8. Centripetal Forces & Gravitation

You stand on the surface of a mysterious planet with a mass of 6 ×10²⁴ kg and measure the surface gravity to be 7 m/s². What must the radius of the planet be?

How far would you have to be above Earth's surface for g to be ½ of its surface value?

A recently discovered extrasolar planet appears to be rockier and denser than earth. It is 16 times as massive as earth, but its diameter is only twice that of earth. What is the free-fall acceleration on the surface of this planet?

What is the free-fall acceleration at the surface of (a) the moon and (b) Jupiter?

At what height above the earth is the free-fall acceleration 10% of its value at the surface?

Titania, the largest moon of the planet Uranus, has 1/8 the radius of the earth and 1/1700 the mass of the earth. What is the average density of Titania? (This is less than the density of rock, which is one piece of evidence that Titania is made primarily of ice.)

Titania, the largest moon of the planet Uranus, has 1/8 the radius of the earth and 1/1700 the mass of the earth. What is the acceleration due to gravity at the surface of Titania?

The mass of Venus is 81.5% that of the earth, and its radius is 94.9% that of the earth. If a rock weighs 75.0 N on earth, what would it weigh at the surface of Venus?