One more gravity question

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In summary, to move a body with mass m from orbiting radius R1 to R2 around the Earth, two steps are required. Firstly, we must give the body enough energy to reach the maximal distance from Earth, which is equal to the desired orbiting radius. Secondly, we must give the body energy at this maximal distance to achieve the appropriate speed for orbiting at R2. The amount of energy needed for each step can be calculated using the Vis-viva equation and the Hohmann transfer orbit method. It is not necessary to know the specific change in speed during the first step, as long as the body has enough energy to reach the desired orbiting radius.
  • #1
assaftolko
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A body with a mass of m is orbiting the Earth with orbiting radius of R1. We want to move the body so it will orbit the Earth with orbiting radius of R2. To achieve this we need to do 2 steps:

1. We need to give the body energy so it will reach the maximal distance from Earth which is exactly equal to the orbit radius we want to achieve.
2. We need to give the body energy at this maximal distance so it could achieve the appropriate speed that will alow it to orbit the Earth at such radius.

How much energy do we need to give the body in each one of the steps?

The orbits are circular.

I have no idea how to do this... I thought maybe to calculate the energy of m when it orbits the Earth with radius R1, and then calculate m's energy when it's at R2 for step 1 - and the difference between them is the answer. But what's the speed of m at the end of the first step? it's of course not the orbiting speed of circular orbit with radius R2...
 

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  • #2
Part one is about changing PE, part two about changing KE.

At the beginning it has PE and KE. After step one PE is changed but it still has same KE. Do you actually need to know how the speed has changed?
 
  • #3
You may want to check your references for the "Vis-viva equation" and "Hohmann transfer orbit".
 
  • #4
CWatters said:
Part one is about changing PE, part two about changing KE.

At the beginning it has PE and KE. After step one PE is changed but it still has same KE. Do you actually need to know how the speed has changed?

As you can see the answers are at the bottom of the picture I uploaded and they do not work out with your way:

Step 1 = [itex]\frac{1}{2}[/itex]GmEm[[itex]\frac{R2-R1}{R1(R2+R1)}[/itex]]

I don't think you can say the KE at the end of step 1 is the same KE as when m orbits the Earth in R1 radius. This KE is the result of a specific orbit velocity that corresponds to the specific circular orbit radius of R1.
 
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  • #5


I can help you with calculating the energy needed for each step. To answer your question, we need to use the formula for gravitational potential energy, which is given by U = -GmM/r, where G is the universal gravitational constant, m is the mass of the orbiting body, M is the mass of the Earth, and r is the distance between the two objects.

For the first step, we need to calculate the energy needed for the body to reach the maximal distance from Earth, which is equal to R2. This can be done by using the formula U = -GmM/R2. This will give us the potential energy at this distance.

For the second step, we need to calculate the energy needed for the body to achieve the appropriate speed to orbit the Earth at R2. This can be done by using the formula for kinetic energy, which is given by K = 1/2mv^2, where m is the mass of the orbiting body and v is the speed.

To calculate the speed needed, we can use the formula for orbital velocity, which is given by v = √(GM/R2), where G is the universal gravitational constant, M is the mass of the Earth, and R2 is the desired orbiting radius. Plugging this value into the formula for kinetic energy will give us the energy needed for the second step.

Therefore, the total energy needed for both steps would be the sum of the potential energy and kinetic energy calculated for each step. I hope this helps in understanding the energy requirements for changing the orbiting radius of an object around the Earth.
 

1. What is gravity?

Gravity is a force of attraction between two objects due to their mass. It is responsible for keeping objects in orbit around larger objects, such as planets around the sun.

2. How does gravity work?

Gravity is a fundamental force of nature that works by pulling objects towards each other. The more massive an object is, the stronger its gravitational pull will be. This is why larger objects, such as planets, have a stronger gravitational force.

3. Why do objects fall towards the ground?

Objects fall towards the ground because the Earth's mass creates a gravitational force that pulls objects towards its center. This force is what keeps us grounded and prevents us from floating off into space.

4. Is gravity the same everywhere?

No, gravity can vary slightly depending on factors such as the mass and distance of objects. For example, the gravitational force on the moon is about one-sixth of the force on Earth due to its smaller mass and distance from the Earth.

5. Can gravity be manipulated or controlled?

Currently, there is no known way to manipulate or control gravity. However, scientists are constantly researching and studying this force to better understand it and potentially find ways to harness its power in the future.

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