Gravity and velocity of a body in an elliptical orbit

  • Thread starter Suraj M
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  • #1
Suraj M
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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??
 

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  • #2
A.T.
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v²/r
That's the centripetal acceleration for circular motion, not elliptical motion in general.
 
  • #3
Suraj M
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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??
 
  • #4
A.T.
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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?
 
  • #5
Suraj M
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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?
 
  • #6
A.T.
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Is the sum of the KE and GPE const.?? thats not necessary is it?
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
Suraj M
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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.
but in that way i would need the mass of the central body to find V ...and that's not a general case..
 

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