Sattelite orbiting mars, work done to change distance.

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Homework Help Overview

The problem involves a spacecraft in a circular orbit around Mars, specifically calculating the work required to change its orbit from 1000 km to 4000 km above the Martian surface. The context includes gravitational potential energy and kinetic energy considerations.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the equations for gravitational potential energy and kinetic energy, with some questioning the correctness of the original poster's equations. There is also a mention of using negative values for potential energy.

Discussion Status

Some participants have provided alternative approaches to the problem, including a different method for calculating energy differences between orbits. There is acknowledgment of discrepancies in calculations, but no explicit consensus has been reached on the correct method.

Contextual Notes

Participants note the complexity of the calculations and the potential for errors in setup, particularly regarding the use of Excel for computations. The original poster expresses uncertainty about the correctness of their equations.

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Homework Statement


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

Homework Equations


TME=U+KE
U=Gm1m2/R
KE=.5Gm1m2/r (this doesn't seem right for some reason)

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.
 
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Are you using a negative for U ?
 
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
 
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 homework in excel)
 

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