Mass and Gravity
Date: Around 1993
Is it possible to measure mass in a weightless environment? Also,
why does mass exert gravitational forces? Does it go down to the atomic level
where different particles have different charges, therefore attracting each
Yes, mass can be measured in a weightless environment.
Basically, "inertial" mass is defined by Newton's law: F = m a. So, if you
can measure a force and acceleration on an object, you can measure its mass.
The standard method on earth uses force-balance, with one of the forces being
the gravitational one, which is itself proportional to the "gravitational"
mass, which has been experimentally shown to be exactly the same as "inertial"
mass up to quite high precision. In weightlessness you could not use the
gravitational force to measure mass and so you would have to measure it by the
inertial approach, using an unbalanced force. For example, measuring the
frequency of oscillation of a spring with the mass to be measured attached
would give the mass pretty accurately. Gravity is not associated with the
charges on things - otherwise it would not depend just on mass, but on what
kind of microscopic relation there was between charge and mass. It is a very
weak force, at least on a human scale, but it is indeed completely independent
from the electrical forces. It was a good suggestion though - practically all
the interactions of matter we run into in our lives are through
electromagnetism - gravity is the one exception. There are two other forces
at very short distances in the nucleus. One of the goals of physics is to try
and unify all four forces to treat them as one, but there is no working theory
of this yet!
I add that gravitational mass equals inertial mass by definition.
That is the way the gravitation constant (big "G") is defined, in the equation
F=GmM/r^2 in the equation for the force between masses m and M separated by a
distance r (r^2 means "r-squared). What is important is that G is the same
for ALL pairs of masses, no matter what they are made of. This fact, which is
what has been verified to high precision by experiment, is sometimes referred
to as "the principle of equivalence".
Correction Submitted November, 2013
At the bottom of the page it states I add that gravitational mass equals inertial mass by definition. This statement is wrong. Gravitational mass and inertial mass aren't equal by definition but by observation. i.e. it is an empirical fact. Thank you.
Peter M. Brown
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Update: June 2012