Exam 12: Gravitation

Two moons orbit a planet in nearly circular orbits. Moon A has orbital radius r, and moon B has orbital radius 4r. Moon A takes 20 days to complete one orbit. How long does it take moon B to complete an orbit?

What is the ratio of the escape speed of a rocket launched from sea level to the escape speed of one launched from Mt. Everest (an altitude of 8.85 km)? The radius of the earth is 6.38 × 10⁶ m.

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 12.0 hours and an orbital radius 6.00 × 10⁷ m. The second planet has a period 16.0 hours. What is the orbital radius of the second satellite?

Spaceman Speff orbits spherical asteroid X with his spaceship. To remain in a circular orbit at 421 km from the asteroid's center, he should maintain a speed of 80 m/s. What is the mass of planet X? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Find the orbital speed of an ice cube in the rings of Saturn. The mass of Saturn is 5.68 × 1026 kg and the rings have an average radius of 100,000 km. (G = 6.67 × 10^-11 N ∙ m²/kg²)

The moons of Mars, Phobos (Fear) and Deimos (Terror), are very close to the planet compared to Earth's Moon. Their orbital radii are 9,378 km and 23,459 km respectively. What is the ratio of the period of revolution of Phobos to that of Deimos?

A satellite that weighs 4900 N on the launchpad travels around the earth's equator in a circular orbit with a period of 1.667 h. The earth's mass is 5.97 × 10²⁴ kg, its equatorial radius is 6.3 × 10⁶ m, and G = 6.67 × 10^-11 N ∙ m²/kg². (a) Calculate the magnitude of the earth's gravitational force on the satellite. (b) Determine the altitude of the satellite above the Earth's SURFACE.

A small-sized 155-kg mass is located 1.50 m from a small-sized 275-kg mass, with both masses fixed in place. Where should you place a third small-sized mass so that the net gravitational force on it due to the original two masses is zero?

What is the period (in hours) of a satellite circling Mars 100 km above the planet's surface? The mass of Mars is 6.42 × 10²³ kg, its radius is 3.40 × 10⁶ m, and G = 6.67 × 10^-11 N ∙ m²/kg².

A certain spherical asteroid has a mass of 3.5 × 10¹⁶ kg and a radius of 8.8 km. What is the minimum speed needed to escape from the surface of this asteroid? (G = 6.67 × 10^-11 N ∙ m²/kg²)

Two planets having equal masses are in circular orbit around a star. Planet A has a smaller orbital radius than planet B. Which statement is true?

An astronaut is standing on the surface of a planetary satellite that has a radius of 1.74 × 10⁶ m and a mass of 7.35 × 10²² kg. An experiment is planned where a projectile needs to be launched straight up from the surface. What must be the minimum initial speed of the projectile so it will reach a height of 2.55 × 10⁶ m above this satellite's surface? (G = 6.67 × 10^-11 N ∙ m²/kg²)

A certain planet has an escape speed V. If another planet of the same size has twice the mass as the first planet, its escape speed will be

A planet has two small satellites in circular orbits around the planet. The first satellite has a period 18.0 hours and an orbital radius 2.00 × 10⁷ m. The second planet has an orbital radius 3.00 × 10⁷ m. What is the period of the second satellite?

Neptune circles the Sun at a distance of 4.50 × 10¹² m once every 164 years. Saturn circles the Sun at a distance of 1.43 x 10¹² m. What is the orbital period of Saturn?

An astronaut is in equilibrium when he is positioned 140 km from the center of asteroid X and 581 km from the center of asteroid Y, along the straight line joining the centers of the asteroids. What is the ratio of the masses X/Y of the asteroids?

Suppose we want a satellite to revolve around the earth 5 times a day. What should be the radius of its orbit? (The mass of the earth is 5.97 × 10²⁴ kg, G = 6.67 × 10^-11 N ∙ m²/kg², and you can neglect the presence of the moon.)

The reason an astronaut in an earth satellite feels weightless is that

Beings on spherical asteroid Π have observed that a large rock is approaching their asteroid in a collision course. At 7514 km from the center of the asteroid, the rock has a speed of 136.0 m/s and later at 2823 km it has a speed of 392.0 m/s. Use energy conservation to find the mass of asteroid Π. You can neglect any effects due to the parent star of the asteroid. (G = 6.67 × 10^-11 N ∙ m²/kg²)

Ekapluto is an unknown planet that has two moons in circular orbits. The table summarizes the hypothetical data about the moons. (G = 6.67 × 10^-11 N ∙ m²/kg²) The mass of Ekapluto is closest to