8. Centripetal Forces & Gravitation

a) How fast does a spaceship have to go to escape Earth, starting from the launch pad on the surface? Assume it burns all its fuel very fast and then shuts off the engines.

b) One idea to make getting to space easier is to build a space elevator, a large platform high above Earth's surface where spaceships can land and take off. How high above Earth would this platform have to be for the escape velocity to be 1/5 of its surface value? (For multiple choice, select the correct answer for part (b).)

In 2000, NASA placed a satellite in orbit around an asteroid. Consider a spherical asteroid with a mass of 1.0 x 10¹⁶ kg and a radius of 8.8 km. (b) What is the escape speed from the asteroid?

A planet orbiting a distant star has radius 3.24 * 10^6 m. The escape speed for an object launched from this planet’s surface is 7.65 * 10^3 m/s. What is the acceleration due to gravity at the surface of the planet?

(II) Take into account the Earth’s rotational speed (1 rev/day) and determine the necessary “escape velocity,” with respect to the Earth, for a rocket to escape if fired from the Earth at the equator in a direction

(c) vertically upward.

(I) The escape velocity from planet A is double that for planet B. The two planets have the same mass. What is the ratio of their radii, r_A / r_B?