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chrishobo
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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
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 spacecraft s 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.
Energy Initial = Energy Final + work (both the spacecraft and planet are in the system, so work is 0)
Kinetic Energy = .5*mass*velocity^2
Potential energy = -G*mass1*MASS2/radius
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 doesn't give any work) states 4.3e3 m/s
I believe it is a Energy Principle question
Homework Statement
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 spacecraft s 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.
Homework 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
Potential energy = -G*mass1*MASS2/radius
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 doesn't give any work) states 4.3e3 m/s