# Calculating Escape Velocity

1. Apr 20, 2009

### Stratosphere

How do you Calculating the escape velocity? I googled it but they give bad instructions on how to do it. What is the formula?

Last edited: Apr 20, 2009
2. Apr 20, 2009

### Stratosphere

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 dont get the right answer.

Last edited: Apr 20, 2009
3. Apr 20, 2009

### mgb_phys

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. Apr 20, 2009

### Stratosphere

I set KE=GPE i get a velocity of 465,561 for a 10kg object. This doesnt seem right.

5. Apr 20, 2009

### Nabeshin

Well escape velocity is a function of radius so this question, as you stated, makes no sense...

6. Apr 20, 2009

### Janus

Staff Emeritus
What formula are you using?

7. Apr 20, 2009

### Stratosphere

V$$^{2}$$=$$\frac{2GM}{R}$$ to find the escape velocity of the earth and i get, 465561.808.

8. Apr 20, 2009

### sylas

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.

Last edited: Apr 20, 2009
9. Apr 20, 2009

### Janus

Staff Emeritus
Okay, from this answer, I'd say that you are using kilometers instead of meters for the radius of the Earth.

10. Apr 20, 2009

### mgb_phys

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)