Posted by: movieotaku | April 2, 2007

## Gravity of Small Bodies

Christian Mueller wrote in (back in Feb 2003 — yes, I’m slowly getting caught up on my e-mail ):

I recently saw the first season of the new Star Trek Show with Capt. Archer. (this show is not translated into German yet and therefore not aired over here till now)Maybe someone else mentioned this. If yes I haven’t found it on your pages yet.

In one of the very first episodes (forgot which one) the Enterprise approaches a comet and they decide to land an away team on it to take probes. They mention that the comets diameter is some 80 Kilometers.

As the landing party later steps on the comets surface, the gravity seems to be just as on earth, the two guys dont even show this “jumpy” behavior like the astronauts on the moon… thus the gravity is larger then on the moon.

Calculating the possible mass of an object with only 80 Kilometers diameter the gravity should be VERY low. I guess that a normal humans weight should be only grams. On wrong step would give HUGE jumps. (Note that later in this episode problems arise because one member of the team slips and falls about only 40 centimeters while on the comet and gets injured. Thats even hard to do given earths gravity)

This is also true for the Movie ARMAGEDDON.

The real reason for this is production budgets. Doing this on Earth is expensive and finicky. The movie Apollo 13 only used a few minutes of actual zero-g; the rest was done on the ground using special teeter totters and acting.

Using quick calculations via Google, I get:

Density of Ice = 0.92 g/mL (this is very generous. Current estimates I found on the web give comet densities less than this)

Radius of planet = 40 km

$\frac{4}{3}{\pi}{\times}{40}km^{3}{\times}{9.2} g/mL = {1.5414748}{\times}10^{15} kilograms$

${\approx} {1.5} {\ quadrillion\ tonnes}$

At the surface of the commet, the accleration should be:

0.00257156534 m / s2

Or 0.02% of Earth’s gravity. If anything, they should have launched themselves into orbit with each step.

[1] John S. Lewis, “Rain of Iron and Ice”, Addison-Wesley Publishing Company, New York, 1996