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gpax42
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Tricky Question --> gravitational pull problem
NASA sends up a satellite that just escapes Earth's gravitational pull. If the satellite is sent to Jupiter (Mass = 2*10^7kg Radius = 70,000km) how much energy must be released by the satellite such that it will successfully enter a stable circular orbit at an altitude of 10,000km from Jupiter's surface? Keep in terms of satellite's mass
G=6.67*10^-11
(KEf-KEi)+(PEf-PEi)=0
PE= -(GMm)/r
PEi= -(GMm)/r1 = -(6.67E-11*2E27)/70000 = -1.906E9*m
PEf= -(GMm)/r2 = -(6.67E-11*2E27)/80000 = -1.334E10*m
KEi=0 --> reference point
KEf=(1/2)*m([tex]\Delta[/tex]v)^2
(-1.334E10*m)-(-1.906E9*m) = [tex]\Delta[/tex]PE = -1.143E10*m = [tex]\Delta[/tex]KE
[tex]\Delta[/tex]PE=[tex]\Delta[/tex]KE
1.143E10*m=(1/2)m([tex]\Delta[/tex]v)^2
[tex]\Delta[/tex]v^2=2*(1.14E10)
[tex]\Delta[/tex]v^2=2.287E10 m/s
[tex]\Delta[/tex]v=1.51E5 m/s
I believe that the satellite must release 1.143E10*m J in the form of increased velocity (KE, 1.51E5 m/s), to maintain that orbit. So it must release energy to increase thrust (velocity)
... Not sure what made the professor take off points. His Comment was "what about V"
does anyone know how I could solve for V?
Homework Statement
NASA sends up a satellite that just escapes Earth's gravitational pull. If the satellite is sent to Jupiter (Mass = 2*10^7kg Radius = 70,000km) how much energy must be released by the satellite such that it will successfully enter a stable circular orbit at an altitude of 10,000km from Jupiter's surface? Keep in terms of satellite's mass
Homework Equations
G=6.67*10^-11
(KEf-KEi)+(PEf-PEi)=0
PE= -(GMm)/r
The Attempt at a Solution
PEi= -(GMm)/r1 = -(6.67E-11*2E27)/70000 = -1.906E9*m
PEf= -(GMm)/r2 = -(6.67E-11*2E27)/80000 = -1.334E10*m
KEi=0 --> reference point
KEf=(1/2)*m([tex]\Delta[/tex]v)^2
(-1.334E10*m)-(-1.906E9*m) = [tex]\Delta[/tex]PE = -1.143E10*m = [tex]\Delta[/tex]KE
[tex]\Delta[/tex]PE=[tex]\Delta[/tex]KE
1.143E10*m=(1/2)m([tex]\Delta[/tex]v)^2
[tex]\Delta[/tex]v^2=2*(1.14E10)
[tex]\Delta[/tex]v^2=2.287E10 m/s
[tex]\Delta[/tex]v=1.51E5 m/s
I believe that the satellite must release 1.143E10*m J in the form of increased velocity (KE, 1.51E5 m/s), to maintain that orbit. So it must release energy to increase thrust (velocity)
... Not sure what made the professor take off points. His Comment was "what about V"
does anyone know how I could solve for V?