Re: OT: Fun for the math buffs

On Sep 30, 4:16 pm, <castlebravo...@xxxxxxx> wrote:
"John R." <jdr...@xxxxxxxxxxxxx> wrote in message

news:Xns9B28E07019671jdri63sbcglobalnte@xxxxxxxxxxxxxxxxx



Richard Jernigan <rnjerni...@xxxxxxxxx> wrote in news:c00cea5a-397e-
46ae-8a1d-2a9b45f69...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx:

On Sep 30, 11:27 am, dsi1 <d...@xxxxxxxxxxxxx> wrote:
Richard Jernigan wrote:
Suppose an object is 500 kilometers above the Earth's surface.
Assume
that the acceleration due to gravity is the same as it is at the
Earth's surface, 9.8 meters/sec^2. How far from the Earth is the
object 10 seconds later?

RNJ

499.02KM?

Is this a trick question? It sounds like a trick question. :-)

It depends on what you mean by "trick question". In a way it is, but
any true math buff would have answered, "The question as posed has no
answer".

What is left out is the velocity of the object. If the object were
initially at rest relative to the center of the Earth, then John
Nguyen's answer would be correct. If, on the other hand the object
were the rocket described here

http://www.spacex.com/updates.php

then 10 seconds after its perigee (closest approach to Earth) of 500
km, it would actually be further from the Earth's surface--headed for
apogee of 700 km--due to the velocity imparted by the rocket engines.
But the only significant force acting on it in orbit is gravity,
tugging it toward the center of the Earth. It keeps on in its repeated
elliptical path due to the momentum imparted by the rocket engines,
which were turned off yesterday. It repetitively rises and falls
relative to the Earth's surface, continuing to follow the same path,
while gravity, the only significant force acting on it always tugs it
earthward.

I say "significant force". Above 500 km there is sometimes a tiny
amount of air, especially during sunspot episodes. This may retard the
satellite a few thousandths of a second in its orbit. Eventually, over
a number of decades this can cause the orbit to decay to lower
altitudes, where there is enough air to slow it down to reentry
velocity over a few years' time.

The satellite with the tank of frozen hydrazine, that was shot down
over the Pacific earlier this year, was placed in a much lower orbit,
only a couple hundred kilometers. The plan was to boost it to a much
higher orbit, but the satellite malfunctioned. In the lower orbit,
comparable to the Space Shuttle's, the air slowed it nearly to reentry
velocity in a couple of years.

Any freshman physics or math student knows that to predict the course
of an object you must know not only its initial position and the
forces acting on it, you must know its initial velocity as well.

Augustine's questions are barely, if at all, beyond middle school
caliber. Any competent Arabic speaking mathematician of the 12th
century could have solved them.

Newton's solution of the orbital equation of motion was a great
breakthrough in the late 17th century, with immediate consequences for
philosophy and the world view of those who understood it. There has
been a significant amount of progress since then, especially in the
20th century with the development of relativity and quantum mechanics.
The vast majority of mankind remain unaware of these developments,
holding world views unchanged from Medieval times.

As you can see, I'm taking the day off after yesterday's mission.

RNJ

You could say what its change in velocity was, assuming it does not burn
up or hit a terminal velocity.

John

What about frontal area and co-efficient of friction, initial velocity,
direction of motion, gravitation at 500km, and mass? drag at 500km?

Bob

Bob

There is very little air at 500 km altitude, and the amount there
varies. There is a good deal less air at 700 km. The air is only
enough to retard the orbital period by a few thousandths of a second
per hundred revolutions. This translates into a few meters change in
the orbit, per hundred revolutions

RNJ.

RNJ
.

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