# Momentum and Energy Problem

OshKosh

## Homework Statement

Determine the energy and change in orbital speed required for the Earth to escape from its orbit around the Sun.

## Homework Equations

I guess:
Change In E = E total of o - E total of s (Egs)
E total of orbit = (0.5)Eg of oribit

## The Attempt at a Solution

Don't really know how to begin with this one considering it's not something like a satellite leaving Earth's orbit but rather it's the Earth leaving the sun's orbit.

cupid.callin
energy required will be Final E - total E ... what you think will be final energy

OshKosh
Yeah but I don't get how to calculate final energy if the Earth is leaving the sun's orbit.

cupid.callin
What will be the distance b/w earth and sun when earth has escaped?

OshKosh
I guess greater than 150 000 000 km, but how would I use that?

cupid.callin
escaping means that you are out of reach of gravitational forces of sun.

GMm/r^2 is 0 for what value of r ???

OshKosh
So I would put the distance between the earth and sun's orbit for r? Then just sub in the rest of the values?

cupid.callin
No ...
my question is simple .... 1/r is 0 for what value of r ??

OshKosh
Maybe it's so simple that it's under my nose but isn't that not possible for it to be 0? Can't it only approach 0?

cupid.callin
that very large value is called to be infinity for which 1/r is 0

not what will be the potential energy of earth at r=infinity?

OshKosh
Wouldn't it be just close to 0? (In a negative number)

I also have a test on this tomorrow so if you're going to take a really long time to explain this might as well tell me now.

cupid.callin
only when you are talking about real numbers ...

lets leave this debate for now and concentrate on the question

OshKosh
Well you're the one who brought it up...

After a half of hour of explaining something that doesn't seem to be that useful for the actual problem, I still don't get how to do the problem. Surprise?

cupid.callin
Yes, surprised!!!

you have E(initial) and E(final) is 0
can you find change in E?