- #1
DuckAmuck
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- TL;DR Summary
- Trying to make sense of the math here.
It is easy to find that the equation for an ellipse is:
$$1 = x^2/a^2 + y^2/b^2$$
Then according to Kepler's equation:
$$x = a(\cos(E)-e)$$
$$y = b\sin(E)$$
where E is the eccentric anomaly and e is the eccentricity.
If you plug the Kepler's equations' x and y into the equation for the ellipse, you get a relationship that does not hold:
$$\cos(E) = e/2$$
Are the Kepler's equations approximate? I thought they were exact. What is wrong here?
$$1 = x^2/a^2 + y^2/b^2$$
Then according to Kepler's equation:
$$x = a(\cos(E)-e)$$
$$y = b\sin(E)$$
where E is the eccentric anomaly and e is the eccentricity.
If you plug the Kepler's equations' x and y into the equation for the ellipse, you get a relationship that does not hold:
$$\cos(E) = e/2$$
Are the Kepler's equations approximate? I thought they were exact. What is wrong here?