The astronaut orbiting the Earth in Figure P4.32 is preparing to dock with a Westar VI satellite. The satellite is in a circular orbit 700 km above the Earth's surface, where the free-fall acceleration is 8.12 m/s2. Take the radius of the Earth as 6400 km.
2. Relevant equations
I am not sure if this is relevant, but the distance from the the satellite to the center of the earth is 6400km+700km=7100km.
Next I try to find the time it takes the satellite to reach the center:
First I find velocity from the radial acceleration equation. I set a=8.12m/s^2 (not sure if this is right)
Next I solve for velocity=sqrt(a*r) where r=6400
Next I use the velocity to calculate the time it takes for the object to reach the center using the equation T=2(pi)radius/velocity
=92.98 min (I already converted it back to minutes from seconds)
I am not sure what I am doing wrong.