# Talk:Elliptic orbit

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## Animated two body problem

The animation of the three body system is good but more complicated than needed. I think an animation of a two body system would help explain the mechanics in a simpler and better way.90.205.123.233 (talk) 10:07, 5 January 2011 (UTC)

## Orbital parameters

I edited the orbital parameters section (previously it was only a stub template), but I don't know how readable it is. The way I see it, anything is better than saying "This section is a stub. You can help by adding to it." Anyways, if you think it isn't clear, please rewrite it to make it clearer. NHammen 19:38, 5 August 2006 (UTC)

## Figure?

The figure appears to be broken.192.160.51.70 13:04, 13 September 2006 (UTC)

## Improvement

It should say:

"An elliptic orbit is a Kepler orbit with the eccentricity greater than 0 and less than 1."

It is fine to have a figure with an elliptic orbit but do not write "planet/Sun" on a highly eccentric orbit. Comet/Sun or Spacecraft/Earth would be better!

Nice to have a moving picture but not "Two bodies with similar mass". Does not exist in the Solar system!

It is true that the total energy is :${\displaystyle -{\frac {\mu }{2\cdot a}}}$, "vis viva",

But why the conclusion:

• Velocity does not depend on eccentricity but is determined by length of semi-major axis (${\displaystyle a\,\!}$),
• Velocity equation is similar to that for hyperbolic trajectory with the difference that for the latter, ${\displaystyle {1 \over {2a}}}$ is positive.

Strange conclusion!

The correct formulas for velocity can be found in Kepler orbit article

The formula

${\displaystyle T={2\pi \over {\sqrt {\mu }}}a^{3 \over {2}}}$

derived in Kepler orbit article

Under heading "Energy" the same "vis viva" is repeated

${\displaystyle {v^{2} \over {2}}-{\mu \over {r}}=-{\mu \over {2a}}=\epsilon <0}$

Kepler orbit covers "elliptic orbit" but I think it is OK with a short separate article with a picture of an ellips. There should be arrows to "apocentre" and "pericentre" to cover those words too!

I think there should be 3 standardized articles for elliptic, parabolic and hyperbolic orbits with picture (moving!) and apsis marked. With reference to the Kepler orbit article where all details for all 3 types of orbits are derived! —Preceding unsigned comment added by Stamcose (talkcontribs) 15:32, 12 July 2008 (UTC)

## Hohmann transfer?

From the first paragraph, should

"Homanice transfer orbit,"

be Hohmann transfer orbit?

210.49.253.179 (talk) 23:59, 17 March 2009 (UTC) Beth

## Explanation

A specific explanation of why the planets move in eliptical orbits rather than circular orbits would be great. Wapondaponda (talk) 02:52, 4 June 2009 (UTC)

I think that the 'standard assumptions' mentionned several times need to be listed or at least linked. Alphonsus (talk) 00:39, 11 September 2010 (UTC)

This most likely refers to the restricted two-body problem... I've seen 'standard assumptions' mentioned all over the place without explanation. Something should probably be added in Kepler orbit if no where else. Jaxcp3 (talk) 01:16, 8 August 2012 (UTC)

## something must be missing from the orbital speed equation

v = sqrt (mu * (2/R - 1/A) )

"R" is the distance from Pluto to the Sun. "A" is the distance of the semi-major axis, which is the same.

Now, let's say a ship at that orbit wants to enter a new orbit, one that at its furthest is at Pluto, and at its closest is at Earth. "R" would be the same. "A" would also be the same, since the semi-major axis is still the same (about 39.53 AU).

What am I missing? — Preceding unsigned comment added by 98.23.85.204 (talk) 20:30, 11 June 2011 (UTC)

R would be the same only when the ship is at Pluto's distance; since R is the distance between the ship and the Sun, R varies over the course of the orbit. A, the semimajor axis, would be 1/2 the long axis of the orbit -- that is, 1/2 the sum of Pluto's distance from the Sun and Earth's distance from the Sun. Duoduoduo (talk) 21:19, 11 June 2011 (UTC)
Yes, the math looks good if I say "A" stands for "average radius of orbit" instead of "semi-major axis." Semi-major axis seems to be defined as one-half the longest radius. Do astronomers use the phrase differently from mathematicians? 98.23.85.204 (talk) 21:27, 11 June 2011 (UTC)
No, astronomers and mathematicians use the term the same way -- the major axis is the long axis (presumably what you mean to call the longest diameter); the semi-major axis is half of that. Duoduoduo (talk) 21:36, 11 June 2011 (UTC)
This feels like we're going around in circles (or ellipses). Let me figure out two basic facts. If a body is orbiting the sun with its perihelion at 1 AU from the sun and its apehelion at 39.53 AU, what is the length of its semi-major axis? (Remember the longest diameter is twice 39.53 AU.) What number would you plug in for "A" in the equation "v = sqrt (mu * (2/R - 1/A) )"? 98.23.85.204 (talk) 21:46, 11 June 2011 (UTC)
I'm not sure what you mean by "the longest diameter is twice 39.53 AU". In any event, if a body is orbiting the sun with its perihelion at 1 AU from the sun and its aphelion at 39.53 AU from the sun (so that the sun is on a line segment -- the major axis-- between the perihelion and the aphelion), then the distance from the perihelion to the aphelion is 39.53+1 AU, and the length of its semi-major axis is (39.53+1)/2 AU. So A = (39.53+1)/2 AU. Duoduoduo (talk) 23:53, 11 June 2011 (UTC)
To help you visualize this, refer to the picture at the top of this article. The perihelion is the blue point directly to the left of the sun, in your example distant from the sun by 1AU, and the aphelion is the blue point directly to the right of the sun, distant from the sun by 39.53 AU. These two blue points -- the leftmost one and the rightmost one -- are distant from each other by 1 + 39.53 AU. Duoduoduo (talk) 23:59, 11 June 2011 (UTC)
Oh, dammit, I finally figured out why I suck. I was imagining the ellipse was reaching out 39.53 AU along one axis and 1 AU on the other. But bodies don't orbit the center, they orbit one of the focal points. Thanks for you patience while I got my head unstuck from my posterior. 98.23.85.204 (talk) 01:13, 12 June 2011 (UTC)
Heh, that was one of my favourite (and persistent!) mistakes too when I was learning about elliptical orbits. It may have a special appeal to the uninitiated... Martijn Meijering (talk)

## elliptical?

For an orbit to be an ellipse doesn't the end point have to meet up with the starting point? Given earth is always in more or less a forward motion (sometimes faster than the sun and sometimes a little slower) how can an elopes be formed? If I try draw it on paper with a very rough inaccurate representation of motion of the sun planets solar system and galaxy I end up with a squiggle that never crosses its previous path at all. A simple experiment to prove the point. While in a moving car spray paint an ellipse on the fence as you are moving. ZhuLien 66.249.80.203 (talk) 16:22, 12 March 2014 (UTC)

## elliptical or elliptic?

I think elliptical is preferred over elliptic. Bubba73 You talkin' to me? 01:32, 18 September 2014 (UTC)

## Velocity

What are the standard assumptions referred to at the beginning of the Velocity section? 108.72.4.161 (talk) 03:47, 14 December 2014 (UTC)

## Orbital Speed and Other Parameters

From Kepler's Laws and the geometry of the ellipse, it can be shown that P = [2(pi)ab]/[pv] where P=period, a=semi-major axis, b=semi-minor axis, p=perihelion distance, v=orbital speed at p. Alternatively, qv can be used, with q=aphelion distance, v=orbital speed at aphelion. Eroica (talk) 15:36, 28 April 2016 (UTC)

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