Exam 13: Newtons Theory of Gravity

A small planet having a radius of 1000 km exerts a gravitational force of 100 N on an object that is 500 km above its surface. If this object is moved 500 km farther from the planet, the gravitational force on it will be closest to

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 × 10¹² m. What is the orbital period of Saturn?

A satellite of mass m has an orbital period T when it is in a circular orbit of radius R around the earth. If the satellite instead had mass 4m, its orbital period would be

Three identical very small 50-kg masses are held at the corners of an equilateral triangle, 0.30 m on each side. If one of the masses is released, what is its initial acceleration if the only forces acting on it are the gravitational forces due to the other two masses? (G = 6.67 × 10^-11 N ∙ m²/kg²)

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

A very small round ball is located near a large solid sphere of uniform density. The force that the large sphere exerts on the ball

A 910-kg object is released from rest at an altitude of 1200 km above the north pole of the earth. If we ignore atmospheric friction, with what speed does the object strike the surface of the earth? (G = 6.67 × 10^-11 N ∙ m²/kg², M_earth = 5.97 × 10²⁴ kg, the polar radius of the earth is 6357 km)

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 International Space Station is orbiting at an altitude of about 370 km above the earth's surface. The mass of the earth is 5.97 × 10²⁴ kg, the radius of the earth is 6.38 × 10⁶ m, and G = 6.67 × 10^-11 N ∙ m²/kg². Assuming a circular orbit, (a) what is the period of the International Space Station's orbit? (b) what is the speed of the International Space Station in its orbit?

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?

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?

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8 × 10⁷ m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 1.8 × 10¹¹ m from its star with a period of 402 earth days. Once on the surface you find that the acceleration due to gravity is 59.7 m/s². What are the mass of (a) the planet and (b) the star? (G = 6.67 × 10^-11 N ∙ m²/kg².)

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 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 orbital speed of Phobos to that of Deimos?

A satellite is in circular orbit at an altitude of 1500 km above the surface of a nonrotating planet with an orbital speed of 9.2 km/s. The minimum speed needed to escape from the surface of the planet is 14.9 km/s, and G = 6.67 × 10^-11 N ∙ m²/kg². The orbital period of the satellite is closest to

A baseball is located at the surface of the earth. Which statements about it are correct? (There may be more than one correct choice.)

A satellite in a circular orbit of radius R around planet X has an orbital period T. If Planet X had one-fourth as much mass, the orbital period of this satellite in an orbit of the same radius would be

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 meteoroid, heading straight for Earth, has a speed of 14.8 km/s relative to the center of Earth as it crosses our moon's orbit, a distance of 3.84 × 10⁸ m from the earth's center. What is the meteroid's speed as it hits the earth? You can neglect the effects of the moon, Earth's atmosphere, and any motion of the earth. (G = 6.67 × 10^-11 N ∙ m²/kg², M_earth = 5.97 × 10²⁴ kg)

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?