How Does Satellite Velocity Change with Altitude?

[Chip90]

Homework Statement

The problem is that a satellite is ejected from a planet radius R and mass M, that has no atmosphere, 30 degrees from vertial with velocity vo.

This is a multi part problem dealing with center of mass/inertia, the part I need help with is the following:

1. When the satellite is at point B, what is the velocity in terms of point A?

Point A is R away from the center of the planet (so it is on the surface of the planet) and Point B is 3R from the center of the planet.

2. What is equation to relate vo to R?

Homework Equations

conservation of E and angular momentum

The Attempt at a Solution

For 2, I am very lost.

For 1:
I did

KEi + PEi = KEf +PEf

(1/2)*m(satellite)*vo^2 - G*m(earth)*m(satellite)/R= (1/2)*m(satellite)*vb^2 - G*m(earth)*m(satellite)/3R

this simplifies to Vb^2=Vo^2 - 16/9 * G*m*(earth)/R

 

[mark726]

Answer:

1. The velocity at point B is related to the velocity at point A by the equation Vb^2=Vo^2 - 16/9 * G*m*(earth)/R.

2. To relate vo to R, you can use the equation Vb^2=Vo^2 - 16/9 * G*m*(earth)/R and solve for vo. This will give you an equation that relates vo to R.