8. Centripetal Forces & Gravitation

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.

A satellite orbits the sun with a period of 1.0 day. What is the radius of its orbit?

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)? $T^2=\frac{a^3}{k}$

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 ($\mathrm{a.u.}$)?