We watch two identical astronomical bodies A and B, each of mass m, fall toward each other from rest because of the gravitational force on each from the other. Their initial center-to-center separation is Ri. Assume that we are in an inertial reference frame that is stationary with respect to the center of mass of this twobody system. Use the principle of conservation of mechanical energy (Kf + Uf = Ki + Ui) to find the following when the centerto- center separation is 0.5Ri : (a) the total kinetic energy of the system, (b) the kinetic energy of each body, (c) the speed of each body relative to us, and (d) the speed of body B relative to body A. Next assume that we are in a reference frame attached to body A (we ride on the body). Now we see body B fall from rest toward us. From this reference frame, again use Kf + Uf = Ki + Ui to find the following when the center-to-center separation is 0.5Ri : (e) the kinetic energy of body B and (f) the speed of body B relative to body A. (g) Why are the answers to (d) and (f) different? Which answer is correct?
We watch two identical astronomical bodies A and B, each of
mass m, fall toward each other from rest because of the gravitational
force on each from the other. Their initial center-to-center
separation is Ri. Assume that we are in an inertial reference frame
that is stationary with respect to the center of mass of this twobody
system. Use the principle of conservation of mechanical
energy (Kf + Uf = Ki + Ui) to find the following when the centerto-
center separation is 0.5Ri : (a) the total kinetic energy of the system,
(b) the kinetic energy of each body, (c) the speed of each body
relative to us, and (d) the speed of body B relative to body A.
Next assume that we are in a reference frame attached to
body A (we ride on the body). Now we see body B fall from rest toward
us. From this reference frame, again use Kf + Uf = Ki + Ui to
find the following when the center-to-center separation is 0.5Ri : (e)
the kinetic energy of body B and (f) the speed of body B relative
to body A. (g) Why are the answers to (d) and (f) different? Which
answer is correct?
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