Consider the two orbits around the sun shown below. Orbit P is circular with radius R, orbit Q is elliptical such that the farthest point b is between 2R and 3R, and the nearest point a is between R/3 and R/2 . Consider the magnitudes of the velocity of the circular orbit $v_{c}$ , the velocity of the comet in the elliptical orbit at the farthest point $v_{b}$ , and the velocity of the comet in the elliptical orbit at the nearest point $v_{a}$ . Which of the following ranking is correct?

v_{b} > v_{c} > 2 v_{a}

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2 v_{c} > v_{b} > v_{a}

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10 v_{b} > v_{a} > v_{c}

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v_{c} > v_{a} > 4 v_{b}

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Solution

The correct option is A $v_{b} > v_{c} > 2 v_{a}$
According to the Kepler's law,
the thing will be added a formula is called $T^{2} \times R^{3}$
and velocity $α \frac{1}{t i m e}$
The $2 R, 3 R$ and $R / 3$ and $R / 2$ .
hence $v_{b} > v_{c} > {2 v}_{a}$

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The correct option is A vb>vc>2vaAccording to the Kepler's law,the thing will be added a formula is called T2×R3and velocity α1timeThe 2R,3R and R/3 and R/2.hence vb>vc>2va

The correct option is A $v_{b} > v_{c} > 2 v_{a}$
According to the Kepler's law,
the thing will be added a formula is called $T^{2} \times R^{3}$
and velocity $α \frac{1}{t i m e}$
The $2 R, 3 R$ and $R / 3$ and $R / 2$ .
hence $v_{b} > v_{c} > {2 v}_{a}$