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?

In 2014, the European Space Agency placed a satellite in orbit around comet 67P/Churyumov-Gerasimenko and then landed a probe on the surface. The actual orbit was elliptical, but we’ll approximate it as a 50-km-diameter circular orbit with a period of 11 days. What is the mass of the comet?

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?

(I) The asteroid Icarus, though only a few hundred meters across, orbits the Sun like the planets. Its period is 410 d. What is its mean distance from the Sun?

The dwarf planet Pluto has an elliptical orbit with a semimajor axis of 5.91 × 10¹² m and eccentricity 0.249. During Pluto's orbit around the sun, what are its closest and farthest distances from the sun?

A new planet is discovered orbiting the star Vega in a circular orbit. The planet takes 55 earth years to complete one orbit around the star. Vega's mass is 2.1 times the sun's mass. What is the radius of the planet's orbit? Give your answer as a multiple of the radius of the earth's orbit.