How to Calculate Work for Lunar Lander Orbit Change

In summary, the lunar lander needs to move from a 10 km-high orbit to a 100 km-high orbit in order to link up with the mother ship. To calculate the work needed, you would need to integrate the force over the distance the object moves or use the formula for potential energy at a distance 'r' from the center of the moon. The difference in potential energy between the two orbits should be taken into account, as well as the difference in kinetic energy. To calculate the orbital speed, you can use the equation for centripetal acceleration, where gravity is equal to the square of the velocity divided by the distance to the center of the moon.
  • #1
sam2k2002
10
0

Homework Statement


A 6000 kg lunar lander is in orbit 10 km above the surface of the moon. It needs to move out to a 100 km-high orbit in order to link up with the mother ship that will take the astronauts home.
How much work must the thrusters do?


Homework Equations


U_s = -GMm/r
F_g = GMm/r^2


The Attempt at a Solution


I tried to calculate the difference in force between the two orbits and then calculate the change in energy to get the work, but I've had no luck.
 
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  • #2
You would need to integrate the force over the distqance the object moves, or
use the formula for the potential energy at a a distance 'r' , pe= -GMm/r

Remember r is the total distance from the centre of the moon
 
  • #3
I'm not sure how to do that.. I get:

U_g(10km) = -2.67*10^17
U_g(100km) = -2.67*10^16

the difference is only 26.7J... that can't be right.
 
  • #4
sam2k2002 said:
I'm not sure how to do that.. I get:

U_g(10km) = -2.67*10^17
U_g(100km) = -2.67*10^16

the difference is only 26.7J... that can't be right.

I can't see why you think the difference is only 26.7 J. But this does not matter because:

The r in -GMm/r is the distance to the center of the moon, not the distance to the surface.

You'll need to calculate the orbital speed at 10 and 100 km as well and account for the
difference in kinetic energy.
 
  • #5
How do I calculate the orbital speed?

I assume after I get that, i can compute the change in kinetic energy?
 
  • #6
sam2k2002 said:
How do I calculate the orbital speed?

I assume after I get that, i can compute the change in kinetic energy?

For a circular orbit: centripetal acceleration = gravity
 
  • #7
so g=v^2/r ?
 
  • #8
sam2k2002 said:
so g=v^2/r ?

Yes. Of course you have g = GM/r^2 here for the acceleration of gravity
(M is mass of moon)
 

1. What is an object in orbit around Earth?

An object in orbit around Earth is any object that is moving around the Earth in a continuous circular or elliptical path due to the Earth's gravitational pull. This includes natural satellites such as the moon, as well as human-made satellites and spacecraft.

2. How does an object stay in orbit around Earth?

An object stays in orbit around Earth because of the balance between the Earth's gravitational pull and the object's forward motion. The object's speed and distance from the Earth must be just right for it to continue orbiting without falling back to Earth or flying off into space.

3. What factors affect an object's orbit around Earth?

The main factors that affect an object's orbit around Earth are its speed, distance from Earth, and the mass of the Earth. Objects with higher speeds and farther distances from Earth will have larger orbits, while objects with lower speeds and closer distances will have smaller orbits. The mass of the Earth also plays a role in determining an object's orbit, as it affects the strength of the gravitational force.

4. Can an object's orbit around Earth change?

Yes, an object's orbit around Earth can change due to different factors such as atmospheric drag, gravitational influences from other celestial bodies, or propulsion from a spacecraft. These changes can cause an object to move into a higher or lower orbit, or even leave Earth's orbit entirely.

5. How do scientists track objects in orbit around Earth?

Scientists track objects in orbit around Earth using various methods, such as radar, telescopes, and satellite tracking systems. These systems can monitor an object's position, speed, and trajectory to predict its future orbit and potential collisions with other objects in space.

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