Geostationary satellite collision - Orbits

[unscientific]

Homework Statement

A geostationary satellite of mass m, speed v orbits earth.

(a) Find expressions for
(i) Radius of the orbit, r₀.
(ii) Satellite's Speed

(b) A meteorite with mass m and speed v approaches in the direction towards the centre of the Earth and collides with the satellite. What is the linear and angular momentum after the collision?

(c) Find the minimum and maximum radius of orbit. Hence find out whether the body would collide with Earth eventually.

Use GM = 4 * 10¹⁴ Nm²kg^-1

The Attempt at a Solution

So I found that the satellite will collide with earth.

 

[Simon Bridge]

That looks nice - do you have a question?

Some things spring out at me right away:
1. there is no discussion or statements about assumptions - i.e. there should be more writing.
2. the speed of an object in a circular orbit is easily found from the circumference and period of the orbit.

 

[unscientific]

That looks nice - do you have a question?

Some things spring out at me right away:
1. there is no discussion or statements about assumptions - i.e. there should be more writing.
2. the speed of an object in a circular orbit is easily found from the circumference and period of the orbit.

Is there anything wrong with my answer?

 

[Simon Bridge]

Apart from what I already said?
Depends on what you hoped to achieve - what you really need is some way to tell for yourself when you have the right answer. One approach is to work out what your answer means physically and see if that makes sense.

After all - what would you do if two of us replied and one said you were right but the other said you were wrong?
Mind you, it's a lot easier to check if you explained your reasoning as you go.

 

[gneill]

Homework Statement

A geostationary satellite of mass m, speed v orbits earth.

(a) Find expressions for
(i) Radius of the orbit, r₀.
(ii) Satellite's Speed

(b) A meteorite with mass m and speed v approaches in the direction towards the centre of the Earth and collides with the satellite. What is the linear and angular momentum after the collision?

Is the collision elastic or inelastic? Are you looking for the total momenta of the system, or the individual linear and angular momenta for two separate objects (assuming perfectly elastic collision).

(c) Find the minimum and maximum radius of orbit. Hence find out whether the body would collide with Earth eventually.

Again, is the satellite stuck to the meteorite at this point, or are they separate objects?

 

[unscientific]

Is the collision elastic or inelastic? Are you looking for the total momenta of the system, or the individual linear and angular momenta for two separate objects (assuming perfectly elastic collision).

Again, is the satellite stuck to the meteorite at this point, or are they separate objects?

The collision is inelastic, as the object sticks together with the satellite. I used the conservation of angular momentum. But since it is an inelastic collision, is energy conserved?

 

[gneill]

The collision is inelastic, as the object sticks together with the satellite. I used the conservation of angular momentum. But since it is an inelastic collision, is energy conserved?

Kinetic energy is not conserved over an inelastic collision. Momentum is always conserved.

It should be straightforward to use conservation of momentum to determine the post-collision velocity of the combined object. Then you have position and velocity vectors, hence enough information to determine the orbit elements.

 

[unscientific]

Kinetic energy is not conserved over an inelastic collision. Momentum is always conserved.

It should be straightforward to use conservation of momentum to determine the post-collision velocity of the combined object. Then you have position and velocity vectors, hence enough information to determine the orbit elements.

With the new velocity, i can determine the total energy after the collision, which will give the right answers. So the value of E in my previous answer is wrong then.