How Do You Calculate the Velocity of a Planet in Orbit?

[ehrenfest]

Homework Statement

I am trying to find the velocity vectors for a planet in orbit.

$$dx/dt = -a sin \theta \dot{\theta}$$
$$dy/dt = b cos \theta \dot{\theta}$$

Where a and b are the lengths of the sem-major and semi-minor axes, resp?

What is the time derivative of theta expressed in terms of a and b?

Homework Equations

The Attempt at a Solution

 

[D H]

I am trying to find the velocity vectors for a planet in orbit.
$$dx/dt = -a sin \theta \dot{\theta}$$
$$dy/dt = b cos \theta \dot{\theta}$$

You are using the wrong equation of an ellipse. The sun is at one of the foci of the ellipse, not the center. The correct set of equations for the ellipse are

$$r = \frac {a(1-e^2)}{1+e\cos \theta}$$

$$x = r \cos \theta$$

$$y= r \sin \theta$$

where $r(t)$ is the radial distance, $\theta(t)$ is the true anomaly, $a$ is the semi-major axis, and $e$ is the eccentricity. To get the velocity vector you will need to add mean anomaly and eccentric anomaly to the mix.