How Much Work Must Be Done for Earth to Escape the Sun?

[hsphysics2]

Homework Statement

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

Homework Equations

E= K + U_G where K= 1/2(mv²) and U_G=-(GmM)/r
W= E₂- E₁
F_c=ma_c

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.

 

[berkeman]

Homework Statement

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

Homework Equations

E= K + U_G where K= 1/2(mv²) and U_G=-(GmM)/r
W= E₂- E₁
F_c=ma_c

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...

 

[assassinsdoc]

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?

 

[berkeman]

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...

 

[Doc Al]

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

Looks good to me. So what's the initial energy? The final energy?

 

[BruceW]

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 :)

 

[hsphysics2]

W=E₂- E₁
W=0- 1/2(M_Ev₁²)- (GM_EM_S)/r₁

I don't know v₁ so how can I solve for work?

 

[gildomar]

The initial velocity can be found by setting the centripetal force equal to the gravitational force and solving for v^2.