6
$\begingroup$

From the wiki article about eccentric anomaly follows:

$$\cos E = \frac{x}{a}$$ $$\sin E = \frac{y}{b}$$

where E - eccentric anomaly, a - semi-major axis, b - semi-minor axis, P = P(x,y) a point on elleptic orbit. So if you know an E, you can find a position on an orbit:

$$x = a \cos E$$ $$y = b \sin E$$

However, from article on Kepler's eqution follows:

$$x = a (\cos E - e)$$ $$y = b \sin E$$

Please, help to understand why these formaluae differ? I expect them to be the same.

| improve this question | | | | |
$\endgroup$
6
$\begingroup$

Both formulae are correct. The discrepancy is because the formula from the eccentric anomaly article uses the centre of the ellipse as the origin, but the formula from the Kepler's equation article uses a focus of the ellipse (i.e, the central gravitating body, eg the Sun) as the origin. Note that $c = ae$ is the distance from the ellipse centre to a focus

| improve this answer | | | | |
$\endgroup$
  • 1
    $\begingroup$ Thank you, now it's clear. Can't upvote the answer since I don't have enough rep. $\endgroup$ – Jonas Dec 27 '19 at 17:27
  • $\begingroup$ @Jonas I've upvoted both question and answer, we'll get you there soon! $\endgroup$ – uhoh Dec 28 '19 at 1:46

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.