Need help finding energy for escape velocity

Click For Summary

Homework Help Overview

The discussion revolves around calculating the energy required for a rocket to reach escape velocity from a height of 300 km above the Earth's surface. The problem involves gravitational potential energy and kinetic energy, with specific values provided for the potential energy at different heights.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relationship between gravitational potential energy and kinetic energy, questioning the reasoning behind the calculations for energy required to achieve escape velocity.
  • Some participants express uncertainty about how to determine the mass of the rocket and its implications for the kinetic energy calculations.
  • Questions arise regarding the implications of reaching escape velocity and the potential energy and kinetic energy states of the rocket at that point.
  • There is a discussion about the additional energy required to transition from hovering at 300 km to achieving orbit, with some participants questioning the relevance of previous calculations.

Discussion Status

The discussion is ongoing, with participants actively questioning assumptions and clarifying concepts related to energy calculations. Some guidance has been offered regarding the distinction between energy needed to reach a height and energy required for orbital motion, but no consensus has been reached on the specific calculations or interpretations.

Contextual Notes

Participants note that the mass of the rocket is constant but express confusion about its role in the calculations. There is also a mention of homework constraints that may affect the approach to the problem.

Jared
Messages
3
Reaction score
0

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.
 
Physics news on Phys.org
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?
 

Similar threads

Where in orbit should a rocket fire to escape with minimum ΔV
  • · Replies 17 ·
Replies
17
Views
3K
Velocity required to escape the solar system
  • · Replies 15 ·
Replies
15
Views
2K
Finding r of a Jovian-synchronous orbit and escape velocity
  • · Replies 7 ·
Replies
7
Views
2K
Potential Energy and raising a satellite from Earth into a Circular Orbit
  • · Replies 5 ·
Replies
5
Views
3K
Escape velocity of an iron asteroid
  • · Replies 5 ·
Replies
5
Views
2K
Intuition for why escape velocity doesn't depend on angle
  • · Replies 9 ·
Replies
9
Views
2K
Additional Velocity Required for a Satellite Already in Orbit to Escape
  • · Replies 4 ·
Replies
4
Views
2K
Escape Velocity from Earth-Moon System
  • · Replies 3 ·
Replies
3
Views
7K
Using Orbital Energy to Calculate Velocity
  • · Replies 3 ·
Replies
3
Views
2K
Escape Velocity of a Neutron Star: Relativistic Calculation
  • · Replies 1 ·
Replies
1
Views
2K