(Gravitational) Binding Energy

In summary: Then use that in your expression for the initial energy.In summary, to determine the work needed for the Earth to escape the Sun, you can use the equations E= K + UG, W= E2- E1, and Fc=mac, where K is the kinetic energy, UG is the gravitational potential energy, W is work, Fc is the centripetal force, and m, v, G, M, and r represent the mass, velocity, gravitational constant, mass of the Sun, and distance between the Earth and the Sun, respectively. By setting the centripetal force equal to the gravitational force and solving for v^2, you can find the initial velocity. This can then be used in
  • #1
hsphysics2
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Homework Statement


How much work must be done to allow the Earth to escape the Sun?


Homework Equations


E= K + UG where K= 1/2(mv2) and UG=-(GmM)/r
W= E2- E1
Fc=mac

The Attempt at a Solution


I have no idea where to start this, I missed the class where they took this up and I want to be at least familiar with it for the test.
 
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  • #2
hsphysics2 said:

Homework Statement


How much work must be done to allow the Earth to escape the Sun?


Homework Equations


E= K + UG where K= 1/2(mv2) and UG=-(GmM)/r
W= E2- E1
Fc=mac

The Attempt at a Solution


I have no idea where to start this, I missed the class where they took this up and I want to be at least familiar with it for the test.

What does this question have to do with Binding Energy?

One way to solve it is to remember that Work = Force * Distance. What is the equation for gravitational force as a function of distance? Try integrating that from the orbit of Earth out to infinity...
 
  • #3
tell me if I'm wrong, but isn't binding energy defined as the amount of energy needed to keep a particular amount of matter together? so, to break up that matter, we need an equivalent amount of energy.
The question is to move the Earth away from the sun. So, in a way, won't binding energy be involved?
 
  • #4
assassinsdoc said:
tell me if I'm wrong, but isn't binding energy defined as the amount of energy needed to keep a particular amount of matter together? so, to break up that matter, we need an equivalent amount of energy.
The question is to move the Earth away from the sun. So, in a way, won't binding energy be involved?

Interesting. I did just now find "Gravitational Binding Energy" at wikipedia:

http://en.wikipedia.org/wiki/Gravitational_binding_energy

I'm more familiar with the term Binding Energy referring to Nuclear Binding Energy.

I'll change the thread title to avoid any more confusion... :smile:
 
  • #5
hsphysics2 said:
E= K + UG where K= 1/2(mv2) and UG=-(GmM)/r
W= E2- E1
Looks good to me. So what's the initial energy? The final energy?
 
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  • #6
the problem is simpler if you just think about energy. What is the initial energy, and what is the final energy when the Earth has escaped the Sun? (I'm guessing you are allowed to make certain assumptions about the Kinetic energy).

edit: Doc Al beat me to it :)
 
  • #7
W=E2- E1
W=0- 1/2(MEv12)- (GMEMS)/r1

I don't know v1 so how can I solve for work?
 
  • #8
The initial velocity can be found by setting the centripetal force equal to the gravitational force and solving for v^2.
 
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1. What is (gravitational) binding energy?

(Gravitational) binding energy refers to the minimum amount of energy required to completely separate a system of objects held together by gravity. It is the result of the attractive force of gravity between the objects and can be calculated using the mass, distance, and gravitational constant of the system.

2. How is gravitational binding energy related to the formation of celestial bodies?

Gravitational binding energy plays a crucial role in the formation of celestial bodies such as planets, stars, and galaxies. As particles and matter come together due to the force of gravity, their potential energy is converted into kinetic energy, causing the particles to collide and merge. This process continues until the objects have enough binding energy to maintain their shape and resist further collapse.

3. Can gravitational binding energy be negative?

No, gravitational binding energy cannot be negative as it represents the minimum amount of energy needed to overcome the force of gravity holding a system together. If the energy is negative, it means that the system is already in a state of collapse and does not require any additional energy to overcome gravity.

4. How does the distance between objects affect gravitational binding energy?

The distance between objects has a significant impact on gravitational binding energy. As the distance between objects increases, the gravitational force decreases, resulting in a decrease in the binding energy. Similarly, as the distance decreases, the force of gravity increases, leading to a higher binding energy.

5. Can gravitational binding energy be converted into other forms of energy?

Yes, gravitational binding energy can be converted into other forms of energy, such as kinetic energy, thermal energy, and electromagnetic radiation. This conversion can occur when the objects within a system move closer together or collide, releasing energy in the form of heat or light. This process is responsible for the energy output of celestial bodies, such as stars and black holes.

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