# Homework Help: Satellite Collision

1. Feb 18, 2012

### vivekrai

1. The problem statement, all variables and given/known data
A satellite is revolving around the Earth in a circular orbit with radius of 2R, where R is radius of earth.If suddenly,its velocity becomes zero in the orbit due to collision with some inter-stellar object(like a satellite),find the time which it takes to hit surface of the earth. Ignore the effect of atmosphere and treat earth to be perfect sphere.

2. Relevant equations
Necessary formulas. . all are at hand.

3. The attempt at a solution

There are a no. of confusions I'm having. Firstly, What is aftermath motion of the satellite. Does it swirl inwards towards the earth or fall directly.
Secondly, Since there is no energy dissipation the energy remains conserved ie., Since PE decreases the KE should increase. Also the Angular Momentum should remain conserved about the earth.

Will it suffice to solve this? Or Am I missing something?

2. Feb 18, 2012

### tiny-tim

hi vivekrai!

you're reading too much into this!

… zero velocity = zero KE = zero angular momentum

3. Feb 19, 2012

### vivekrai

So Initial Angular momentum is zero which implies that the satellite must fall in such a way that it's Angular Momentum remains zero for along the motion. This is only possible if it falls in a straight line joining the Center of earth and the satellite?

The problem then reduces to just finding the time taken by the satellite to hit the surface of earth under a variable force of gravitation due to the earth. Does it? This would however require Integration and I'' handle it.

Now Is there any other method based purely on Kepler's Laws which can help to solve this without the maths? [Just for Knowledge]

4. Feb 19, 2012

### tiny-tim

hi vivekrai!
yes!
well, you could get if from kepler's third law
the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit​

if you had another orbital period to compare it with!

5. Feb 19, 2012

### vivekrai

In this case, the ellipse that we thought for its motion becomes flat ie., Converges to a straight line. Now what after this?

6. Feb 20, 2012

### tiny-tim

you still need another orbital period to compare it with

7. Feb 20, 2012

### vivekrai

8. Feb 20, 2012

### tiny-tim

there isn't a way using kepler's laws!

use the way you mentioned earlier

9. Feb 21, 2012

### vivekrai

Sir Please tell me that you're not hiding something. If there is really , then please tell. I've come to know that indeed there (based on some assumption) , which I'm not getting.

10. Feb 21, 2012

### tiny-tim

it falls in a straight vertical line

just find the time taken by the satellite to hit the surface of earth under the variable force of gravitation