8. Centripetal Forces & Gravitation

Satellite Motion: Speed & Period

Multiple Choice
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.
Multiple Choice
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?
Multiple Choice
A satellite orbits at an orbital period of 2 hours around the Moon. What is the satellite's orbital altitude?
Multiple Choice
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?
Open Question
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?
Open Question
Three satellites orbit a planet of radius R, as shown in FIGUREEX13.24. 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.(b) What are the forces of S₂ and S₃?
Open Question
Three satellites orbit a planet of radius R, as shown in FIGUREEX13.24. 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.(c) What is the kinetic-energy ratio for K₁ / K₃ for S₁ and S₃?
Open Question
Large stars can explode as they finish burning their nuclear fuel, causing a supernova. The explosion blows away the outer layers of the star. According to Newton's third law, the forces that push the outer layers away have reaction forces that are inwardly directed on the core of the star. These forces compress the core and can cause the core to undergo a gravitational collapse. The gravitational forces keep pulling all the matter together tighter and tighter, crushing atoms out of existence. Under these extreme conditions, a proton and an electron can be squeezed together to form a neutron. If the collapse is halted when the neutrons all come into contact with each other, the result is an object called a neutron star, an entire star consisting of solid nuclear matter. Many neutron stars rotate about their axis with a period of ≈ 1 s and, as they do so, send out a pulse of electromagnetic waves once a second. These stars were discovered in the 1960s and are called pulsars. (e) What is the radius of a geosynchronous orbit?
Open Question
A satellite of mass 5200 kg orbits the Earth and has a period of 6800 s. Determine
(b) the magnitude of the Earth’s gravitational force on the satellite
Open Question
(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?
Open Question
(III) (b) 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.
Open Question
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?
Open Question
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.
Open Question
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.]