On Jun 8, 11:56 am, dotcom wrote:
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?


OK , I think I have the answer now. it was to do with the folly of
simply adding velocities. if we convert teh original speed to kinetic
energy , add the kinetic energy that is gained by the loss of
potential energy as the ht reduced from 2000 to 800 km then convert
the total kinetic energy back to speed we get the "right?" answer. I
guess what the question meant was that even though the satellite had
the correct speed for a circular orbit at 2000km , if that speed was
not in the right direction , ie perpendicular to a line towards the
center of the earth, then in fact it would be an elliptical orbit that
may come down to 800km ? I think!