A space craft's speed due to gravitaitonal force

1. Nov 9, 2009

chrishobo

I have this question on a practice test I am using to study. Thanks for any assistance.

I believe it is a Energy Principle question

1. The problem statement, all variables and given/known data
A spacecraft is coasting towards mars. The mass of Mars is 6.4e^23 kg and its radius is 3400km. When the spacecraft is 7000km from the center of mars, the spacecrafts speed is 3000 m/s. Later, when the spacecraft is 4000 km from the center of mars, what is its speed?

(i think the following is unimportant, but here it is anyways:)
Assume that the effects of mars two tiny moons, the other planets, and the sun are negligible. Precision is required to land on mars, so make an accurate calculation, not a rough, approximate calculation. Start from a fundamental principle.

2. Relevant equations

Energy Initial = Energy Final + work (both the spacecraft and planet are in the system, so work is 0)

Kinetic Energy = .5*mass*velocity^2

3. The attempt at a solution

Ksi+KMi+Ui+mc2+Mc2=Ksf+KMf+Uf+mc2+Mc2

Mc2 cancels
mc2 cancels
KM has a near zero change, so it cancels

Leaving

Ksi+Ui=Ksf+Uf

Plugging in I get

.5*m*(3000)2+(-6.7e-11)*(m*(6.4e23)/(7000)=.5*m*(v)2+(-6.7e-11)*(m*(6.4e23)/(4000)

The m's (mass of craft) should cancel out on both sides,

and solving for v i get 95904 m/s

The key for the practice test (which doesnt give any work) states 4.3e3 m/s

2. Nov 9, 2009

ideasrule

You've got a unit problem because you used m/s for v but km for r. Be sure to use only meters (you can't only use kilometers because 6.7e-11 has units of m^3/(kgs^2).

3. Nov 9, 2009

ideasrule

Also, it's unnecessary to include the rest mass energy or the kinetic energy change of the planet when doing problems like this. Just write Ki+Ui=Kf+Uf and everyone will understand what you mean.

4. Nov 9, 2009

chrishobo

sweet. i feel silly for overlooking that

glad i did that now and not on the test.

Thanks!