I thought I understood basic gravity problems but the following high
school physics problem from my daughter has me stumped ( I think)
Q. a disabled ( meaning of disable not defined) satellite of mass
2400kg is in orbit at a ht of 2000 km above the earth at a speed of
6900 m/s. ( my calc show that is exaclty the speed required for a
circular orbit at that ht). it then says the satelite falls to a ht
of 800 km calculate what the new speed at the lower ht..
well I simply calculated the gain in potential energy ( PE = delta
GMm/r) and equated this to the gain in kinetic energy ( =0.5 mv^2)
as the satellite must speed up. and added this to the original speed
of 6900 m/s to get 10870 m/s , but I am not sure that this correct.
it certainly doesnt give me the answer in the school text book of 7900
m/s

( I used G=6.67E-11, M =5.98E24 kg and r= 6.38E6 m.
using this the loss in potential energy = 1.9E10 J

I suspect I am going wrong somewhere in not accounting for the fact
velocity is a vector quantitiy. Surely it must depend on the direction
the satellite is heading initally. is this really a solvable problem?