Two hypothetical planets of masses \( m_{1} \) and \( m_{2} \) are at rest when they are infinit...
0Two hypothetical planets of masses \( m_{1} \) and \( m_{2} \) are at rest when they are infinite distance apart. Because of the gravitational force, they move toward each other along the line joining their centers. What is their speed when their separation is \( d \) ?
(Speed of \( m_{1} \) is \( v_{1} \) and that of \( m_{2} \) is \( v_{2} \).)
(A) \( v_{1}=v_{2} \)
(B) \( v_{1}=m_{2} \sqrt{\frac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{1} \sqrt{\frac{2 G}{d\left(m_{1}+m_{2}\right)}} \)
(C) \( v_{1}=m_{1} \sqrt{\frac{2 G}{d\left(m_{1}+m_{2}\right)}} ; v_{2}=m_{2} \sqrt{\frac{2 G}{d\left(m_{1}+m_{2}\right)}} \)
(D) \( v_{1}=m_{2} \sqrt{\left.\frac{2 G}{m_{1}}\right)} ; v_{2}=m_{1} \sqrt{\frac{2 G}{\left.m_{1}\right)}} \)
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