# Gravity and velocity of a body in an elliptical orbit

1. Jan 21, 2015

### Suraj M

consider a body revolving around a star and having a velocity v when closest to the star ( distance r) then the velocity of the body at a point farthest ( distance R) is?
1)by angular momentum conservation ::
r × mv = R× mV
»V = (r/R).v

2) By centrifugal and gravitatinal force
v²/r = GM/r²
v² α 1/r
in this we can get V = (r/R)½ v

the angular momentum method is the right method .... but what am i missing out on from method no. 2??

2. Jan 21, 2015

### A.T.

That's the centripetal acceleration for circular motion, not elliptical motion in general.

3. Jan 21, 2015

### Suraj M

considering a small sector of the particles motion ..can't we use this
if not then how do we solve this through gravitational force??

4. Jan 21, 2015

### A.T.

No.

Gravitational potential energy vs. kinetic energy?

5. Jan 21, 2015

### Suraj M

how'd you do that? Is the sum of the KE and GPE const.?? thats not necessary is it?

6. Jan 21, 2015

### A.T.

If M >> m then it's approximately true in the approximately inertial rest frame of M. Otherwise you have to consider the KE of M too.

7. Jan 21, 2015

### Suraj M

but in that way i would need the mass of the central body to find V ...and that's not a general case..