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Two planets orbit a star. you can ignore the gravitational interactions between the planets.

planet 1 has orbital radius r1 and planet 2 has r2 = 16r1. planet 1 orbits with period T1. planet 2 orbits with what period?

User Kett
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1 Answer

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Final answer:

The period of planet 2 orbiting a star is 64 times longer than the period of planet 1.

Step-by-step explanation:

The period of planet 1, denoted as T1, is related to the orbital radius r1 by Kepler's third law which states that T^2 is proportional to r^3. Therefore, T1^2 is proportional to r1^3. Given that planet 2 has an orbital radius of r2=16r1, we can find the period T2 of planet 2 by substituting r2 into the equation. Since r2 is 16 times larger than r1, T2^2 will be 16^3 times larger than T1^2. This implies that T2 will be 64 times larger than T1. Therefore, the period of planet 2 is 64 times longer than the period of planet 1.

User Polyccon
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