Elliptical Motion: Formulating Object Motion & Finding Theta

[vaishakh]

How can we formulate the elliptical motion of an object apparently observed by us when it moves linearly infront of us. The position vector with respect to us makes an elliptical motion at that time. To start with let's take the velocity as v, the perpendicular distance of the line of motion from observer as x and now find the rate of change of theta with respect to us.

 

[Astronuc]

One could right the equation of motion for an ellipse, and then determine the lateral component as a function of time with respect to the line of the observer. Assume that the observer is far way. If $\theta$ is the position angle with respect of the object from some reference, say the major axis, then one could write the general equation for an observer at $\theta_o$