# Gravity and velocity of a body in an elliptical orbit

Gold Member
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??

A.T.
v²/r
That's the centripetal acceleration for circular motion, not elliptical motion in general.

Gold Member
That's the centripetal acceleration for circular motion, not elliptical motion in general.
considering a small sector of the particles motion ..can't we use this
if not then how do we solve this through gravitational force??

A.T.
considering a small sector of the particles motion ..can't we use this
No.

if not then how do we solve this through gravitational force??
Gravitational potential energy vs. kinetic energy?

Gold Member
No.

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

A.T.