8. Centripetal Forces & Gravitation

According to Kepler's Third Law, if a planet orbits a star in a year of length $T$, which of the following correctly relates the orbital period $T$ to the semi-major axis $a$ of its orbit (assuming the mass of the star is much greater than the planet's mass)?

According to Kepler's Third Law, what is the orbital period (in years) of a planet with a semimajor axis of $35au$ around the Sun?

According to Kepler's Third Law, which of the following planets (on average) takes the longest to orbit the Sun (has the longest orbital period)? $T^2=\frac{a^3}{k}$

According to Kepler's Third Law, what is the orbital period in Earth-years of a planet whose average distance from the Sun is $3$ astronomical units ($\mathrm{a.u.}$)?

Why is Newton's version of Kepler's Third Law so useful to astronomers?

According to Kepler's Third Law, what is the orbital period in Earth-years of a planet whose average distance from the Sun is $3$ astronomical units (AU)?

According to Kepler's Third Law, which of the following correctly relates the square of the orbital period $P^2$ to the cube of the semi-major axis $a^3$ for a planet orbiting the Sun?

According to Kepler's Third Law, what is the semimajor axis in astronomical units ($au$) of a planet that has an orbital period of $P=75$ years around the Sun?

All the following statements are true. Which one follows directly from Kepler's Third Law ($P^2=a^3$)?

According to Kepler's Third Law, what is the orbital period (in years) of a planet with a semimajor axis of $65au$ around the Sun?

Io and Ganymede are two of Jupiter's four Galilean moons. Io orbits at an average distance of 422,000km in 1.77 days. What is Ganymede's average orbital distance (in km), if it takes 4 times longer to orbit Jupiter?