8. Centripetal Forces & Gravitation

According to Kepler’s First Law, which objects in the Solar System typically have the most elliptical and tilted orbits?

According to Kepler's First Law and the properties of planetary orbits, which statement best explains why $\mathrm{Jupiter}$'s average orbital speed is less than half that of $\mathrm{Earth}$?

According to Kepler’s First Law, what is the shape of Earth’s orbit around the $Sun$?

Pluto's orbit is the most eccentric of the 9 large objects in our solar system, with e = 0.25. The total distance from Pluto's closest to farthest point from the Sun is 1.18×10¹³m. a) How close does it get to the Sun? b) How far does it get from the Sun?

In 2004 astronomers reported the discovery of a large Jupiter-sized planet orbiting very close to the star HD 179949 (hence the term 'hot Jupiter'). The orbit was just 1/9 the distance of Mercury from our sun, and it takes the planet only 3.09 days to make one orbit (assumed to be circular). How fast (in km/s) is this planet moving?

The star Rho¹ Cancri is 57 light-years from the earth and has a mass 0.85 times that of our sun. A planet has been detected in a circular orbit around Rho¹ Cancri with an orbital radius equal to 0.11 times the radius of the earth's orbit around the sun. What are (a) the orbital speed and (b) the orbital period of the planet of Rho¹ Cancri?

In March 2006, two small satellites were discovered orbiting Pluto, one at a distance of 48,000 km and the other at 64,000 km. Pluto already was known to have a large satellite Charon, orbiting at 19,600 km with an orbital period of 6.39 days. Assuming that the satellites do not affect each other, find the orbital periods of the two small satellites without using the mass of Pluto.

On October 15, 2001, a planet was discovered orbiting around the star HD 68988. Its orbital distance was measured to be 10.5 million kilometers from the center of the star, and its orbital period was estimated at 6.3 days. What is the mass of HD 68988? Express your answer in kilograms and in terms of our sun's mass.

(II) The masses of the Earth and Moon are 5.98 x 10²⁴ kg and 7.35 x 10²² kg, respectively, and their centers are separated by 3.84 x 10⁸ m. What can you say about the motion of the Earth–Moon system about the Sun, and of the Earth and Moon separately about the Sun?

Determine the radius of a neutron star using the same argument as in Problem 65 but for N neutrons only. Show that the radius of a neutron star, of 1.5 solar masses, is about 11 km.