help - gravity problem

In sci.space.tech message 97af933c-beda-4dba-aa2e-81364d4202ef@e20g2000
vbc.googlegroups.com, Tue, 9 Jun 2009 06:09:45, dotcom
posted:

I quoted the problem verbatim from my daughters text book.

In that case, assuming that you actually understand and mean "verbatim",
move the daughter to a different school - one that uses a better grade
of textbook. What you gave cannot be verbatim from a well-written book.

To go further, we need the exact words, warts and all, of the book,
without any intermingled comment from yourself or your daughter. The
title, author, ISBN and page reference could also be useful; some here
may have access to the book and be able to see more context than it
would be proper to copy here.

Your daughter can copy the words, and you can certify it as a true copy.

See signature below.

= = =

I predict that I will again receive a false message from the moderation.

--
(c) John Stockton, Surrey, UK. Turnpike v6.05 MIME.
Web URL:http://www.merlyn.demon.co.uk/ - FAQish topics, acronyms, & links.
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Ken S. Tucker wrote:
It's ok, some specific info is lacking.
How does a disabled satellite retro fire?

Maybe it collides with an asteroid or an exhausted rocket stage. Then it
has 0 velocity and drops vertically to 800 km.

Bernhard

Dr J R Stockton wrote:
In sci.space.tech message 97af933c-beda-4dba-aa2e-81364d4202ef@e20g2000
vbc.googlegroups.com, Tue, 9 Jun 2009 06:09:45, dotcom
posted:

I quoted the problem verbatim from my daughters text book.

In that case, assuming that you actually understand and mean "verbatim",
move the daughter to a different school - one that uses a better grade
of textbook. What you gave cannot be verbatim from a well-written book.


It's not so bad. Although its stated initial speed corresponds to a
circular orbit at 2000km (apparently, I haven't checked), the question
doesn't say that the satellite is in such an orbit. It does say that it
falls to a height of 800km.

So the reasonable assumption is that it's in an orbit that allows it to
be at 2000km at one point in time, and 800km at another.

Sylvia.

Sylvia Else wrote:
Dr J R Stockton wrote:
In sci.space.tech message 97af933c-beda-4dba-aa2e-81364d4202ef@e20g2000
vbc.googlegroups.com, Tue, 9 Jun 2009 06:09:45, dotcom
posted:

I quoted the problem verbatim from my daughters text book.

In that case, assuming that you actually understand and mean "verbatim",
move the daughter to a different school - one that uses a better grade
of textbook. What you gave cannot be verbatim from a well-written book.


It's not so bad. Although its stated initial speed corresponds to a
circular orbit at 2000km (apparently, I haven't checked), the question
doesn't say that the satellite is in such an orbit. It does say that it
falls to a height of 800km.

So the reasonable assumption is that it's in an orbit that allows it to
be at 2000km at one point in time, and 800km at another.

That would be my guess, too; it sounds asking what the speed of the
satellite will be if it has a perigee of 800 km altitude and an apogee
of 2000 km altitude. It's a bit glib and not terribly clear, though. I
agree with the others that it's not a very useful question, especially
for high school students.

--
Erik Max Francis && && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
Most men do not mature, they simply grow taller.
-- Leo Rosten

Erik Max Francis wrote:
Sylvia Else wrote:
Dr J R Stockton wrote:
In sci.space.tech message 97af933c-beda-4dba-aa2e-81364d4202ef@e20g2000
vbc.googlegroups.com, Tue, 9 Jun 2009 06:09:45, dotcom
posted:

I quoted the problem verbatim from my daughters text book.

In that case, assuming that you actually understand and mean "verbatim",
move the daughter to a different school - one that uses a better grade
of textbook. What you gave cannot be verbatim from a well-written book.


It's not so bad. Although its stated initial speed corresponds to a
circular orbit at 2000km (apparently, I haven't checked), the question
doesn't say that the satellite is in such an orbit. It does say that
it falls to a height of 800km.

So the reasonable assumption is that it's in an orbit that allows it
to be at 2000km at one point in time, and 800km at another.

That would be my guess, too; it sounds asking what the speed of the
satellite will be if it has a perigee of 800 km altitude and an apogee
of 2000 km altitude. It's a bit glib and not terribly clear, though. I
agree with the others that it's not a very useful question, especially
for high school students.


It couldn't have an apogee at 2000km, because it's going at the wrong
speed. But the question doesn't require any assumptions about the actual
orbit.

I don't really see the objection to the question.

It requires the ability to calculate the potential energy of an object
in a gravitational field, an understanding of kinetic energy, and the
application of the law of conservation of energy.

Is this not highschool maths/physics?

Sylvia.

In article
,
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)

Presumably it doesn't have any propulsion systems so it is in free-fall.

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).

I haven't done the calculation, but assuming that you did it correctly:

If the orbital speed for a circular orbit is 6900 m/s at 2000 km
height, that does not mean that an object with that height and that
speed is in a circular orbit.

Suppose you climb a 2000 km tall ladder (from Antarctica so you can
ignore Earth's rotation and are initially motionless), and then fire a
rifle that has a muzzle speed of 6900 m/s. Every bullet you fire will
have a 6900 m/s speed at 2000 km height. If you fire it horizontally,
then you will have a circular orbit. If you fire it straight up then
it will have a long, skinny orbit that intersects Earth before it gets
all the way around. If you fire it straight down it will have the same
orbit, only it will complete even less of an orbit. If you fire it at
an angle, then it will have a perigee below 2000 km and a apogee above
that height. It will, of course, travel faster at perigee and slower
at apogee.

If the apogee is below 800 km, then you can complete the question. It
turns out to have the same answer for all orbits with an apogee below
800 km (including the shoot-straight-down case).

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


You can't take E = 1.9e10 J - 3970 m/s and add that to 6900 m/s to get
the new speed.

You have to take
Ekinetic_start = 5.7e10 J
+ Epotential_change = 1.9e10 J
= Ekinetic_end = 7.6e10 J
And 7.6e10 J - the 7900 m/s that's the textbook answer.

Basically, you have to add the energies, not the velocities.

Which means that you have to add the square of the velocity and the
square of the KE-equivalent velocity and take the square root of the
sum. (The phrase used is 'add in quadrature')


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?

Yes, the stated problem is a conservation of energy problem, and
solvable.

--
David M. Palmer (formerly @clark.net, @ematic.com)

Sylvia Else wrote:
Erik Max Francis wrote:
Sylvia Else wrote:
So the reasonable assumption is that it's in an orbit that allows it
to be at 2000km at one point in time, and 800km at another.

That would be my guess, too; it sounds asking what the speed of the
satellite will be if it has a perigee of 800 km altitude and an apogee
of 2000 km altitude. It's a bit glib and not terribly clear, though.
I agree with the others that it's not a very useful question,
especially for high school students.

It couldn't have an apogee at 2000km, because it's going at the wrong
speed.

That seems in direct contradiction to what you just said above

It starts with an altitude of 2000 km, is hit by something, and ends up
at 800 km altitude. There's nothing about it ending up in a 800 km
_circular_ orbit.

--
Erik Max Francis && && http://www.alcyone.com/max/
San Jose, CA, USA && 37 18 N 121 57 W && AIM/Y!M/Skype erikmaxfrancis
Only the ephemeral is of lasting value.
-- Ionesco

Erik Max Francis wrote:
Sylvia Else wrote:
Erik Max Francis wrote:
Sylvia Else wrote:
So the reasonable assumption is that it's in an orbit that allows it
to be at 2000km at one point in time, and 800km at another.

That would be my guess, too; it sounds asking what the speed of the
satellite will be if it has a perigee of 800 km altitude and an
apogee of 2000 km altitude. It's a bit glib and not terribly clear,
though. I agree with the others that it's not a very useful
question, especially for high school students.

It couldn't have an apogee at 2000km, because it's going at the wrong
speed.

That seems in direct contradiction to what you just said above

It starts with an altitude of 2000 km, is hit by something, and ends up
at 800 km altitude. There's nothing about it ending up in a 800 km
_circular_ orbit.


I haven't said it's hit by something. Indeed, if it is, then the
question is unanswerable.

My view is that it's in some orbit, being an orbit that rises above
2000km, and falls below 800km.

Sylvia.

Erik Max Francis wrote:
Sylvia Else wrote:
Erik Max Francis wrote:
Sylvia Else wrote:
So the reasonable assumption is that it's in an orbit that allows it
to be at 2000km at one point in time, and 800km at another.

That would be my guess, too; it sounds asking what the speed of the
satellite will be if it has a perigee of 800 km altitude and an
apogee of 2000 km altitude. It's a bit glib and not terribly clear,
though. I agree with the others that it's not a very useful
question, especially for high school students.

It couldn't have an apogee at 2000km, because it's going at the wrong
speed.

That seems in direct contradiction to what you just said above

It starts with an altitude of 2000 km, is hit by something, and ends up
at 800 km altitude. There's nothing about it ending up in a 800 km
_circular_ orbit.


Also, look at David M Palmers response to the OP.

Sylvia.

In article
,
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?

Sadly I dont have the maths to work this out, but since this is only
high school work, perhaps you just need to calculate the speed at 800km

You guys are very cluey, but you wouldn't expect a school student to do
all other stuff you are considering



Perhaps someone could just calculate the speed required to keep it in
orbit at 800km

David who is trying to learn maths, but...