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

In summary, the homework statement is asking for the energy and change in orbital speed required for the Earth to escape from its orbit around the sun. The attempt at a solution states that the potential energy of Earth at r=infinity would be just close to 0.
  • #1
OshKosh
7
0

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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  • #2
energy required will be Final E - total E ... what you think will be final energy
 
  • #3
Yeah but I don't get how to calculate final energy if the Earth is leaving the sun's orbit.
 
  • #4
What will be the distance b/w Earth and sun when Earth has escaped?
 
  • #5
I guess greater than 150 000 000 km, but how would I use that?
 
  • #6
escaping means that you are out of reach of gravitational forces of sun.

GMm/r^2 is 0 for what value of r ?
 
  • #7
So I would put the distance between the Earth and sun's orbit for r? Then just sub in the rest of the values?
 
  • #8
No ...
my question is simple ... 1/r is 0 for what value of r ??
 
  • #9
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?
 

1. What is the difference between momentum and energy?

Momentum is a measure of an object's motion, determined by its mass and velocity. Energy, on the other hand, is the ability of an object to do work or cause change. While both are related to motion, they are fundamentally different concepts.

2. How is momentum conserved in a closed system?

In a closed system, the total momentum remains constant. This means that the momentum before an event or interaction is equal to the momentum after, even if there are internal changes or collisions within the system.

3. Can an object have momentum without energy?

Yes, an object can have momentum without energy. This is seen in the case of an object at rest, where it has no kinetic energy but still has a non-zero mass and therefore has momentum.

4. How is kinetic energy related to momentum?

Kinetic energy is directly proportional to an object's momentum. This means that as an object's momentum increases, so does its kinetic energy. This relationship is described by the formula KE = 1/2 * mv^2, where m is the mass and v is the velocity of the object.

5. Can momentum and energy be transferred between different forms?

Yes, momentum and energy can be transferred between different forms. For example, when a moving object collides with another object, momentum can be transferred and cause the second object to move. Similarly, energy can be transferred between forms, such as kinetic energy being converted into potential energy when an object is lifted against gravity.

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