Re: Cavorite Travel Times

On Mon, 1 Dec 2003 23:13:54 -0500, "Charles Talleyrand"
<[EMAIL PROTECTED]> wrote:

>Cavorite is a useful material.  It blocks the force of gravity and can be used to
>make a space ship in the following way:
>
>Make a large sphere with Cavorite shutters.
>Close the shutters on the Earth's side blocking the Earth's gravity
>Open the shutters on the Moon's side, letting the Moon pull us towards it.
>
>
>Has anyone ever calculated the travel times this method requires?  It would
>seem important to include a decelloration phase some time before
>impact.  I would also like to go to other places beyond the moon.
>
>I just want to be sure this is where my investment dollar should go.
>
>-Thanks
>-C.Talleyrand

Well, essentially you'll be in an orbit around the moon when you
activate the cavorite.

We know that the moon orbits the Earth in about a month.

We also know that the orbital period follows the following
relationship:

T^2 = (2*pi)^2 a^3 / GM

where a is radius of the orbit (for circular orbits), or the
semi-major axis (for elliptical orbits).  (Keppler's law, basically,
though I refreshed my memory from my physics textbook).

Therefore T is inversely proportional to the square root of the mass
ratio.

The earth-moon mass ratio is .0123 (from the NASA planetary data fact
sheet), so the period of an orbit is about 9 times larger.

This means that you'd have a 9 month period for a complete orbit.  The
time from closest to furthest approach will be 1/4 an orbital period,
or about 2.25 months.

Unfortunately, your velocity relative to the moon will be the negative
of the moon's velocity relative to the earth.

The moon is moving at the right velocity to orbit a more massive body.
Thus your velocity will be too high for a circular orbit around the
moon.  I may be visualizing this wrong, but I think that you'll start
out as close to the moon as you ever get, and as your orbit proceeds
you'll get further away.

So you'd better have a third body (probably the sun) in the right
position to kill off some of your excess lunar orbital velocity, and
use its gravity to do some braking.