Solution

Since the mass of the Sun is so much greater than that of the Earth, we can approximate the sum of the masses as being the mass of the Sun, M0. Equation (5.20) then becomes

4^2R3 GP2

(6.67 X 10"8 dyn cm2/g2)(3.16 X 107 s)2 = 2 X 1033g

We call this quantity a solar mass. It becomes a convenient quantity for expressing the masses of other stars.

From the Earth and Sun we know that for a pair of objects orbiting with a period of 1 yr, at a distance of 1 AU (defined in Section 2.6), the sum of the masses must be one solar mass. This suggests a convenient system of units for equation (5.20). If we express masses in solar masses, distances in astronomical units, and periods in years, the constants must equal one to give the above result. We can therefore rewrite equation (5.20) as

" R '

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