Two black holes moving in a circular orbit around a point

[slogals]

Homework Statement

Two black holes move in a circular orbit around a point, O. The two black holes have the same mass, equal to 10 solar masses = 1.99⋅10^31 kg. The radius of the circular path is 1.00⋅10^6 m.

a)Find the gravitational force that acts on one black hole from the other.

Point P is 3.00⋅10^6 m from O. At some point the two black holes are positioned so that we can draw a straight line through the black holes, point O and point P.

b)Find the gravitational field strength at point P.

At one point in time, the orbital speed of each of the black holes is 1.82⋅10^7 m/s.
c) Calculate the mechanical energy of the black holes at this time.

One second later, the distance between the black holes has decreased by 0.05⋅10^6 m. At the same time, the orbital speed has increased from 1.82⋅10^7 m/s to 1.88⋅10^7 m/s for both. When the two black holes rotate around each other, they create gravitational waves. This results in the system losing mechanical energy.

d) How much energy has been converted into gravitational waves during this second?

Relevant Equations

F = Gm1m2/r
K = ½m2v2
U=- GMm / r
E = K + U

I tried solving it and i was able to do a) and b)

here is what i did on c), but its not correct according to the solution

 

[kuruman]

It's not correct because there are two black holes with speed v. Your kinetic energy term 0.5*m*v^2 is that of a single black hole.

 

[slogals]

It's not correct because there are two black holes with speed v. Your kinetic energy term 0.5*m*v^2 is that of a single black hole.

Hmm, but what is the radius then?

 

[slogals]

It's not correct because there are two black holes with speed v. Your kinetic energy term 0.5*m*v^2 is that of a single black hole.

So i should just muliply it by 2?

 

[kuruman]

So i should just muliply it by 2?

Are you asking me or are you telling me? What do you think?

 

[slogals]

Are you asking me or are you telling me? What do you think?

Im asking you, cus the anwser is still wrong

 

[kuruman]

If you add two quantities that are equal, you should get twice the amount of one. The problem is not with the kinetic energy. Check your potential energy. How did you get U = -(G(v^2*r)/G*m)/(r)? I would recommend simplifying the expression before putting in the numbers.