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Use Kepler's third law to show that the closer a planet is to the Sun, the...

Use Kepler's third law to show that the closer a planet is to the Sun, the shorter its period.

Kepler's third law relates a planet's period around the Sun to the length of the (select) (semimajor or semiminor) axis such that

T2 = kR3. It is obvious from this expression that as the distance from the Sun (select) (T or k or R) decreases the period (select) (T or k or R) decreases as well.

I have to find the correct answer that fits, help me with this question please. I will rate you.

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Answer #1

from equation (1) it is clear that the left-hand side is a constant since G is universal gravitational constant, M is the mass of the star( which is also constant for a particular star) and the denominator also a constant. so, as the distance "a" the semimajor axis increases the time period "T" must increase. which means, shorter the semimajor axis, the planet will have shortest period.

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