-Z- (Z@Gundam.Com)
Sun, 10 Oct 1999 17:56:47 -0700


At 23:15 10/10/1999 +0000, you wrote:
>>Quick science question...
>>
>>If the LaGrange points L3, L4, L5 are at an equal distance from
>>the Earth as the moon is from Earth, they share its elipse round
>>the Earth. Correct, or am I missing something?

What you're missing is the key fact that the colonies don't orbit the Earth
AT the Lagrange point, but rather orbit the Lagrange point at a mean
distance of about 10,000 kilometers. The Lagrange point isn't a location,
it's a locus of equilibrium between the gravitational fields of the Earth
and the Moon. This locus shifts, but L4 and L5 are always the third apex
of an eqilateral triangle, the other apexes of which are the centers of
mass of the Earth and Moon. L1 and L2 are at the points where the
Earnt-Moon gravity cancel and synchronize, while L3 is at a point
diametrically opposite the Moon's center of mass. The actual distances
vary with the distance between the centers of mass of Earth and Moon.

>>Then if that was correct, L3 which is on the opposite side of Earth
>>from the Moon would be at its closest to the Earth, when the Moon
>>is at its furthest, I.E. a Full Moon. Likewise L4, and L5 would orbit
>>just a little closer/further than the moon respectively, depending on
>>which end of the Elipse they are in at the time. Correct?

Again, all five of the Lagrange points vary as the Earth and Moon approach
and recede from one another throughout the monthly transit. And the
colonies, in orbit about the Lagrange point, follow their own patterns of
apogee, perigee and conjunction, in cycles driven by the gravitation forces
of Earth and Moon.

>>I'm trying to come up with Adjusted flight times for the Earth to the
>>colonies, there are only 30 distances, and they are symmetrical, so
>>there would only really be 15. But depending on what time you leave
>>the distance between the Earth any your destination can vary up to
>>37 thousand kilometers, adding hours to the trip, and probably heavy
>>fuel costs.

But the distance is ALWAYS changing and you don't aim for where an object
IS, but where it will be when you get there.

Part of your confusion is that you are thinking linearly and space travel
is a non-linear milieu. You don't travel in straight lines, but in arcs
whose curve is determined by your acceleration, mass and those two
ever-present gravity fields of Earth and Moon. (Luna-2, the former
asteroid 3Juno, is too small to be significant and the colonies are orders
of magnitude smaller still.)

More importantly, distance is not a really a factor here. What's important
is not how far away your destination is, but how much change in velocity
(delta V) is required to move from your present orbit to that of your
destination -- in other words, how much mass and energy you must expend to
match orbits.

If we'd been going to and from the Moon for the last 30 years, instead of
to and from Near Earth Orbit, you might already be thinking in these terms.
 Most of the fuel and energy expended in the Moon flights was expended in
getting out of the Earth's gravity well and into Near Earth Orbit. Once
you've done that, you're halfway to anywhere in the Solar System. You need
only expend the mass and energy to change velocity (in the correct vector,
of course) to match orbits with your destination. That and spend the time
it takes to transit along the arc connecting the two orbits, which is NOT
the straightline distance between the two points along those orbits.

>>I'm trying to peice together a calendar of events during the one year
>>war for a 0079 Gundam game, and flight times will be important.
>-Z-'s High Frontier website should answer all your questions, Paul. This is
>the source I use for Gundam MUSH.
>
>http://www.halcyon.com/dyar/msgundam/frontier.html

Yes, it's all worked out for you in a neat little table:

http://www.halcyon.com/dyar/msgundam/frontier.html#Lagrange

Bear in mind that "Moon" and "Earth" here refer to low orbit around those
bodies, not the surface. It'll take another hour or so to travel to or
from the Earth's surface from Earth orbit and about 45 minutes to travel to
or from the Moon's surface from lunar orbit.

You'll also find my observations regarding weather in the colonies at:

http://www.halcyon.com/dyar/msgundam/frontier.html#Weather

-Z-

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