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Two newly discovered planets follow circular orbits around a star in a distant part of the...

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 44.3 km/s and 59.8 km/s. The slower planet's orbital period is 6.92 years. (a) What is the mass of the star? (b) What is the orbital period of the faster planet, in years?


Solutions

Expert Solution

(a) Mass of the star

Consider the slower planet and the star

Given the time period and orbital speed

Orbital Speed = Circumference of the orbit/Time period

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Given that the planet follows a circular orbit around the star.

So the gravitational force experienced by the slower planet is equal to the centripetal force.

ANSWER :

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(b) What is the orbital period of the faster planet, in years?

Consider the faster planet and the star

Given that the planet follows a circular orbit around the star.

So the gravitational force experienced by the faster planet is equal to the centripetal force.

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Orbital Speed = Circumference of the orbit/Time period

ANSWER :

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genius_generous answered 2 years ago
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