Question

Question 1: How would you determine the length of Jupiter's orbit using Kepler's third
law? What information would you need?

Answer 1

Answer:

$\frac{T_1^2}{T_2^2} = \frac{R_1^3}{R_2^3}$

In order to find the orbital radius of the Jupiter we need to know its time period around Sun

Explanation:

As we know by Kepler's III law of planetary motion that the square of the time period of the planet must be proportional to the cube of the orbital radius of the planet

so we can say that

$\frac{T_1^2}{T_2^2} = \frac{R_1^3}{R_2^3}$

so here we can find the orbital radius of the jupitor by the formula

$R_2^3 = \frac{T_2^2}{T_1^2} R_1^3$

here we can say that T1 and R1 is for earth which we know as

$T_1 = 24 hr$

$R_1 = 1.5 \times 10^8 km$

now in order to find the orbital radius of the Jupitor we need to know its time period around Sun