# Gravitational Potential and Total Energy

cde42003
Two stars with the mass and radius of the sun are separated by distance 10*r_sun, measured between their centers. A 10,000 kg space capsule moves along a line between the stars.

Suppose the space capsule is at rest 1.0 m closer to one star than the other. What will be the speed of the space capsule when it meets its ultimate fate?

Can anyone help with this problem? I thought that you need to to use the energy equation K1+U1=K2+U2 but can seem to get the correct answer.

My work
let mass capsule= m_c, mass stars= m

.5*m_c*0^2 - 2((G*m*m_c)/(5*r_sun)) = .5*m_c*v^2 - ((G*m_c*m)/(r_sun)) - ((G*m_c*m)/(9*r_sun))

Let me know what I did wrong. Thanks

## Answers and Replies

Homework Helper
Gold Member
You could simple calculate the work done by the gravitational force of each stars in the capsule going from 0 to 4R (i.e. when the capsule meets the surface of the star). Add those (actually they will substract). This is the change in kinetic energy of the capsule.

cde42003
quasar987, I am not following you. Can you explain your method in more detail?

Any other options out there?

Homework Helper
Your equation looks right, make sure you did the math correctly.

shyboy
the change in the potential energy due to interaction with the first star

U1=-GMm(1/R-1/5R)

the change in the potential energy due to ineraction with the second satar
U2=-GMm(1/9R-1/5R)

the total change in the potential energy u=U1+U2 is equal kynetic energy of the capsule

P.S. BTW, the answer does not depend on the capsule's mass

Last edited:
cde42003
Thanks to everyone. I got the answer.

Staff Emeritus