Exam 13: Gravity

An object drops a distance h in a time of 6.3 s on the surface of the earth (neglecting air effects).How long would it take the same object to drop the same distance on the surface of spherical asteroid X having a mass of 1.1 × 10²² kg and a radius of 4.0 × 10⁵ m? (G = 6.67 × 10^-11 N • m²/kg²,M_earth = 5.97 × 10²⁴ kg,R_earth = 6.38 × 10⁶ m)

Because the earth's orbit is slightly elliptical,the earth actually gets closer to the sun during part of the year.When the earth is closer to the sun its orbital speed is

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)

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.