Orbital eccentricity

Elliptical orbit with an eccentricity of 0.7 (red), a parabolic orbit (green) and a hyperbolic orbit with an eccentricity of 1.3 (blue)

Eccentricity of the orbit (indicated by " $e$ ${\ displaystyle e}$ $e$ ”Or“ ε ”) is the numerical characteristic of the orbit of a celestial body (or spacecraft ), which characterizes the“ compression ”of the orbit. In the general case, the orbit of a celestial body is a conical section (i.e. an ellipse , parabola , hyperbola or straight line ), and the eccentricity of the orbit is the eccentricity of the corresponding curve . The orbits of many bodies in the solar system are ellipses .

Content

Orbit eccentricity calculation

In appearance, the orbits can be divided into five groups:

$\varepsilon =0$ ${\ displaystyle \ varepsilon = 0}$ - circle
$0<\varepsilon <1$ ${\ displaystyle 0 <\ varepsilon <1}$ - ellipse
$\varepsilon =1$ ${\ displaystyle \ varepsilon = 1}$ - parabola
$1<\varepsilon <\infty$ ${\ displaystyle 1 <\ varepsilon <\ infty}$ - hyperbole
$\varepsilon =\infty$ ${\ displaystyle \ varepsilon = \ infty}$ - direct (degenerate case)

For elliptical orbits, the eccentricity is calculated by the formula:

\varepsilon ={\sqrt {1-{\frac {b^{2}}{a^{2}}}}}

{\ displaystyle \ varepsilon = {\ sqrt {1 - {\ frac {b ^ {2}} {a ^ {2}}}}}}

where

b

{\ displaystyle b}

- minor axis,

a

{\ displaystyle a}

- semi-major axis of the ellipse.

For hyperbolic orbits, the eccentricity is calculated by the formula:

\varepsilon ={\sqrt {1+{\frac {b^{2}}{a^{2}}}}}

{\ displaystyle \ varepsilon = {\ sqrt {1 + {\ frac {b ^ {2}} {a ^ {2}}}}}}

where

b

{\ displaystyle b}

- imaginary axis,

a

{\ displaystyle a}

- the actual semi-axis of the hyperbola.

Some orbit eccentricities

The table below shows the orbit eccentricities for some celestial bodies (sorted by the major semi-axis of the orbit, except for 1I / Oumuamua, which has a hyperbolic orbit, and except for satellites that are grayed out).

Heavenly body	Orbital eccentricity
Mercury	0.205 ^[1]	0.205
Venus	0.007 ^[1]	0.007
Land	0.017 ^[1]	0.017
Moon	0,05490 ^[2]	0.0549
(3200) Chaise	0.8898 ^[3]	0.8898
Mars	0,094 ^[1]	0.094
Jupiter	0,049 ^[1]	0.049
And about	0.004 ^[4]	0.004
Europe	0.009 ^[4]	0.009
Ganymede	0.002 ^[4]	0.002
Callisto	0.007 ^[4]	0.007
Saturn	0,057 ^[1]	0.057
Titanium	0,029 ^[4]	0.029
Comet Halley	0.967 ^[5]	0.967
Uranus	0,046 ^[1]	0.046
Neptune	0.011 ^[1]	0.011
Nereid	0.7512 ^[4]	0.7512
Pluto	0.244 ^[1]	0.244
Haumea	0.1902 ^[6]	0.1902
Makemake	0.1549 ^[7]	0.1549
Eris	0.4415 ^[8]	0.4415
Sedna	0.85245 ^[9]	0.85245
1I / Oumuamua	1,1995 ^[10]	1.1995

Eccentricity is invariant under plane motions and similarity transformations ^[11] .

Notes

↑ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ Planetary Fact Sheet
↑ Clabon Walter Allen, Arthur N. Cox. Allen's Astrophysical Quantities . - Springer, 2000. - P. 308. - ISBN 0-387-98746-0 .
↑ 3200 Phaethon (1983 TB) (neopr.) . Jet Propulsion Laboratory (2015-10-22 last obs). Date of treatment October 23, 2015.
↑ ¹ ² ³ ⁴ ⁵ ⁶ Clabon Walter Allen, Arthur N. Cox. Allen's Astrophysical Quantities . - Springer, 2000 .-- P. 305-306. - ISBN 0-387-98746-0 .
↑ JPL Small-Body Database Browser: 1P / Halley (neopr.) . Jet Propulsion Laboratory (11 January 1994 last obs). Date of treatment October 23, 2015. Archived on August 20, 2011.
↑ Jet Propulsion Laboratory Small-Body Database Browser: 136108 Haumea (2003 EL ₆₁ ) (neopr.) . Jet Propulsion Laboratory (2015-07-26 last obs). Date of treatment October 23, 2015.
↑ JPL Small-Body Database Browser: 136472 Makemake ( 2005 FY ₉ ) (unspecified) . Jet Propulsion Laboratory (2015-07-26 last obs). Date of treatment October 23, 2015.
↑ JPL Small-Body Database Browser: 136199 Eris (2003 UB313) ( unspecified ) . Jet Propulsion Laboratory (October 26, 2014 last obs). Date of treatment October 23, 2015.
↑ JPL Small-Body Database Browser: 90377 Sedna (2003 VB12) (unspecified) . Jet Propulsion Laboratory (2014-11-17 last obs). Date of treatment October 23, 2015.
↑ JPL Small-Body Database Browser: 'Oumuamua (A / 2017 U1) (unspecified) . Jet Propulsion Laboratory (2017-11-17 last obs). Date of treatment November 22, 2017.
↑ Akopyan A.V., Zaslavsky A.A. Geometric properties of second-order curves - M.: MCCNMO , 2007. - 136 p.

[fs-1] ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ Planetary Fact Sheet

[2] Clabon Walter Allen, Arthur N. Cox. Allen's Astrophysical Quantities . - Springer, 2000. - P. 308. - ISBN 0-387-98746-0 .

[3] 3200 Phaethon (1983 TB) (neopr.) . Jet Propulsion Laboratory (2015-10-22 last obs). Date of treatment October 23, 2015.

[A305-4] ¹ ² ³ ⁴ ⁵ ⁶ Clabon Walter Allen, Arthur N. Cox. Allen's Astrophysical Quantities . - Springer, 2000 .-- P. 305-306. - ISBN 0-387-98746-0 .

[jpldata-5] JPL Small-Body Database Browser: 1P / Halley (neopr.) . Jet Propulsion Laboratory (11 January 1994 last obs). Date of treatment October 23, 2015. Archived on August 20, 2011.

[6] Jet Propulsion Laboratory Small-Body Database Browser: 136108 Haumea (2003 EL ₆₁ ) (neopr.) . Jet Propulsion Laboratory (2015-07-26 last obs). Date of treatment October 23, 2015.

[7] JPL Small-Body Database Browser: 136472 Makemake ( 2005 FY ₉ ) (unspecified) . Jet Propulsion Laboratory (2015-07-26 last obs). Date of treatment October 23, 2015.

[8] JPL Small-Body Database Browser: 136199 Eris (2003 UB313) ( unspecified ) . Jet Propulsion Laboratory (October 26, 2014 last obs). Date of treatment October 23, 2015.

[9] JPL Small-Body Database Browser: 90377 Sedna (2003 VB12) (unspecified) . Jet Propulsion Laboratory (2014-11-17 last obs). Date of treatment October 23, 2015.

[10] JPL Small-Body Database Browser: 'Oumuamua (A / 2017 U1) (unspecified) . Jet Propulsion Laboratory (2017-11-17 last obs). Date of treatment November 22, 2017.

[11] Akopyan A.V., Zaslavsky A.A. Geometric properties of second-order curves - M.: MCCNMO , 2007. - 136 p.

Orbital eccentricity

Content

Orbit eccentricity calculation

Some orbit eccentricities

See also

Notes

More articles: