You throw a baseball horizontally while on the surface of a small, spherical asteroid of mass 7×10¹⁶ kg and diameter of 22km. What is the minimum speed so that it just barely goes around the asteroid without hitting anything?

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.

(b) If the satellite circles the planet once every 2.0 h in the larger orbit, what is the mass of the planet?

The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed around the Earth, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical mile = 1.852km = 6076ft].

(a) Determine the speed of each satellite.

The Navstar Global Positioning System (GPS) utilizes a group of 24 satellites orbiting the Earth. Using “triangulation” and signals transmitted by these satellites, the position of a receiver on the Earth can be determined to within an accuracy of a few centimeters. The satellite orbits are distributed around the Earth, allowing continuous navigational “fixes.” The satellites orbit at an altitude of approximately 11,000 nautical miles [1 nautical mile = 1.852km = 6076ft].

(b) Determine the period of each satellite. [Originally, 1 nautical mile was defined as one minute ( 1/60 of a degree) of latitude on Earth’s surface. 1 knot is a speed of 1 nautical mile/h.]

Suppose that you used some geometry and kinematics to estimate that the Earth goes around the Sun with an orbital speed of approximately 30,000 m/s (60,000 mph), and that the Sun is approximately 150 million kilometers away from the Earth. Use this information to estimate the mass of the Sun.

A satellite orbits at an orbital period of 2 hours around the Moon. What is the satellite's orbital altitude?

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?