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27 October, 08:25

A planet has two

moons. The first moon has an orbital

period of 1.262 Earth days and an orbital radius of 2.346 x 104

km. The second moon has an orbital

radius of 9.378 x 103 km.

What is the orbital period of the second moon?

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Answers (1)
  1. 27 October, 08:28
    0
    Kepler's third law hypothesizes that for all the small bodies in orbit around the

    same central body, the ratio of (orbital period squared) / (orbital radius cubed)

    is the same number.

    Moon #1: (1.262 days) ² / (2.346 x 10^4 km) ³

    Moon #2: (orbital period) ² / (9.378 x 10^3 km) ³

    If Kepler knew what he was talking about ... and Newton showed that he did ...

    then these two fractions are equal, and may be written as a proportion.

    Cross multiply the proportion:

    (orbital period) ² x (2.346 x 10^4) ³ = (1.262 days) ² x (9.378 x 10^3) ³

    Divide each side by (2.346 x 10^4) ³:

    (Orbital period) ² = (1.262 days) ² x (9.378 x 10^3 km) ³ / (2.346 x 10^4 km) ³

    = 0.1017 day²

    Orbital period = 0.319 Earth day = about 7.6 hours.
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