Talk:Elliptic orbit

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

I think this article should be radically rewritten

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 :$-{\frac {\mu }{2\cdot a}}$, "vis viva",

But why the conclusion:

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

Strange conclusion!

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

The formula

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

derived in Kepler orbit article

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

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

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 (talk • contribs) 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

Please help me understand. Let's talk about Pluto orbiting the Sun (assume its orbit is circular).

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)

You are right. BUT! For the purposes of orbit calculation you can declare the Earth to be stationary or the Sun to be stationary. (Remember the Sun is orbiting the Galaxy at 250 km/s.) This gives you the classic elliptical or hyperbolic orbit. Then if you want, you can consider the movement of the parent body. So for an Earth satellite you calculate assuming the Earth is stationary then you can change your Frame of reference by assuming that the Sun to be stationary and the Earth to be moving at 30 km/s. That changes the ellipse into a cycloid. As an example if we consider the Moon to be in orbit round the Earth then it traces an ellipse about every 29 days. To this we can add various perturbing factors such as Earth not being perfectly spherical and the gravitational effects of raising tides on a rotating planet and we can get a very accurate picture. We could note that Earth-Moon together rotate about their Barycenter - a point 4761 km from the Earth's center - but changing the frame too early just makes the detailed calculations more complex. If you took a Sun-centered approach then the Moon's orbit becomes a near perfect ellipse with 26 tiny wiggles - 13 towards the Sun and 13 away. But the wiggles are too small to be detected by looking. If you drew the orbit on a large sheet of graph paper (1m square say) the wiggles would be less than the thickness of the pencil line defining the orbit but these wiggles are everything we see when we consider the Earth-Moon orbiting system.OrewaTel (talk) 09:49, 20 July 2020 (UTC)

elliptical or elliptic?

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

Standard Assumptions

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)

Two main assumptions

1. The parent body is stationary and only the satellite is moving. (Although you still get the same equation if you assume that both bodies are orbiting their Barycenter the meanings of the parameters 'a' and 'v' are harder to describe.)
2. Newtonian rather than Einsteinian mechanics

Whilst these are automatic assumptions for anyone who has actually done these calculations, perhaps they should be explicitly stated in the article. OrewaTel (talk) 10:18, 20 July 2020 (UTC)

I agree. "Standard Assumptions" are invoked in four different sections in the main article. There have been many requests over the years to add an explanation/definition of them, but until now no one has responded with what those standard assumptions are. I think it would be an excellent improvement if you would add a small section at the beginning with this title and description.

RBarryYoung (talk) 15:16, 13 August 2020 (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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Audience

This page suffers from the following common Wikipedia issue (highlighted in Why Wikipedia is not so great: Readability and writing style):

• Many Wikipedians write in a way that is considered acceptable within the author's peer group, but is less comprehensible to the general reader. This may include the use of jargon.

This article consists almost entirely of jargon or non-contextualized formulae, such that it provides little value to anyone who is not already an astronomy expert. It is not until section 7 (Solar System) before there is anything comprehensible to the average reader and that turns into gibberish (to everyone) by the second sentence, as it references 'both bodies' when 2 bodies have not been introduced and only gets more incomprehensible from there (I imagine someone edited the first sentence without bothering to confirm that the paragraph as a whole still made sense).

The one saving grace of this page is the graphic of a small body orbiting a large one at the top of the page. It is extremely helpful in answering a number of the reader's most likely questions and providing a visual and intuitive understanding of elliptic orbit.

Almost all of the formulae and technical jargon needs to be moved down the article and several sections introduced which offers some insight into the reader's most likely question, namely: Why do planets (and other bodies) have an elliptic orbit in the first place? This should be comprehensively explained before diving into computations of velocity, orbital period, or energy. The technical definition from the first paragraph can be left in the opening section, but needs to come after a coherent explanation of elliptic orbit. The second paragraph about the 'gravitational two-body problem with negative energy' should maybe be removed entirely, as it illuminates little and the reader has to do some serious digging through multiple links to comprehend what that even means.--BrianMakesEdits (talk) 06:39, 2 April 2019 (UTC)

Multiple eccentricity, single semi-major axis animation needs a caption.

It should be STRONGLY noted under the "File:Animation of Orbital eccentricity.gif" image that it is not possible for a planet to change from one of these orbits to another. That is, a planet cannot maintain its semi-major axis and change its eccentricity. To do so has no change in orbital energy. That means it takes no work to do so. So, if it ever happened, it would mean than orbits could spontaneously evaporate. That is, they could transition from a circular orbit to a parabolic one without any work done on it. That just isn't possible.

See the book "Air of Doubt" (airofdoubt.com) for the correct way to model orbits with a time-dependent Hamiltonian. — Preceding unsigned comment added by AoDFT (talk • contribs) 21:51, 27 October 2020 (UTC)