Question

1. if you can measure the time that mars takes to travel around the sun, what other variable could you calculate using kepler’s 3rd law?

Explanation:

Step1: Recall Kepler's 3rd Law

Kepler's third law is given by the formula $$\frac{T^2}{r^3} = \text{constant}$$ for a planet orbiting the Sun, where \( T \) is the orbital period (time to travel around the Sun) and \( r \) is the average distance (semi - major axis) of the planet from the Sun.

Step2: Analyze the variables

We know the orbital period \( T \) of Mars (the time it takes to travel around the Sun). From Kepler's third law, if we know \( T \), and we know the constant (since it is the same for all planets orbiting the Sun), we can solve for the average distance \( r \) of Mars from the Sun. The formula can be rearranged to \( r^3=\frac{T^2}{\text{constant}} \), and then we can find \( r \) by taking the cube - root of both sides.

Answer:

Using Kepler's 3rd law, if we know the orbital period (time for Mars to travel around the Sun), we can calculate the average distance (semi - major axis) of Mars from the Sun.