate) whenever they intersect in exactly one point. A "coin graph" is a graph...

members and a few collisional families. Their orbit is defined by an osculating semi-major axis of 3.27 to 3.70 AU, with an eccentricity of less than...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

the conical sections, adding canopies and fuselage areas, led to the "osculating cones waverider", which develops several conical shock waves at different...

Laboratory. Retrieved 14 November 2024. Horizons output. "Barycentric Osculating Orbital Elements for Comet McNaught–Russell (C/1993 Y1)". Retrieved 25...

Astronomical Telegrams. 6299. Horizons output (30 January 2011). "Barycentric Osculating Orbital Elements for Comet Hyakutake (C/1996 B2)". Archived from the original...

objects. It is defined as the distance between the closest points of the osculating orbits of two bodies. Of greatest interest is the risk of a collision...

3847/1538-3881/ac617f. S2CID 248458067. 241. "JPL Horizons On-Line Ephemeris for 2002N5 Osculating Orbit (1600-Feb-01 to 2399-Dec-01)". JPL Horizons On-Line Ephemeris System...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

the osculating circles of a plane curve and the tangent directions is realised, and the first analytical formula for the radius of an osculating circle...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

cyclides both sheets form curves. * For the sphere the center of every osculating circle is at the center of the sphere and the focal surface forms a single...

(SOHO)". Central Bureau for Astronomical Telegrams. 5261. "Barycentric Osculating Orbital Elements for Comet C/2023 F2 (SOHO) in epoch 1800 and 2200". JPL...

8 million km; 15.4 million mi) from Jupiter. Horizons output. "Jovian Osculating Orbital Elements for 2017J7 (568)". Retrieved 2026-02-17. MPC Natural...

2014-Q10. Bibcode:2014MPEC....Q...10C. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2014 Q2 (Lovejoy)". Retrieved 5 January 2015...

Planet Center. Retrieved 5 March 2018. Horizons output. "Barycentric Osculating Orbital Elements for Asteroid (A/2017 U7)". JPL Solar System Dynamics...

center)", and selected each object's barycenter. Results are instantaneous osculating values at the precise J2000 epoch, and referenced to the ecliptic. "HST...

International Comet Quarterly. Retrieved 14 July 2025. "Barycentric Osculating Orbital Elements for Comet C/1885 X1 (Fabry) in epoch 1800 and 2200"....

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

(2): 247–253. Bibcode:2015RMxAA..51..247B. Horizons output. "Barycentric Osculating Orbital Elements for Great comet (C/1861 J1) at epoch 1900". Retrieved...

coordinates. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

Orbital maneuver — Orbital node — Orbital period — Orbital stationkeeping — Osculating orbit — Parallel axes rule — Parasitic drag — Parawing — Perpendicular...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

R_{\mathrm {c} }} over the full circle. It corresponds to the radius of the osculating sphere that best fits the ellipsoid locally. Earth's radius of mean curvature...

Designations". International Comet Quarterly. Retrieved 3 July 2025. "Barycentric Osculating Orbital Elements for Comet C/1874 H1 (Coggia) in epoch 1800 and 2200"...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

of a ball, the local boundary osculates a hyperellipsoid (i.e. a quadratic hypersurface). In particular, the osculating hyperellipsoid can be uniquely...

2004 by Kitt Peak National Observatory Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2001 Q4 (NEAT)". Retrieved 10 March 2011...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

the comet's absolute total magnitude (M1) Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2007 E2 (Lovejoy)". Solution using the Solar...

irregular moons are averaged over a 30,000-year period: these may differ from osculating orbital elements provided by other sources. The orbital elements of the...

conjecture Natural representation Opisometer Orbital elements Osculating circle Osculating plane Osgood curve Parallel (curve) Parallel transport Parametric...

(Pojmański)". IAU Circular. 8653 (1). Bibcode:2006IAUC.8653....1R. "Barycentric Osculating Orbital Elements for Comet C/2006 A1 (Pojmański) in epoch 1800 and 2200"...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

doi:10.1038/nature01725. PMID 12904784. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1999 F1 (Catalina)". Archived from the original...

101: 119. Bibcode:1991JBAA..101..119H. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1980 E1". Retrieved 9 March 2011. (Solution...

  A cardioid   Evolute of the cardioid   One point P; its centre of curvature M; and its osculating circle....

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

publication. Dan Sun at the Mathematics Genealogy Project. Dan Sun (1927,8) "Osculating derivative of a ruled surface", Annals of Mathematics 29(1-4): 95–105...

elements in the approximate ranges At the present epoch, the range of osculating orbital elements of these core members is The namesake is 1272 Gefion...

disintegrated near perihelion in November 2013. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2011 L4 (PANSTARRS)". Solution using the...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

(31 million km; 20 million mi) from Jupiter. Horizons output. "Jovian Osculating Orbital Elements for 2017J1 (559)". Retrieved 2026-01-20. "Apojove on...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

triangle Orthocentroidal circle – Circle constructed from a triangle Osculating circle – Circle of immediate corresponding curvature of a curve at a point...

as Mimas' perturbations on Methone. The perturbations cause Pallene's osculating orbital elements to vary with an amplitude of about 4 km in semi-major...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Planet Electronic Circulars. 2025-S104. Horizons output. "Barycentric Osculating Orbital Elements for PanSTARRS (C/2025 R3)". Archived from the original...

Predicted or False Positives?". 20 May 2022. Horizons output. "Barycentric Osculating Orbital Elements". Retrieved 4 February 2020. (Solution using the Solar...

Williams, professor of mathematics at Indiana University. Based on its osculating Keplerian orbital elements, Williams qualifies as a member of the Flora...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

Propulsion Laboratory's Small-Body Database still provides an Apollo-type osculating orbit for 2020 VT4 based on the epoch 31 May 2020 (JD 2459000.5) before...

determined by their tangent spaces. This provides a natural realisation of the osculating circle to a curve, and the curvature spheres of a surface. It also allows...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

curve such that, at each point, the plane tangent to the surface is an osculating plane of the curve. Asymptotic directions can only occur when the Gaussian...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

normal), and r is its instantaneous radius of curvature based upon the osculating circle at time t. These components are called the tangential acceleration...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements and in previous analysis by Zappalà, the asteroid...

Organization www.imo.net accessed 11.10.11 Horizons output. "Barycentric Osculating Orbital Elements for Comet Kiess (C/1911 N1)". Retrieved 14 September...

Gaussian curvature of S as being defined by the maximum and minimum radii of osculating circles; they seem to be fundamentally defined by the geometry of how...

al. (2024) give the mean, minimum, and maximum values for Margaret's osculating orbital elements in Table 5: semi-major axis 14425000+113500 −106500 km...

Sheppard et al. (2024) give the mean, minimum, and maximum values for Neso's osculating orbital elements in Table 6: semi-major axis 49897800+2912900 −2242500 km...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been considered a member...

Quarterly. Retrieved 12 December 2024. Horizons output. "Barycentric Osculating Orbital Elements for C/1911 N1 (Kiess) at epoch 2100". Retrieved 2025-10-02...

(Garradd)". IAU Circular (2). Bibcode:2009IAUC.9062....2M. "Barycentric Osculating Orbital Elements for Comet C/2009 P1 (Garradd) in epoch 1800 and 2200"...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

point, angle, or curvature (which is the reciprocal of the radius of an osculating circle). Angle and curvature constraints are most often added to the ends...

is estimated to be about 60–95 km (37–59 mi) in diameter. Barycentric osculating parameters from HORIZONS show that C/2019 U5 is a dynamically new comet...

The Minor Planet Bulletin. 29: 48–49. Bibcode:2002MPBu...29...48C. "Osculating elements from astorb-database for 286 Iclea". The Centaur Research Project...

al. (2024) give the mean, minimum, and maximum values for Ferdinand's osculating orbital elements in Table 5: semi-major axis 20421400+455900 −338500 km...

and Speeches of James Louis Petigru, p. 318 Horizons output. "Jovian Osculating Orbital Elements for Eupheme (560)". Retrieved 30 November 2025. "Apojove...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

al. (2024) give the mean, minimum, and maximum values for Ferdinand's osculating orbital elements in Table 5: semi-major axis 4275700+700 −700 km, eccentricity...

Equivalently it is the surface formed by the centers of the circles which osculate the curvature lines. As the principal curvatures are the eigenvalues of...

Comet Quarterly. Retrieved 2 December 2024. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1956 R1 (Arend–Roland)". ssd.jpl.nasa.gov...

Laboratory. Retrieved 15 October 2018. Horizons output. "Barycentric Osculating Orbital Elements for 2013 SY99". Retrieved 6 April 2017. (Ephemeris Type:Elements...

curvature of a curve is by definition the reciprocal of the radius of the osculating circle. The curvature is taken to be positive if the curve turns in the...

the eccentricity. For e = 0 {\displaystyle e=0} the conic is a circle (osculating circle of the pencil), for 0 < e < 1 {\displaystyle 0<e<1} an ellipse...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

slightly below the aphelion of Mars (1.67 AU), not crossing the Red Planet's osculating orbit. It is classified as an "inner main-belt asteroid" in the JPL's...

Kay twelve hours later on its northwesterly trek. While easterly shear osculated in strength, Kay peaked with winds of 50 mph, after a microwave data indicated...

hypersurface touches itself, or an invariant of several hypersurfaces that osculate, meaning that they have a common point where they meet to unusually high...

(Christensen)". IAU Circular. 8777 (1). ISSN 0081-0304. "Barycentric Osculating Orbital Elements for Comet C/2006 W3 (Christensen) in epoch 1800 and 2200"...

18 August 2010. Retrieved 17 July 2008. Horizons output. "Barycentric Osculating Orbital Elements for 2004 VN112". Retrieved 20 September 2021. (Ephemeris...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

numerical integration by Sheppard et al. (2024). These may differ from osculating orbital elements provided by other sources. The orbital elements of the...

similar to that of another TNO, 2015 KG163. Horizons output. "Barycentric Osculating Orbital Elements for 2013 FT28". Retrieved 8 February 2017. (Ephemeris...

Archived from the original on 15 June 2014. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2013 A1 (Siding Spring)". Solution using...

plane. If a portion of the Earth is modeled as spherical, e.g. using the osculating sphere at a point on an ellipsoid of revolution, the hyperbolae used in...

Milani and Knežević). In a previous HCM-analysis (Zappalà) and based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

al. (2024) give the mean, minimum, and maximum values for Laomedeia's osculating orbital elements in Table 6: semi-major axis 23499900+186000 −152000 km...

orbits. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

"2017 OF201". Minor Planet Center. Retrieved 1 June 2025. "Barycentric osculating orbital elements for 2017 OF201". Horizons output – via ssd.jpl.nasa.gov...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

defined at will change every 6 months or so) Horizons output. "Barycentric Osculating Orbital Elements for 2013 BL76". Retrieved 6 March 2014. (Solution using...

al. (2024) give the mean, minimum, and maximum values for Halimede's osculating orbital elements in Table 6: semi-major axis 16590500+42000 −36700 km...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

construction relies on approximating a curve as a sequence of osculating parabolas. Obviously, osculating parabolas of a parabola are just the parabola itself...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid is considered a member of the...

original on 20 October 2022. Retrieved 20 October 2022. Horizons output. "Osculating Orbital Elements for 2022 UQ1 at Oct + Nov 2022". Archived from the original...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Jupiter 2002 May 15 (discovery and ephemeris) Horizons output. "Jovian Osculating Orbital Elements for Sponde (536)". Retrieved 2026-01-10. MPC Natural...

Center. 26 May 2014. Retrieved 15 June 2014. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2012 K1 (PANSTARRS)". Solution using the...

The members of the Ananke group are (in order of date announcement): Osculating orbital parameters of irregular satellites of Jupiter change widely in...

Q1". IAU Circular. 6206 (1). Bibcode:1995IAUC.6206....1B. "Barycentric Osculating Orbital Elements for Comet C/1995 Q1 (Bradfield) in epoch 1800 and 2200"...

4817: 1. Bibcode:2020CBET.4817....1Y. Horizons output. "Barycentric Osculating Orbital Elements for Comet Lemmon (C/2019 O3)". Retrieved 1 December 2025...

the parameters needed to specify a Newtonian two-body orbit uniquely. Osculating orbit is the temporary Keplerian orbit about a central body that an object...

maint: deprecated archival service (link) Horizons output. "Barycentric Osculating Orbital Elements for 2010 GB174". Retrieved 20 September 2021. (Ephemeris...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

25 November 2024. B. G. Marsden; Z. Sekanina; E. Everhart (1978). "New osculating orbits for 110 comets and analysis of original orbits for 200 comets"...

– periodic comet with a 366-year orbit Horizons output. "Barycentric Osculating Orbital Elements for Thatcher (C/1861 G1) at epoch 1900". Retrieved 26...

the comet's absolute total magnitude (M1) Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1910 A1 (Great January comet)". Retrieved...

Retrieved 26 August 2025. B. G. Marsden; Z. Sekanina; E. Everhart. "New osculating orbits for 110 comets and analysis of original orbits for 200 comets"...

November 2020. Retrieved 15 October 2014. Horizons output. "Barycentric Osculating Orbital Elements for 2012 DR30". Archived from the original on 28 November...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

International Comet Quarterly. Retrieved 23 June 2025. "Barycentric Osculating Orbital Elements for Comet C/1862 N1 (Schmidt) in epoch 1800 and 2200"...

3847/1538-3881/ac617f. S2CID 248458067. 241. "JPL Horizons On-Line Ephemeris for 2023U1 Osculating Orbit (1600-Feb-01 to 2399-Dec-01)". JPL Horizons On-Line Ephemeris System...

and "Center: Sun" should be defaulted to.) Results are instantaneous osculating values at the precise J2000 epoch. Williams, David (2018). "Mars Fact...

to be to squeeze in as many massive close-ups of guns, telephones and osculating lips as possible. 'It happens in all the Bogart movies,' says Clegg at...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

require two "sheets"[clarification needed] of the Gibbs free energy to osculate exactly, which was considered so unlikely as to likely never occur.[citation...

Joyce and the difference of language. p. 149. Horizons output. "Jovian Osculating Orbital Elements for Pasiphae (508)". Retrieved 30 November 2025. Grav...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Curves in differential geometry Line element Curvature Radius of curvature Osculating circle Curve Fenchel's theorem Theorema egregium Gauss–Bonnet theorem...

Bibcode:2014A&A...568A...3P. doi:10.1051/0004-6361/201423762. "Barycentric Osculating Orbital Elements for Comet 78P/Gehrels 2 in epoch 1800 and 2200". JPL...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

Laboratory. Retrieved 15 November 2024. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1989 Y1 (Skorichenko-George)". Retrieved...

Electronic Circulars. 2025-R102. ISSN 1523-6714. Horizons output. "Barycentric Osculating Orbital Elements for SWAN (C/2025 R2)". Retrieved 9 March 2025. (Solution...

Planet Electronic Circulars. 2021-U187. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2021 T4 (Lemmon)". Retrieved 26 April 2023...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

orbits. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

defined at will change every 6 months or so) Horizons output. "Barycentric Osculating Orbital Elements for 2005 VX3". Retrieved 6 March 2014. (Solution using...

(Machholz) C/2018 V1 (Machholz–Fujikawa–Iwamoto) Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2004 Q2 (Machholz)". Solution using the Solar...

International Comet Quarterly. Retrieved 10 June 2025. "Barycentric Osculating Orbital Elements for Comet C/1957 P1 (Mrkos) in epoch 1800 and 2200"....

the comet had fainted to magnitude 10. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2014 E2 (Jacques)". (Solution using the Solar...

Designations". International Comet Quarterly. Retrieved 9 June 2025. "Barycentric Osculating Orbital Elements for Comet C/1974 C1 (Bradfield) in epoch 1800 and 2200"...

Center. 12 May 2014. Retrieved 15 June 2014. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2013 V5 (Oukaimeden)". Solution using the...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

usual Euclidean curvature of a curve at a point is the curvature of its osculating circle, the unique circle making second order contact (having three point...

formation. The Carme group members are (in order by date announcement): Osculating orbital parameters of irregular satellites of Jupiter change widely in...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

manifold is strongly pseudoconvex, for then one can replace the manifold by osculating it to a high enough order with the Heisenberg group. Then using the group...

faculty, Argrow's research team was the first to verify the method of osculating cones for supersonic waverider design. He also created a shock tube to...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

the Double Cluster on January 23, 2020 Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2017 T2 (PANSTARRS)". Solution using the...

Pisa, Italy. Retrieved 18 February 2016. Horizons output. "Barycentric Osculating Orbital Elements for 2010 NV1". Retrieved 18 February 2016. (Solution...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid is located in the densely populated...

of 5.26 hours. It was named for the Chinese city of Zhuhai. Based on osculating Keplerian orbital elements, Zhuhai has also been classified as a member...

International Comet Quarterly. Retrieved 12 July 2025. "Barycentric Osculating Orbital Elements for Comet C/1956 F1 (Wirtanen) in epoch 1800 and 2200"...

belt's second-largest and second-most-massive body after Ceres. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

Sheppard et al. (2024) give the mean, minimum, and maximum values for Sao's osculating orbital elements in Table 6: semi-major axis 22239900+128200 −116900 km...

2011. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Comet Quarterly. Retrieved 19 June 2025. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1948 V1 (Eclipse Comet)". ssd.jpl.nasa.gov...

..D...55P. doi:10.48377/MPEC/2025-D55. Horizons output. "Barycentric Osculating Orbital Elements for Comet Lemmon (C/2025 A6)". Retrieved 10 March 2026...

elements (averaged over time) are used to identify the groupings rather than osculating elements at the given date. (Similarly, the proper orbital elements are...

Designations". International Comet Quarterly. Retrieved 2 July 2025. "Barycentric Osculating Orbital Elements for Comet C/1886 J1 (Brooks) in epoch 1800 and 2200"...

APEX". arXiv:2604.02613 [astro-ph.EP]. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2021 A1 (Leonard)". Retrieved 2021-01-13...

University of Pisa, Italy. Retrieved 2016-02-11. Horizons output. "Barycentric Osculating Orbital Elements for 2009 MS9". Retrieved 2016-02-11. (Solution using...

Bibcode:1970QJRAS..11..221M. B. G. Marsden; Z. Sekanina; E. Everhart (1978). "New osculating orbits for 110 comets and analysis of original orbits for 200 comets"...

(PanSTARRS)". Minor Planet Center. Retrieved 21 October 2017. "Barycentric Osculating Orbital Elements for Comet C/2017 K2 (PanSTARRS) in epoch 1800 and 2200"...

Charles Anthony (1902). The Eastern Oblique Arc of the United States and Osculating Spheroid. Washington, D.C.: Government Printing Office. p. 227. United...

Electronic Telegrams. 3104. Bibcode:2012CBET.3104....1G. "Barycentric Osculating Orbital Elements for Comet C/2012 J1 (Catalina) in epoch 1800 and 2200"...

controversial, as it seems to require two sheets of the Gibbs free energy to osculate exactly, which is so unlikely as to never occur in practice. Gorter replied...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Quarterly. Retrieved 12 November 2024. Horizons output. "Barycentric Osculating Orbital Elements for C/1979 K1 (White-Ortiz-Bolelli)". Retrieved 21 February...

ISSN 1523-6714. Retrieved 13 April 2011. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2007 W1 (Boattini)". Retrieved 13 April 2011...

Astronomical Telegrams. 3921. Bibcode:2014CBET.3921....1B. "Barycentric Osculating Orbital Elements for Comet C/2014 N3 (NEOWISE) in epoch 1800 and 2200"...

solution. The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

tensor, divergent series, linear operator, unit vector, parallelepiped, osculating plane, standard candle Technology Solenoid, electro-magnets, Nicol prisms...

Designations". International Comet Quarterly. Retrieved 6 June 2025. "Barycentric Osculating Orbital Elements for Comet C/1958 R1 (Burnham–Slaughter) in epoch 1800...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

oratory, orifice, oscitate, oscitation, osculant, oscular, oscularity, osculate, osculation, osculator, osculatory, osculatrix, oscule, osculum †osculum...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

Propulsion Laboratory. Retrieved 23 March 2010. Horizons output. "Barycentric Osculating Orbital Elements for Comet Lulin (C/2007 N3)". Retrieved 20 January 2011...

2018. Retrieved 4 March 2018. (AK18C020) Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2018 C2 (Lemmon)". Retrieved 15 October 2022...

of the Maria family (506), a large family of stony asteroids. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

January 2016. Retrieved 22 October 2016. Horizons output. "Barycentric Osculating Orbital Elements for 2013 RF98". Retrieved 8 February 2017. (Ephemeris...

the comet's absolute total magnitude (M1) Horizons output. "Barycentric Osculating Orbital Elements for Comet C/1858 L1 (Donati)". Retrieved 2023-07-27....

non-family asteroid from the main belt's background population. Based on osculating Keplerian orbital elements, it is located in the region of the Eunomia...

transfer can be realized through a local differential curve model of osculating circles (i.e., curvature), which can then be transferred as conics. The...

the 3rd order variance. Nevertheless, as expected, the two MSE curves do osculate near ρ 3 = 1.4 {\displaystyle \rho _{3}=1.4} , where μ 2 {\displaystyle...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been considered a member...

trajectory, the orbit of a long-period comet is properly obtained when the osculating orbit is computed at an epoch after leaving the planetary region and is...

group, as its perihelion was slightly less than 1.3 AU due to the body's osculating orbit. In July 2072, Rees will pass 20,686,000 km (0.13828 AU) from Mars...

Designations". International Comet Quarterly. Retrieved 9 July 2025. "Barycentric Osculating Orbital Elements for Comet C/1991 Y1 (Zanotta–Brewington) in epoch 1800...

3847/1538-3881/ac617f. S2CID 248458067. 241. "JPL Horizons On-Line Ephemeris for 2021N1 Osculating Orbit (1600-Feb-01 to 2399-Dec-01)". JPL Horizons On-Line Ephemeris System...

distances. The orbit of a long-period comet is properly obtained when the osculating orbit is computed using the Solar System barycenter as its reference frame...

parallel curve for parameter t {\displaystyle t} . When they exist, the osculating circles to parallel curves at corresponding points are concentric. As...

elements lie in the approximate ranges At the present epoch, the range of osculating orbital elements of these core members is The 1995 analysis by Zappalà...

1.27 AU (190 million km) from the Sun. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2009 F6 (Yi-SWAN)". Retrieved 3 February...

doi:10.1086/111516. B. G. Marsden; Z. Sekanina; E. Everhart (1978). "New Osculating Orbits for 110 Comets and Analysis of Original Orbits for 200 comets"...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

proper orbital elements. In the HCM assessment by Zappala and based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

1819–1820. In a mystical scheme this grouped separately created genera in "osculating" (kissing) circles. Both Ernst Mayr and Cyril Darlington interpret Blyth's...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

point where the perpendicular from an arbitrary fixed origin meets the osculating plane. Other expressions for a can be found in , where a new proof of...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, it has also been classified as a member of...

plane, while the torsion of a curve is also a dislocation out of its osculating plane. In the geometry of surfaces, the geodesic torsion describes how...

Oscillator linewidth Oscillator phase noise Oscillatory universe Oscillon Osculating orbit Oseen's approximation Oseen equations Oskar Heil Oskar Klein Oskar...

actual forces acting on a particle are often referred to the instantaneous osculating circle tangent to the path of motion, and this circle in the general case...

additional regions could be scanned. Osculating orbit – In astronomy, and in particular in astrodynamics, the osculating orbit of an object in space at a...

generally the mot juste". These included references to "venereal blinds" and "osculating fans" in the Catalog Room, equipment that had "outlived its uselessness"...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

South pole, formed as a result of a subcatastrophic collision. Based on osculating Keplerian orbital elements, De Sanctis has also been classified as a member...

Horseshoe Hyperbolic trajectory Inclined / Non-inclined Kepler Lagrange point Osculating Parabolic / Escape / Capture Parking Prograde / Retrograde Radial Synchronous...

to order at least 3. (Cayley 1852) osculate Kiss; to meet with high order. See Salmon (1879, p. 356). osculating plane A tangent plane of a space curve...

presumably C-type asteroid has a rotation period of 23.2 hours. Based on osculating Keplerian orbital elements, Janice is located in the region of the Themis...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

belt's second-largest and second-most-massive body after Ceres. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

Planet Electronic Circulars. 2020-W177. ISSN 1523-6714. "Barycentric Osculating Orbital Elements for Comet C/2020 V2 (ZTF) in epoch 1800 and 2200". JPL...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

Planet Center. Retrieved 26 November 2018. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2016 R2 (PANSTARRS)". Retrieved 26 August...

a spherical Earth. Williams and Last extended Razin's solution to an osculating sphere Earth model. When necessitated by the combination of vehicle-station...

March 2013. Retrieved 28 January 2013. Horizons output. "Barycentric Osculating Orbital Elements for Comet C/2012 F6 (Lemmon)". Retrieved 23 April 2013...

hierarchical clustering method to its proper orbital elements. Based on osculating Keplerian orbital elements, the asteroid has also been classified as a...

components is uncountable. Koebe (1936) also considered the limiting case of osculating or tangential circles which has continued to be actively studied in the...

asteroid that belongs to the main belt's background population. On its osculating Keplerian orbital elements, it is located in the Eunomia region (502)...

October 2014. Retrieved 3 November 2014. Horizons output. "Heliocentric Osculating Orbital Elements for Comet C/2014 Q3 (Borisov)". Retrieved 3 November...

Justice and Peace embracing before the gates, with the motto Justitia et pax osculate sunt. Psal. 84. (Justice and peace have kissed); and a smaller one showing...