A distant planet orbits a star 3 times the mass of our Sun. This planet of mass 8 × 10²⁶ kg feels a gravitational force of 2 × 10²⁶ N. What is this planet's orbital speed and how long does it take to orbit once?

The Lunar Reconnaissance Orbiter (LRO) is a NASA Moon-orbiting spacecraft in an orbit with an altitude of 50 km above the Moon’s surface. What is the period of the LRO as it orbits the Moon?

Three satellites orbit a planet of radius R, as shown in FIGURE EX13.24. Satellites S₁ and S₃ have mass m. Satellite S₂ has mass 2m. Satellite S₁ orbits in 250 minutes and the force on S₁ is 10,000 N. What is the kinetic-energy ratio for K₁ / K₃ for S₁ and S₃?

A satellite of mass 5200 kg orbits the Earth and has a period of 6800 s. Determine the magnitude of the Earth’s gravitational force on the satellite.

(II) In a remote region of space, far from any other objects, a small ball is in a 30.0-cm-radius circular orbit around a 7.0-kg bowling ball. How long does it take the small ball to complete one orbit?

Estimate the density of the Earth, given that a satellite near the surface orbits with a period of 85 min. Approximate the Earth as a uniform sphere.

A satellite circles a spherical planet of unknown mass in a circular orbit of radius 1.6 x 10⁷ m. The magnitude of the gravitational force exerted on the satellite by the planet is 120 N. If the satellite circles the planet once every 2.0 h in the larger orbit, what is the mass of the planet?