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A mystery planet and its moon are found revolving around a nearby star. The star is...

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Physics

A mystery planet and its moon are found revolving around anearby star. The star is a K3 Main Sequence star with a mass ofapproximately 0.8 M☉ and a radius of 0.78 R☉. The planet isbelieved to be terrestrial (Earth-like, and therefore of a similardensity) and has an observed orbital period of 243 days. The moonorbits the planet every 13.2 hours with an average orbital radiusof 19,600 km. Using this information, find:

(a)the orbital radius of the planet,

(b)the distance at which another planet in the system would havean orbital speed of 24,000 m/s,

(c)the point between the star and the planets at which the netforce on a spacecraft would be zero, and

(d)the period of a 80-cm long simple pendulum with a mass of 30grams that is swinging on the planet’s surface

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