Exam 13: Gravitation

Of the following where would the weight of an object be the least?

In the formula F = Gm₁m₂/r², the quantity G:

Suitable units for the gravitational constant G are:

Assume that Earth is in circular orbit around the Sun with kinetic energy K and potential energy U, taken to be zero for infinite separation.Then, the relationship between K and U:

A planet travels in an elliptical orbit about a star X as shown.The magnitude of the acceleration of the planet is:

Consider the statement: "Earth moves in a stable orbit around the Sun and is therefore in equilibrium".The statement is:

The mass density of a certain planet has spherical symmetry but varies in such a way that the mass inside every spherical surface with center at the center of the planet is proportional to the radius of the surface.If r is the distance from the center of the planet to a point mass inside the planet, the gravitational force on the mass is:

The escape velocity at the surface of Earth is approximately 11 km/s.What is the mass, in units of M_E (the mass of the Earth), of a planet with twice the radius of Earth for which the escape speed is twice that for Earth?

Each of the four corners of a square with edge a is occupied by a point mass m.There is a fifth mass, also m, at the center of the square.To remove the mass from the center to a point far away the work that must be done by an external agent is given by:

The mass of an object:

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 mass m a distance d from the center, inside the inner radius, 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:

A spring scale, calibrated in newtons, is used to weigh sugar.If it were possible to weigh sugar at the following locations, where will the buyer get the most sugar to a newton?

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?

Let F₁ be the magnitude of the gravitational force exerted on the Sun by Earth and F₂ be the magnitude of the force exerted on Earth by the Sun.Then:

Planet 1 and planet 2 are both in circular orbits around the same central star.The orbit of planet 2 has a radius that is much larger than the radius of the orbit of planet 1.This means that:

A rocket ship is coasting toward a planet.Its captain wishes to know the value of g at the surface of the planet.This may be inferred by:

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

An astronaut on the Moon simultaneously drops a feather and a hammer.The fact that they land together shows that:

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: