On Jun 9, 8:45 am, Dr J R Stockton
wrote:
In sci.space.tech message be0aecfa-e255-449f-8846-1b5c2d10216f@n4g2000v
ba.googlegroups.com, Sun, 7 Jun 2009 21:56:02, dotcom
posted:





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 o
f
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?

No, because we don't know why it fell.

Three extreme cases can be modelled as

(1) Gentle Atmospheric drag; its new speed is that for the lower
circular orbit.

(2) It suddenly lost some speed, so that it is in an elliptical orbit
apogee 2000 km perigee 800 km.

(3) It suddenly lost all speed, is coming straight down, and is passing
800 km now.

Also,

(A) It bounced off something elastically, so that its elliptical orbit
has perigee 800 km and speed crossing 200 km is circular speed for that
height.

(B) It bounced off something elastically, is coming straight down, and
is passing 800 km now.

Probably one of the first two is intended; the first for a mid-range
student or the second for an advanced one.

The first thing is to get the exact question as asked. I was once
requested by a young teenager to give the formula for a tree. First
question to ask : is this chemistry/biology, is it engineering, is it
topology (carbohydrate; Euler's Strut, Euler's polyhedrons). She seeme
d
satisfied to count branches, leaves, and vertices.

== == =
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system mailing me again; but it did not have that effect. It has an
obvious design fault.

--
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Thanks Dr John
I quoted the problem verbatim from my daughters text book. you post
some interesting scenarios, here are my thoughts on them
1. re atmospheric drag. My understanding is that atmospheric drag
would be negligible at 2000km .
2. how could it lose some speed?( lets say it had a retro rocket
firing then in that case you wouldnt be able to solve the
problem anyway because there is an unknown energy source being
applied. the way the problem is posed you
could not possibly get an answer unless you assume only the force
of gravity is involved.
3. If it suddenly lost all speed and was coming straight down then
again it would involve another force other than gravity.
so not solvable
Terry