HOW MASS IS DETERMINED
 

The simplest way to determine the mass of an object is to measure it with a scale. However, this isn’t the best way. When you put something on a scale, you are measuring that object’s weight in the gravitational field of the Earth. The intensity of this field is, for most practical purposes, the same wherever you go on the planet. If you want to get picayune about it, though, there is a slight variation of weight for a given mass with changes in the geographic location. A scale with sufficient accuracy will show a specific object, such as a lead shot, as being a tiny bit heavier at the equator than at the north pole. The weight changes, but the mass does not.
Suppose that you are on an interplanetary journey, coasting along on your way to Mars or in orbit around Earth, and everything in your space vessel is weightless. How can you measure the mass of a lead shot under these conditions? It floats around in the cabin along with your body, the pencils you write with, and everything else that is not tied down. You are aware that the lead shot is more massive than, say, a pea, but how can you measure it to be certain?
One way to measure mass, independently of gravity, involves using a pair of springs set in a frame with the object placed in the middle (Fig. 1). If you put something between the springs and pull it to one side, the object oscillates. You try this with a pea, and the springs oscillate rapidly. You try it again with a lead shot, and the springs oscillate slowly. This “mass meter” is anchored to a desk in the space ship’s cabin, which is in turn anchored to the “floor” (however you might define this in a weightless environment). Anchoring the scale keeps the whole apparatus from wagging back and forth in midair after you start the object oscillating.

Fig. 1. Mass can be measured by setting an object to oscillate between a pair of springs in a weightless environment.

A scale of this type must be calibrated in advance before it can render meaningful figures for masses of objects. The calibration will result in a graph that shows oscillation period or frequency as a function of the mass. Once this calibration is done in a weightless environment and the graph has been drawn, you can use it to measure the mass of anything within reason. The readings will be thrown off if you try to use the “mass meter” on Earth, the Moon, or Mars because there is an outside force, gravity, acting on the mass. The same problem will occur if you try to use the scale when the space ship is accelerating rather than merely coasting or orbiting through space.