Energy required to move an object to an altitude twice the radius of Earth

In summary, the question is asking for the amount of energy needed to move a 1 000-kg object from the surface of Earth to an altitude twice the radius of Earth. The formula for potential energy is used to calculate this, taking into account the difference in potential energy between the two distances. The correct answer is found by considering the altitude to be three times the radius, not two times.
  • #1
aero_zeppelin
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Homework Statement


How much energy is required to move a 1 000-kg object
from the Earth’s surface to an altitude twice the Earth’s
radius?


Homework Equations


U = - G Me m / r


The Attempt at a Solution



I'm just using the above equation with 2r (twice the radius) and get 3.1 x 10e10 J, but the book says different...

Any help?? Thanks!
 
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  • #2
Plugging in a certain radius just tells you the potential energy an object has at that distance from the center. The question is asking you how much energy it takes to move from 1 radius (the surface) to another radius. So you need to find a difference in potential energy.

In this case, you need to find the potential energy difference between the mass at the surface and at that 2r altitude. This must be the energy required to bring it from the surface to the high up distance.
 
  • #3
actually, I think I figured it out. The problem is somewhat bad worded and I believe it can confuse people. It says an ALTITUDE twice the radius of Earth, which means two times that distance ONCE the object has left the Earth, so actually it would be 3r... right?

I guess it's right, I got the correct answer ;) thanks for the help!
 

FAQ: Energy required to move an object to an altitude twice the radius of Earth

How is the energy required to move an object to an altitude twice the radius of Earth calculated?

The energy required to move an object to an altitude twice the radius of Earth is calculated using the formula: E = mgh, where E is the energy, m is the mass of the object, g is the acceleration due to gravity, and h is the height or altitude.

Does the mass of the object affect the energy required to move it to an altitude twice the radius of Earth?

Yes, the mass of the object does affect the energy required to move it to an altitude twice the radius of Earth. The greater the mass, the more energy is required to move it to a higher altitude.

What is the acceleration due to gravity at an altitude twice the radius of Earth?

The acceleration due to gravity at an altitude twice the radius of Earth is approximately 3.11 m/s². This is because the gravitational force decreases with distance from the Earth's center, and at an altitude twice the radius, the distance is doubled, resulting in a weaker gravitational force.

How does the energy required to move an object to an altitude twice the radius of Earth compare to the energy required to move it to the Earth's surface?

The energy required to move an object to an altitude twice the radius of Earth is significantly greater than the energy required to move it to the Earth's surface. This is because at a higher altitude, the object has more potential energy due to its increased distance from the Earth's center.

Can the energy required to move an object to an altitude twice the radius of Earth be reduced?

Yes, the energy required to move an object to an altitude twice the radius of Earth can be reduced by using external forces, such as rockets or propulsion systems, to assist in the movement. These external forces can provide an additional energy input to reduce the amount of energy required from the object's initial state.

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