Exam 13: Gravitation

Two particles, each of mass m, are a distance d apart.To bring a third particle, with mass 2m, from far away to a resting point midway between the two particles, an external agent must do work equal to:

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 magnitude of the acceleration of a planet in orbit around the Sun is proportional to:

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:

Mars has a mass of about 0.1075 times the mass of Earth and a diameter of about 0.533 times the diameter of Earth.The acceleration of a body falling near the surface of Mars is about:

A spherical shell has inner radius R₁, outer radius R₂, and mass M, distributed uniformly throughout the shell.The magnitude of the gravitational force exerted on the shell by a point particle of mass m, located a distance d from the center, outside the inner radius and inside the outer radius, is:

An astronaut finishes some work on the outside of his satellite, which is in circular orbit around the Earth.He leaves his wrench outside the satellite.If there is no air resistance, the wrench will:

In Einstein's theory of gravitation, gravity is due to:

The gravitational constant G has the derived units

The elliptical orbit of a planet around the Sun is shown on the diagram.Which of the following statements is true?

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:

A mass m is located at the origin; a second mass m is at x = d.A third mass m is above the first two so the three masses form an equilateral triangle.What is the net gravitational force on the third mass?

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

To measure the mass of a planet with the same radius as Earth, an astronaut drops an object from rest (relative to the planet)from an altitude of one radius above the surface.When the object hits its speed is 4 times what it would be if the same experiment were carried out for Earth.In units of M_E (the mass of the Earth), the mass of the planet is:

A spaceship is returning to Earth with its engine turned off.Consider only the gravitational field of Earth.Let M be the mass of Earth, m be the mass of the spaceship, and R be the distance from the center of Earth.In moving from position 1 to position 2 the kinetic energy of the spaceship increases by:

Three particles, two with mass m and one mass M, might be arranged in any of the four configurations known below.Rank the configurations according to the magnitude of the gravitational force on M, least to greatest.

An object is raised from the surface of Earth to a height of two Earth radii above Earth.Then:

The approximate value of g at an altitude above Earth equal to one Earth diameter is:

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:

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