A planet is in circular orbit around the Sun.Its distance from the Sun is four times the average distance of Earth from the Sun.The period of this planet is:
A)4 Earth years
B)8 Earth years
C)16 Earth years
D)64 Earth years
E)2.5 Earth years

Question

Quizplus · Accepted Answer

The period of a planet's orbit is given by Kepler's third law:

T² = (4π²/G) × (r³/m)

where:
T = period of orbit
G = gravitational constant
r = distance from the center of the Sun to the center of the planet's orbit
m = mass of the Sun

Since the planet's distance from the Sun is four times the average distance of Earth from the Sun, we have:

r = 4 × 1 AU = 4 AU

where 1 AU is the average distance of Earth from the Sun.

Substituting this into Kepler's third law, we get:

T² = (4π²/G) × (4³/m)

T²/T²(earth) = (4³/1) / (1/(GM))

where T²(earth) and GM are the period and gravitational parameter of Earth, respectively.

Simplifying this expression, we get:

T²/T²(earth) = 64

Taking the square root of both sides, we get:

T/T(earth) = 8

Therefore, the period of the planet's orbit is 8 Earth years.

A Planet Is in Circular Orbit Around the Sun