Calculating Escape Velocity

  • #1
Stratosphere
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How do you Calculating the escape velocity? I googled it but they give bad instructions on how to do it. What is the formula?
 
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  • #2
Stratosphere
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Every time I try using the formula i have i have to solve for V^2 and I get it to equal 35
3541. Is this right? I plug in the numbers like it says it I still don't get the right answer.
 
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  • #3
mgb_phys
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Gravitational potential energy is = GMm/r (where M is the mass of the earth)
Kinetic energy = 1/2 m v^2

You start at r=radius of Earth and end up at r=infinity.
A bit of rearranging and a subtraction and it shoudl be easy
 
  • #4
Stratosphere
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I set KE=GPE i get a velocity of 465,561 for a 10kg object. This doesn't seem right.
 
  • #5
Nabeshin
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I set KE=GPE i get a velocity of 465,561 for a 10kg object. This doesn't seem right.

Well escape velocity is a function of radius so this question, as you stated, makes no sense...
 
  • #6
Janus
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Every time I try using the formula i have i have to solve for V^2 and I get it to equal 35
3541. Is this right? I plug in the numbers like it says it I still don't get the right answer.

What formula are you using?
 
  • #7
Stratosphere
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What formula are you using?


V[tex]^{2}[/tex]=[tex]\frac{2GM}{R}[/tex] to find the escape velocity of the Earth and i get, 465561.808.
 
  • #8
sylas
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[itex]V^{2}=\frac{2GM}{R}[/itex] to find the escape velocity of the Earth and i get, 465561.808.

You've got "tex" tags inside your formula. I've tried to fix tags in the quoted extract; but it is still not displaying for some reason. But the forumla looks fine to me. Just make sure all your variables are in consistent units. You give a number, but no units. Are you meaning km/hr, or m/s, or something else?

The gravitational constant G is usually given in SI units. If you do everything in meters and seconds and kilograms, it will work.
 
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  • #9
Janus
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Every time I try using the formula i have i have to solve for V^2 and I get it to equal 35
3541. Is this right? I plug in the numbers like it says it I still don't get the right answer.

Okay, from this answer, I'd say that you are using kilometers instead of meters for the radius of the Earth.
 
  • #10
mgb_phys
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Why would the mass of the object matter ?

GM for the Earth is almost exactly 400,000 km^3/s^2 (worth remembering)
The radius of the Earth is around 6400km

so v^2 = 2GM/r = 2*400,000/6400 = 225km^2/s^2
v = 11.2km/s (roughly)

edit - sorry i posted this straight after you replied, but it didn't show up (got a database error message)
 

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