Gravitational attraction question

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SUMMARY

The discussion focuses on calculating the velocity of two point masses, each weighing 400 kg, as they move from a distance of 10^14 m to 1000 m apart due to their mutual gravitational attraction. The gravitational force is calculated using Newton's law of universal gravitation, F = G(m1*m2)/r^2. The user integrated this equation to find the work done, equating it to the change in kinetic energy (ΔKE), ultimately determining the velocity of each mass to be approximately 7.3226 x 10^-6 m/s. The user seeks confirmation on whether to use a single mass or the combined mass in their calculations.

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Homework Statement


two point masses (400 kg) are 10^14 m apart in deep space under no gravitational attraction besides each others. find their velocity when they are 1000 m apart.

Homework Equations


-G (m_1m_2)/r^2=F

The Attempt at a Solution


I integrated the equation above plugging in the 400 kg for m1 and m2 from 10^14 to 1000. I believe this gave me the work required to bring one of them to that distance so i set it equal to ΔKE. This became (1/2)mv_f^2 because they start from rest. Now my question is whether that mass is 400 kg or 800 kg or if I'm on the right track. I just put one of the mass in that then solved and got 7.3226*10^-6. And I think that is the velocity of each of the masses. Anybody care to disagree? Thank you.
 
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As they come together, their mutual gravitational PE is transformed into the kinetic energy of both masses.
 

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