Question

Please show the work and answers for these two questions. Thank you!!

Calculate the length R of the semimajor axis of a planet whose period is 160 years.
AU

Determine what the period of revolution of the Earth would be if its distance from the Sun were 7.5 AU rather than 1 AU. Assume that the mass of the Sun remains the same.
y

Answer 1

Kepler’s discovery was that the period T and the average distance R of a planet from the sun obeyed the relation  

T² / R³ = 1

period = 160 years then length of semi major axis

T² = R³

(160)² = R³

25600= R³

^{R =}

R = 25.47 AU

length R of the semi-major axis of a planet whose period is 160 years is 25.47 AU

The period of revolution of earth at 1 AU is 365 days

when Distance between sun and earth is 7.5 AU then the period of revolution is

7.5 multiplies by 365 = 2737.5 days  

the period of revolution of the Earth would be if its distance from the Sun were 7.5 AU is 2737.5 days