-Z- (z@gundam.com)
Tue, 25 Jul 2000 21:49:52 -0700


> -----Original Message-----
> From: owner-gundam@1u.aeug.org [mailto:owner-gundam@1u.aeug.org]On
> Behalf Of Chris Beilby
> Sent: Monday, July 24, 2000 21:37
> To: gundam@aeug.org
> Subject: [gundam] Distances in the Earth Sphere
>
> I hope someone can help me with this one...
>
> I need to know the distances, in kilometers, between the various sides, the
> earth, and the moon. I'm planning to install spacecode on Gundam MUSH, and
> the distances are needed so that I can configure the code, set maximum
> speeds for ships, and set a distance scale into the game. Thanks in
> advance.

Distance, as the Borg might say, is irrelevant. Everything in orbit is
constantly moving and the distance varies from one second to the next. What's
constant is the orbital velocity and the change in velocity (delta-V) necessary
to get from Point A to Point B. You will always have to make this change and it
will always be the same change, so that's what separates one point in space from
another.

What you really want to know is how long it takes to travel from Point A to
Point B. There are myriad solutions to the orbital transfer problem, but we
generally take one or the other end of the spectrum: the minimum-energy (=
maximum time) doubly-tangent transfer orbit -- same thing we used to get to and
from the Moon, back when -- and the minimum-time (= maximum energy) ballistic
curve -- the trajectory one would expect from an ICBM.

As it happens, we've solved the entire set of minimum-energy orbits, which are
posted on my Gundam High Frontier site at:

http://www.dyarstraights.com/msgundam/frontier.html#Lagrange

You'll also find the distances here. In a nutshell, the Earth, Moon and L4
point form an equilateral triangle about 390,000 km (240,000 miles) on a side.
Ditto for the Earth, Moon and L5. L1 and L2 are about 56,000 km (35,000 miles)
this side and the other side of the Moon, respectively. L3 is directly opposite
the Moon, so the same distance from the Earth as the Moon, L4 and L5. L3, L4
and L5 form another equilateral triangle about 750,000 km (500,000 miles) on a
side. Bit, again, it's more important to know how long it takes than to know
how "far" it is.

-Z-

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