How do you do that?
Let's use this result to get an estimate of the mass of the Sun. You need to use something orbiting
with a known radius and speed. The Earth's orbit is roughly circular with radius = 1.5 × 10
11
meters and the Earth moves with a speed 30,000 meters/second (= 30 km/s) in its orbit. The
distance is given in meters to match the units of the speed. The distance unit of a meter is used
because you will be using the gravitational constant
G
in your calculation and it uses the meter
unit. When you do a calculation, you must be sure you check that your units match up or you will
get nonsense answers.
Plug the values into the mass relation:
the Sun's mass = (30,000)
2
× (1.5 × 10
11
)/(6.7 × 10
11
) = 2 × 10
30
kilograms. This is much larger
than the Earth's mass so it was okay to ignore the Sun's movement toward the Earth. Using no
approximations (ie., not assuming a circular orbit and including the Sun's motion toward the
Earth) gives a value for the Sun's mass that is very close to this. Your answer does not depend on
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 Fall '10
 EmilyHoward
 Astronomy, Solar System, Astronomical unit, Celestial mechanics, mass relation

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