Chapter 5, Gravitation and Kepler’s Laws Video Solutions, An Introduction to Astronomy and Astrophysics

01:08

Problem 1

Use Kepler's third law to determine the time period of revolution of the Earth around the Sun.

Prabhu Ramji

Numerade Educator

Problem 2

Verify the virial theorem for the case of periodic motion of two particles gravitationally bound to one another.

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11:14

Verify Equation 5.24 for the difference in gravitational field at A compared to O , for mass $m$ shown in Figure 5.6. Repeat this calculation for points $\mathrm{B}, \mathrm{C}$, and D on mass $m$. The points C and D are shown in Figure 5.7. Show that for B the magnitude of $\Delta \vec{g}$ is the same as at A . The magnitudes at C and D are half in comparison to that at A. The directions at all these points are shown in Figure 5.7.

Donald Albin

Numerade Educator

05:01

Problem 4

Determine the Roche limit for a mass $m$ revolving about the mass $M$ in a circular orbit. Assume that $m$ also rotates about its axis at the same rate as it revolves about $M$. In this case, all points on $m$ move in a circular orbit around the center of $M$ with the same angular speed. Assume a point particle placed at position A (Figure 5.6) that is bound to $m$ only by its gravitational attraction. Find the minimum distance of $m$ from $M$ for which this particle will not leave the surface of $m$.

$$
\text { Ans : } \quad r_{\min }=\left(\frac{3 \rho_M}{\rho}\right)^{1 / 3} R_M
$$

Andy Chen

Numerade Educator

Problem 1

Problem 2

Problem 3

Problem 4