Q. 28

Expert-verifiedFound in: Page 354

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

A new planet is discovered orbiting the star Vega in a circular orbit. The planet takes earth years to complete one orbit around the star. Vega’s mass is times the sun’s mass. What is the radius of the planet’s orbit? Give your answer as a multiple of the radius of the earth’s orbit.

The radius of the planet's orbit is times of the earth's orbit radius.

Time period = mass of the planet =

According to Kepler's 3rd law, the time period is given by

Where, T is the time period, R is the required radius of the orbit, G is the universal gravitational constant and M is the required mass of Vega.

Now solving we get,

The radius of the earth's orbit is

Radius of the planet is times of the earth's orbit radius.

The radius of the planet is times of the earth's orbit radius.

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