Two body escape velocity

After calculating the gravitational PE using :
PE = ( G * m1 * m2 ) / d

Then i split the result into KE between the two bodies according to the ratio of the masses, then calculated the individual velocities from those (based on KE = ½ * m * v ²)

How did you split the KE between the two bodies?

According to my calculation, using your method, v1=v2 regardless of the mass ratio. But I may be doing something wrong.

Keep in mind that according to the conservation of momentum and the third law of motion:
m1v1 = m2v2
must be true.

How did you split the KE between the two bodies?

Assuming a ratio of 2 to 1, I did it like this: x + 2x = KE
So if KE=25, then KE1=8.333 and KE2=16.666.

I suck at math, so I have little confidence in my analogy. :)

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Why don't you use the conservation of momentum result?

If the mass ratio is 1:2, the KE ratio will be 1:4.[/STRIKE]

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Why don't you use the conservation of momentum result?

If the mass ratio is 1:2, the KE ratio will be 1:4.
Yes, you're right. I'll try to fix that. Thanks.

Yes, you're right. I'll try to fix that. Thanks.

No, I was wrong. Sorry for that. The square of the speeds are in the ratio 1:4 but not the KE. You were right the first time.

No, I was wrong. Sorry for that. The square of the speeds are in the ratio 1:4 but not the KE. You were right the first time.

Ok, thanks. I'll go back and edit my post again. I've already reported this thread, so they may delete some of it.

The split of the KE between the two bodies, is based on the mass ratio :
So :
KE (m1) = ( m2 / ( m1 + m2 ) ) * PE
KE (m2) = ( m1 / ( m1 + m2 ) ) * PE

Then the individual velocities from :
v ( m1 ) = sqrt ( ( KE ( m1 ) ) / ( ½ * m1 ) )
v ( m2 ) = sqrt ( ( KE ( m2 ) ) / ( ½ * m1 ) )

Ive ran this through as an example and the equal momentum is preserved.

Basically, in asking if the total KE of both objects is equal to the original PE, this inquiry is based on the widely used statement that the mass of m2 is irrelavent in the caculation of escape velocity.

ehild
Homework Helper
Well, the gravitational potential energy is negative if it is zero at infinite separation, how do you split it into kinetic energy of two bodies?

ehild

Ive ran this through as an example and the equal momentum is preserved.

Yes, it is. I had the masses reversed in my original calculation.

mfb
Mentor
The split of the KE between the two bodies, is based on the mass ratio :
So :
KE (m1) = ( m2 / ( m1 + m2 ) ) * PE
KE (m2) = ( m1 / ( m1 + m2 ) ) * PE

Then the individual velocities from :
v ( m1 ) = sqrt ( ( KE ( m1 ) ) / ( ½ * m1 ) )
v ( m2 ) = sqrt ( ( KE ( m2 ) ) / ( ½ * m1 ) )

Ive ran this through as an example and the equal momentum is preserved.