Need help finding energy for escape velocity

AI Thread Summary
The discussion revolves around calculating the energy required for a rocket to reach escape velocity from a height of 300 km above Earth. The gravitational potential energy at the surface and at 300 km is provided, leading to the calculation of work needed to launch the rocket, which is determined to be 1x10^11 J. Additional kinetic energy required for circular orbit is calculated as 5x10^10 J. The main challenge lies in determining the extra energy needed to achieve escape velocity from this orbit, with confusion about the mass of the rocket and the relationship between potential and kinetic energy. The conversation emphasizes the need to clarify the concept of escape velocity and the implications of reaching it in terms of gravitational influence.
Jared
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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.
 
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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?
Well it asks for the additional energy.

I don't know. How would I find that?
 
Jared said:
Well it asks for the additional energy.
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?
 

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