# Need help finding energy for escape velocity

• Jared
In summary: It asks for the additional energy to go from hovering at a height of 300km to orbiting at a height of 300km. That can have nothing to do with how it got to 300km. Your 1x10^11J was the energy to lift it from Earth's surface to 300km. If it had started at 299km it would have needed far less energy to reach 300km. Would you then have taken that much smaller amount of energy and halved it to find the extra energy to make it orbit at 300km?No, I would not have halved it.
Jared

## Homework Statement

The gravitational potential energy of a certain rocket at the surface of the Earth is -1.9x10^12 J. The gravitational potential energy of the same rocket 300km above the Earth's surface is -1.8x10^12 J. Assume the mass of the rocket is constant for this problem.
A) How much work is required to launch the rocket from the surface of the Earth so it coasts to a height of 300km? (starting and ending at rest, no orbit, just straight up and down): Found to be deltaU= -1.8x10^12- -1.9x10^12= 1x10^11 J. (this mas be wrong but teacher said to just make corrections).

B) What additional Kinetic energy is required to put the rocket into a circular orbit? Found to be KE= 1/2(1x10^11)= 5x10^10 J

Here is where I have trouble.
C) How much extra energy is required for the rocket to reach escape velocity from this orbit?

## Homework Equations

V_esc=(2GM/R)^1/2
I'm sure I am missing something. Also sure it's really easy just blanking on it.

## The Attempt at a Solution

I get V_esc= 10927.99m/s but then I go to use the equation for KE=1/2MV^2 but I don't know how to find the mass of the rocket because we were told it was constant. So I'm just not sure if I should be using a different equation or what.

Jared said:
additional Kinetic energy is required to put the rocket into a circular orbit? Found to be KE= 1/2(1x10^11)
By what reasoning?
Jared said:
How much extra energy is required for the rocket to reach escape velocity from this orbit?
If an object just reaches escape velocity, where can it go, and what PE and KE will it have when it gets there?

haruspex said:
By what reasoning?

If an object just reaches escape velocity, where can it go, and what PE and KE will it have when it gets there?
To be honest I'm not actually sure. It seems to be correct on my quiz, but I just did KE=1/2U_g (gravitational potential energy) which was found in A.

As to your second part, if it reaches escape velocity doesn't it just leave the Earth's orbit and go into space?

Jared said:
KE=1/2U_g (gravitational potential energy)
Well, -1/2U_g, but 1x10^11J is not its PE; that was the change in PE.
Jared said:
doesn't it just leave the Earth's orbit and go into space?
Yes, but to what altitude, in principle?

haruspex said:
Well, -1/2U_g, but 1x10^11J is not its PE; that was the change in PE.

Yes, but to what altitude, in principle?

I don't know. How would I find that?

Jared said:
It asks for the additional energy to go from hovering at a height of 300km to orbiting at a height of 300km. That can have nothing to do with how it got to 300km. Your 1x10^11J was the energy to lift it from Earth's surface to 300km. If it had started at 299km it would have needed far less energy to reach 300km. Would you then have taken that much smaller amount of energy and halved it to find the extra energy to make it orbit at 300km?
Jared said:
I don't know. How would I find that?
What does escape velocity mean? If it were enough velocity to get 1000000km from Earth, but no further, would it have escaped Earth's gravity? Where does Earth's gravity end?

## 1. How do I calculate escape velocity?

The formula for escape velocity is v = √(2GM/r), where G is the gravitational constant, M is the mass of the planet or object you are trying to escape from, and r is the distance from the center of the planet or object to the point where you are trying to escape. Plug in the values and use a calculator to find the escape velocity in meters per second (m/s).

## 2. What is the purpose of escape velocity?

Escape velocity is the minimum speed needed for an object to break free from the gravitational pull of a planet or object. It allows spacecraft and other objects to launch into space and travel to other planets or celestial bodies.

## 3. How does escape velocity vary on different planets?

The escape velocity on different planets depends on the mass and radius of the planet. Generally, planets with larger mass and radius will have a higher escape velocity, while smaller planets will have a lower escape velocity. For example, the escape velocity on Earth is 11.2 km/s, while on the moon it is only 2.4 km/s.

## 4. Can escape velocity be achieved with any type of energy?

No, escape velocity cannot be achieved with any type of energy. It requires a specific amount of kinetic energy, which can be achieved through rocket propulsion or other forms of energy such as solar or nuclear power.

## 5. What factors can impact the ability to reach escape velocity?

The main factors that can impact the ability to reach escape velocity are the mass and radius of the planet or object, as well as the amount of fuel or energy available. Other factors such as atmospheric conditions, gravitational pull from other nearby objects, and the design and efficiency of the spacecraft or object can also play a role.

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