Question

The Mass of the Sun Calculate the mass of the Sun, noting that the period of the Earth's orbit around the Sun is 3.156 x 107 s and its distance from the Sun is 1.496 x 1011 m. SOLUTION Conceptualize Based on the mathematical representation of Kepler's third law expressed as T2 412 3 Ksa3, we realize that the mass of the central object in a gravitational system is related to the orbital size and ---Select--- of objects in orbit around the central object. GM problem. Categorize This example is a relatively simply ---Select-- substitution Solve Kepler's third law for the mass of the S analysis 47293 Ms GT2 = Substitute the known values (Enter your answer in kg.): = MS kg In the Example The Density of Earth, an understanding of gravitational forces enabled us to find out something about the density of the Earth's core, and now we have used this understanding to determine the mass of the Sun! EXERCISE If we find an unknown comet returning to the Sun every 337 years (for example, we know that Comet Halley returns every 75.6 years), determine the radius a (semi-major axis) of its orbit (in m). Hint a = m Need Help? Read It

Answer 1

First blank =>Period

second blank => Substitution

-----------------------------------------------------------------------

From the given formula

$M_{s}=\frac{4\pi ^{2}\times (1.496\times 10^{11})^{3}}{(6.673\times 10^{-11})(3.156\times 10^{7})^{2}}$

$M_{s}=1.9886548\times 10^{30}kg$

--------------------------------------------------------------------------

=>$a=\left ( \frac{GT^{2}M_{s}}{4\pi ^{2}} \right )^{1/3}$

1/3 a (6.673 x 10-11))(337 x 365 x 24 x 60 x 60) (1.9886548 x 1030) 472

$a=7.24\times 10^{12}m$