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gboff21
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Homework Statement
A 2580-kg spacecraft is in a circular orbit a distance 1580km above the surface of Mars.
How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4190km above the surface?
Homework Equations
[tex]\Delta[/tex]U=GMsMm(1/r_2-1/r_1)
[tex]\Delta[/tex]K=1/2GMsMm(1/r_2-1/r_1)
[tex]\Delta[/tex]K derived from [tex]\frac{mv2}{r}[/tex]=[tex]\frac{GMsMm}{r2}[/tex]
The Attempt at a Solution
Adding the energies
[tex]\Delta[/tex]E=[tex]\Delta[/tex]U+[tex]\Delta[/tex]K=3/2GMsMm(1/r_2-1/r_1)
M_s=2580kg
M_m=6.4191×1023kg
r_m=3397 km
r_1=1580km
r_2=4190km
substituting gives:
[tex]\Delta[/tex]U+[tex]\Delta[/tex]K=3/2G*2580*6.4191×1023*(1/(4190×10^3-339710^3)-1/(1580×10^3-3397×10^3)=3×10^11 J
Is this right? Or am I missing something?