Measuring Planetary Masses
How do you find the mass of a planet?
Let us first focus on how we know the mass of the Earth. We find that
when we drop things on the Earth's surface (at sea level), it
accelerates toward the Earth at approximately 9.8m/s/s. We also find that
it does not matter how big or heavy or massive the object is (as long as
there is no air friction), the object falls at the same rate and
acceleration. When we try to do the same experiment on a mountain, we
find that the acceleration is a little bit less. In fact, we have found
that the farther we get away from the center of the Earth, the slower
the acceleration. Thus, it seems that distance (and not how big)
controls how much acceleration an object will have when dropped. Thus we
can say that the Moon is falling (dropping) toward the Earth at a
particular acceleration, and this is a function of the distance of the
Moon to the Earth. This is important because if we look at Mars and see
the distance of its own moons, we can see that the moons of Mars are not
dropping at the same acceleration for their particular distance. We
therefore have to conclude that the difference in mass of Earth and Mars
accounts for the difference in the accelerations despite having the same
distance. From this, we can figure out what the mass of the Earth must
be in order for an object at a particular distance to have the kind of
acceleration it has toward the Earth. Similarly, we can figure out what
is the mass of other planets like Mars depending how quickly its own
moons are falling toward the planet.
For planets like Mercury and Venus which do not have moons we can
observe their effect on other planets and see how much these other
planets wobble when they get a certain distance to the target planet.
The wobble is like a small drop (small because the distance is so
great). And using the same idea that distance and mass control
acceleration, we can figure out the mass.
Greg (Roberto Gregorius)
By studying its composition, it is possible to determine its mass.
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Update: June 2012