Can a simple pendulum oscillate in a moving satellite?

A simple pendulum (a weight hanging from a string swinging back and forth) is a gravity driven system. The pendulum weight is released, falls down, swings through the low point, rises up until it reaches the same height as it was released on the other side, reverses direction and falls down. Satellites in orbit do not have an interior gravity field to drag things down (think of all the Shuttle photos with astronauts demonstrating floating pens and globs of water) so the description of the pendulum action would be: Pendulum weight is released and hangs there.

The equation for the period of a simple pendulum:

T=2 pi (L/g)^0.5 (T=period, L=string length, g=acceleration of gravity)

indicates the need for gravity field for the pendulum to swing. At zero gravity T goes to infinity. The pendulum does not swing.

An Addendum:
There was a followup question - what if the satellite was spinning (e.g. Had an artificial spin induced "gravity"

So so far most of the shuttles and satellites with enough room to swing a pendulum have not enjoyed spin or other induced "artificial gravity" so I didn't consider it in the question. But it does sound like fun to think about.

I had started to develop a long explanation using the vectors of spin induced gravity in a spaceship. Then I had a flashback to a book I had back before satellites were in orbit. The picture was one of those old big wheel type habitats spinning in space. Workers just hung there in the axle area in their own orbit with no impact from the rotation (spin doesn't radiate gravity waves) This is not the case for the pendulum as it is attached to the spinning object and eventually moves in a way that causes it to become part of the rotation. This results from the weight's reaction on being released to move tangentially to the arc of the spin.

Since the spinning satellite is essentially a gyroscope it will orient itself (the axis of rotation)in one direction against space. The pendulum weight swing can have two components: in the same direction as this axis, and with and against the rotation.

In the case of the weight's component of swinging in the rotation plane, the weight is essentially always "down" as far as it can go. Like you spinning with a weight on a string, no matter how close you bring the hand holding the end of the string, the weight always pulls directly out i.e. no swinging

Regarding the component of swing back and forth along the axis, the force pulling on the weight (g) changes with the distance from the axis of rotation the "gravity" changes and the equation I presented for the pendulum in my answer becomes an integral of "g" In addition the weight, it moves antispinward as it falls. An odd image - a chain would hang straight down, a waterfall in a spinning satellite would curve to the antispinaward with every drop at 0 g as it "fell"

NOTE: A bit of experimentation in the back yard indicates that it is hard to get any up and down motion with a weight on a string when I'm spinning. It may be that this motion damps out pretty quickly.

So far we haven't considered pendulum being in the spinning satellite orbiting a planet. If the pendulum were just hanging there in a non-spinning orbiting object it would have a different orbital period from the center of mass of the satellite and a different orbital height for whatever speed it was released at. I think it's faster is lower and slower is further for orbits. We'd have to consider this as well in determining its motion if the pendulum swing took it effectively into a higher or lower orbit .

First answer by Cjonb. Last edit by Woodwose. Contributor trust: 223 [recommend contributor]. Question popularity: 13 [recommend question]