A new planet is discovered orbiting a distant star. Observations have confirmed that the planet has a circular orbit with a radius of 18 AU and takes 109 days to orbit the star. Determine the mass of the star.

AU stands for "astronomical unit". It is the average distance between Earth & the Sun. 1 AU ≈ 1.496 × 1011 m.

Mass of star is kg.

Explanation:

The cube of orbital radius is equal to the square of its orbital time period is known as Kepler's law.

         .....(1)

Here T is time period, r is orbital radius, G is universal gravitational constant and M is the mass of the star.

According to the problem,

Time period, T = 109 days = 109 x 24 x 60 x 60 s = 9.41 x 10⁶ s

Orbital radius, r = 18 AU = 18 x 1.496 x 10¹¹ m = 2.70 x 10¹² m

Gravitational constant, G = 6.67 x 10⁻¹¹ m³ kg⁻¹ s⁻²

Substitute these values in equation (1).

M = kg

the moon affects the earth gravitation ally, causing certain motions of that body and also producing tides in its ocean and atmosphere. the tidal wave in our atmosphere is, however, far too minute to be an effective cause in any known meteorological phenomenon.

explanation:

current flows in a wire