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Introduction to Gravitation : Kepler's Laws

The following...

Question

The following figure shows the elliptical path of a planet about the Sun. The two shaded parts, $S 1$ and $S 2$ , have equal areas. If $t_{1}$ and $t_{2}$ be the time taken by the planet to go from $A$ to $B$ and from $C$ to $D$ respectively, then:

t_{1} > t_{2}

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t_{1} < t_{2}

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t_{1} = t_{2}

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t_{1}

and

t_{2}

cannot be compared.

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Solution

The correct option is C $t_{1} = t_{2}$
According to Kepler’s law, the line joining a planet and the Sun sweeps equal areas in equal intervals of time during the rotation of the planet around it.
Here, the regions $S 1$ and $S 2$ have the same area. Thus, the time taken for the planet to go from $C$ to $D$ is equal to the time taken for the planet to go from $A$ to $B$ . Hence, $t_{1} = t_{2}$

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The following figure shows the elliptical path of a planet about the Sun. The two shaded parts, S1 and S2, have equal areas. If t1 and t2 be the time taken by the planet to go from A to B and from C to D respectively, then:

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