Momentum & gravitation question

[teclo]

hi, here's the problem I'm working on.


a spacecraft is passing by an asteroid. the spaceship is moving at 10 m/s relative to the asteroid. here is picture

X (spaceship) -=> 10 m/s |
|
|
| 1200 km
|
|
A (asteroid)

given is the mass of the spaceship, the volume of the asteroid, and the theoretical density of the asteroid

a) make a rough diagram to show the effect, well obviously the gravitational force will point from X-A and it will incrase the closer they get, then decrase the further away they get. it will accelerate towards the asteroid while the gravitational force is significant

b) make a rought estimate of the change of momentum for the spacecraft from encountering the asteroid.

here I'm not sure how to do it. we've been using vpython to model stuff, and it would seem like i could write a program that would start their interaction at the a fair distance away, where the gravitational force is negligable, and run the program updating the momentum of the spacecraft until it reaches the same distance on the other side of the asteroid. i could then subtract the position that it ends up at, from where it would be at if there would have been no gravitational interaction.

i'm just wondering if anyone could offer some advice on how to look at this without using a program. there has to be a way, hence 'rough estimate'

if anyone could help, i'd be rather appreciative! out of the other two questions, one is easy. the density turned out to be a lot smaller, they would know that because the momentum wouldn't change as much if the mass was smaller than theorized. however, it asks how much the momentum would change during one day.

anyway I'm a bit confused, and i would really appreciate anyone who could offer some insight!

 

[teclo]

well my diagram didn't work out well the x component of the distance vector was a bit larger, i guess you could estimate it (assuming the book is drawn to scale) as 2400 km so you've got a <2400,1200> for the distance (as an assumption, the 2400 is not actually given or eluded to in any way shape or form)

 

[tony873004]

The mass of the spaceship should be irrelivant.

What is the mass of the asteroid?

or are you supposed to compute that from the volume and density?