What is the change in energy required for the Earth to escape the Sun's orbit?

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Homework Help Overview

The discussion revolves around calculating the energy and change in orbital speed required for the Earth to escape from its orbit around the Sun. Participants are exploring concepts related to gravitational forces and energy calculations in an astrophysical context.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to determine the total energy required for the Earth to escape the Sun's gravitational influence, questioning how to define final energy in this context. There are discussions about the distance at which the Earth would be considered to have escaped and the implications of gravitational potential energy at that distance.

Discussion Status

The conversation is ongoing, with participants expressing confusion about the calculations involved and the definitions of energy states. Some have offered insights into the nature of gravitational forces and potential energy, while others are still seeking clarity on how to approach the problem effectively.

Contextual Notes

There is a mention of an impending test, indicating time constraints that may affect the depth of exploration in the discussion. Participants are also grappling with the conceptual understanding of energy at infinity and the implications of gravitational potential energy in this scenario.

OshKosh
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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.
 
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energy required will be Final E - total E ... what you think will be final energy
 
Yeah but I don't get how to calculate final energy if the Earth is leaving the sun's orbit.
 
What will be the distance b/w Earth and sun when Earth has escaped?
 
I guess greater than 150 000 000 km, but how would I use that?
 
escaping means that you are out of reach of gravitational forces of sun.

GMm/r^2 is 0 for what value of r ?
 
So I would put the distance between the Earth and sun's orbit for r? Then just sub in the rest of the values?
 
No ...
my question is simple ... 1/r is 0 for what value of r ??
 
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?
 
  • #10
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?
 
  • #11
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.
 
  • #12
only when you are talking about real numbers ...

lets leave this debate for now and concentrate on the question
 
  • #13
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?
 
  • #14
Yes, surprised!

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

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