How much work is done by the thrusters on a shuttle changing distances of orbit

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Homework Help Overview

The problem involves a lunar lander transitioning from a 40 km orbit to a 500 km orbit around the moon, with a focus on calculating the work done by the thrusters during this maneuver. The subject area includes concepts of work and energy, particularly in the context of gravitational potential energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of energy equations, including potential energy differences and the need for integration of force over distance. There is also a consideration of unit conversion from kilometers to meters.

Discussion Status

The discussion has evolved with participants providing insights into the energy calculations involved and the importance of unit consistency. One participant indicates they have reached a conclusion regarding the work done by the thrusters, while others have contributed thoughts on the necessary equations and methods to approach the problem.

Contextual Notes

There is a mention of potential confusion regarding units (km vs. meters) and the need to integrate force over distance, which highlights the complexity of the calculations involved. The original poster's reference to total energy in orbit suggests an assumption that may require further exploration.

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Homework Statement



a 2000kg lunar lander is in orbit 40km above the surface of the moon. it needs to move out to a 500km orbit in oder to link up with a mothership that will take the astronauts home. it wants the answer in joules

Homework Equations


??E2-E1=Work done by non conservative forces


The Attempt at a Solution


I get answers like 9.91*10^9 joules or negative 9.91*10^9

i thought that Total energy in an orbit=0 so i solved E(@40km)=mv1^2-GMm/r1=2000(v1^2-GM/40000+Rmoon)
 
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Does the topic happen to be work/energy (as in "potential energy")?

If so maybe m*g_moon(h2-h1)... is worth thinking about
 
Ooops - the distances are km! (I was thinking meters).

You'd probably need to integrate f(r)dr [force as a function of distance times incremental change in distance to center of moon - i.e. work] from (40000+R_moon) to (500000+R_moon), where f(r)=Gm1m2/r^2

m1=mass of moon
m2=mass of lander
R=radius of moon
 
Thanks for the help but i finally figured it out.

I had to take the total energy of the second orbit minus the total energy of the first orbit to get the work done by non conservative forces aka the thrusters. Thanks for your assistance though especially about changing it to meters from km
 

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