Exam 13: Gravitation

For a planet in orbit around a star the perihelion distance is r_p and its speed at perihelion is v_p. The aphelion distance is r_a and its speed at aphelion is v_a. Which of following is true?

A small satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy:

Einstein's principle of equivalence states:

In order to fire a projectile upward and have it escape the Earth's gravity,

A planet travels in an elliptical orbit about a star as shown. At what pair of points is the speed of the planet the same?

The orbit of a certain a satellite has a semimajor axis of 1.5 *10⁷ m and an eccentricity of 0.20. Its perigee (minimum distance) and apogee (maximum distance) are respectively:

Earth exerts a gravitational force on the Moon, keeping it in its orbit. The reaction to this force, in the sense of Newton's third law, is:

An artificial Earth satellite is moved from a circular orbit with radius R to a circular orbit with radius 2R. During this move:

The gravitational constant G has the derived units

Suitable units for the gravitational constant G are:

Neglecting air resistance, a 1.0-kg projectile has an escape velocity of about 11 km/s at the surface of Earth. The corresponding escape velocity for a 2.0 kg projectile is:

An astronaut in an orbiting space-craft feels "weightless" because she:

An artificial satellite of Earth nears the end of its life due to air resistance. While still in orbit:

Let M denote the mass of Earth and let R denote its radius. The ratio g/G at Earth's surface is:

An object at the surface of Earth (at a distance R from the center of Earth) weighs 90 N. Its weight at a distance 3R from the center of Earth is: