Potential Energy and Velocity of a Spaceship

In summary, Roger planned to leave the Earth with enough speed to make it to the moon, but needed help from a friend to calculate the minimum speed. He attempted to solve Q1 by adding the potential energy of the spacecraft for both the Earth and the Moon together, but appears to have gotten incorrect results. He is working on a solution to Q2.
  • #1
Drakkith
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Homework Statement


You plan to take a trip to the moon. Since you do not have a traditional spaceship with rockets, you will need to leave the Earth with enough speed to make it to the moon. Some information that will help during this problem:mearth = 5.9742 x 1024 kg
rearth = 6.3781 x 106 m
mmoon = 7.36 x 1022 kg
rmoon = 1.7374 x 106 m
dearth to moon = 3.844 x 108 m (center to center)
G = 6.67428 x 10-11 N-m2/kg21)On your first attempt you leave the surface of the Earth at v = 5534 m/s. How far from the center of the Earth will you get?
2) Since that is not far enough, you consult a friend who calculates (correctly) the minimum speed needed as vmin = 11068 m/s. If you leave the surface of the Earth at this speed, how fast will you be moving at the surface of the moon? Hint carefully write out an expression for the potential and kinetic energy of the ship on the surface of earth, and on the surface of moon. Be sure to include the gravitational potential energy of the Earth even when the ship is at the surface of the moon!

Homework Equations


ΔE = 0
U1+K1 = U2 + K2

The Attempt at a Solution



Found the answer to Q1. It's 8.44x106 meters.

Q2 is where I'm having trouble. I don't know how to set it up. For Q1, ΔE=0 so ΔU + ΔK = 0 as well. And ΔU = U2-U1.

For Q2, I was thinking you would add the potential energy of the spacecraft for both the Earth and the Moon together, like: U1 = U1E + U1M. That would make ΔU = (U2E + U2M) - (U1E + U1M).

Unfortunately my answer using this method appears to be incorrect. Not sure what to do. I made sure to account for the differing distance between the centers of the Earth and Moon, and the distance between the surfaces of each and the center of the other.
 
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  • #2
In principle, you need to consider the PE wrt the moon in Q1 too, but that shot falls too far short for it to matter.
Please post the details of your attempt on Q2. Can't tell where or if you are going wrong otherwise.
 
  • #3
haruspex said:
Please post the details of your attempt on Q2. Can't tell where or if you are going wrong otherwise.

Roger. I'll get on that as soon as I can.
 

FAQ: Potential Energy and Velocity of a Spaceship

What is potential energy and how does it relate to a spaceship?

Potential energy is the energy that an object possesses due to its position or configuration in a force field. In the context of a spaceship, it refers to the energy that the spaceship has based on its position in space and the gravitational force acting upon it.

How is potential energy calculated for a spaceship?

The formula for potential energy is PE = mgh, where m is the mass of the spaceship, g is the acceleration due to gravity, and h is the height of the spaceship from a chosen reference point. This formula can be used to calculate the potential energy of a spaceship at any given point in space.

How does velocity affect potential energy of a spaceship?

Velocity does not directly affect potential energy, but it can affect the kinetic energy of the spaceship. As the spaceship gains velocity, its kinetic energy increases, but its potential energy remains the same unless its position in space changes.

What is the relationship between potential energy and velocity for a spaceship?

The relationship between potential energy and velocity is inverse. As the spaceship gains velocity, its potential energy decreases. This is because the spaceship is moving closer to the reference point, thus decreasing its height and potential energy.

How does a spaceship's potential energy and velocity impact its trajectory and overall motion?

A spaceship's potential energy and velocity play a crucial role in determining its trajectory and overall motion. As the spaceship moves through a gravitational force field, its potential energy is converted into kinetic energy, causing it to accelerate and follow a specific path determined by its initial velocity and the force of gravity.

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