Ellipse from 2 arbitrary points, tangent at P1 and focus

[silkms]

MENTOR Note: Moved this thread from a math forum hence no template

Is it possible to find this? Really only need the semi major axis or even it's orientation.

In the image below, elements in red are known.

 

[jedishrfu]

Have you looked at Kepler's laws for planetary motion?

 

[silkms]

Have you looked at Kepler's laws for planetary motion?

Yup. I am using them to find the velocity for a projectile at p1, when both p1 and p2 are on the surface of the planet, but unfortunately my technique for finding the true anomaly (the angle between p1 and the periapsis), breaks when one of the points leaves the surface and is no longer mirrored across the axis of the ellipse.

A technique for finding the true anomaly for a more general case would also allow me to solve this!

I expect that there is a solution to this using Kepler's laws, but I am struggling to get there and hoping someone here will have some insight.

 

[vela]

Seems solvable. You only need two numbers to specify the ellipse, and it looks like with the information given, you should be able to come up with at least two independent equations. (I take it we can assume the planet is much more massive than the orbiting object and therefore remains at rest.)

When you say, "tangent at P1," do you mean you know the velocity of the object at P1 or just its direction?

 

[silkms]

Seems solvable. You only need two numbers to specify the ellipse, and it looks like with the information given, you should be able to come up with at least two independent equations. (I take it we can assume the planet is much more massive than the orbiting object and therefore remains at rest.)

When you say, "tangent at P1," do you mean you know the velocity of the object at P1 or just its direction?

Just it's direction. Actually hoping to find it's velocity.