# Sattelite orbiting mars, work done to change distance.

#### mark_dollar

1. The problem statement, all variables and given/known data
A 2700 kg spacecraft is in a circular orbit 1000 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4000 km above the surface?

mars: Mass=6.4185*10^23 KG, radius=3397000 m
2. Relevant equations
TME=U+KE
U=Gm1m2/R
KE=.5Gm1m2/r (this doesn't seem right for some reason)

3. The attempt at a solution
U1+k1+work=U2+k2
work=U2+k2-(u1+k1)
u1=2.630*10^10
ke1=1.315*10^10
U2=2.891*10^10
Ke2=1.446*10^10
TME1=3.945*10^10
TME2=4.337*10^10
Work= TME2-TME1=3.92*10^9
webassign says I'm wrong. Is my equation for either KE or potential energy incorrrect? Any help is appreciated.

Are you using a negative for U ?

#### mark_dollar

sure am

Sorry for replying late, I have a final for this intro mechanics tomorrow morning :)
This is the way i did it :

E1 (energy at lower orbit) = -GmM/2r1 where r1 is the radius of mars + 1000 km
E2 (energy at higher orbit)= -GmM/2r2 , r2 is the radius or mars + 1000 km

m is 2700 kg
M is mass of Mars.

E2-E1 = GmM/2 (1/r1 - 1/r2) gives 5.33 x 10^9 J

#### mark_dollar

Thanks Ahmadmz, that's what I got too after I corrected my excel spreadsheet, had the wrong equation in for velocity. ( I do all my hw in excel)

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