Gravity HARD

The mass of Planet X is one-tenth that of the Earth, and its diameter is one-half that of the Earth. The acceleration due to gravity at the surface of Planet X is most nearly

• 2 m/s²

• 4 m/s²

• 5 m/s²

• 7 m/s²

• 10 m/s²

A satellite travels around the Sun in an elliptical orbit as shown above. As the satellite travels from point X to point Y, which of the following is true about its speed and angular momentum?

• Speed remains constant, Angular Momentum remains constant

• Speed increases, Angular Momentum remains constant

• Speed decreases, Angular Momentum decreases

• Speed increases, Angular Momentum decreases

• Speed decreases, Angular Momentum remains constant

A newly discovered planet, "Cosmo," has a mass that is 4 times the mass of the Earth. The radius of the Earth is ( R_E ). The gravitational field strength at the surface of Cosmo is equal to that at the surface of the Earth if the radius of Cosmo is equal to

• ( 1/2 R_E )

• ( R_E )

• ( 2R_E )

• ( √R_E )

• ( R_E^2 )

Two artificial satellites, 1 and 2, orbit the Earth in circular orbits having radii ( R_1 ) and ( R_2 ), respectively, as shown above. If ( R_2 = 2R_1 ), the accelerations ( a_1 ) and ( a_2 ) of the two satellites are related by which of the following?

• ( a_2 = 4a_1 )

• ( a_2 = 2a_1 )

• ( a_2 = a_1 )

• ( a_2 = a_1/2 )

• ( a_2 = a_1/4 )

The radius of the Earth is approximately 6,000 kilometers. The acceleration of an astronaut in a perfectly circular orbit 300 kilometers above the Earth would be most nearly

• 0 m/s²

• 8.0 m/s²

• 5 m/s²

• 9 m/s²

• 11 m/s²

A satellite moves in a stable circular orbit with speed ( v_o ) at a distance ( R ) from the center of a planet. For this satellite to move in a stable circular orbit a distance ( 2R ) from the center of the planet, the speed of the satellite must be

• ( v_o/2 )

• ( v_o/√2 )

• ( v_e )

• ( √2v_o )

• ( 2v_o )

A ball that is tossed straight up from the surface of a small, spherical asteroid with no

atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the

surface of the asteroid. What forces, if any, act on the ball while it is on the way up?

• (A) Only a decreasing gravitational force that acts downward

• (B) Only an increasing gravitational force that acts downward

• (C) Only a constant gravitational force that acts downward

• (D) Both a constant gravitational force that acts downward and a decreasing force that acts upward

• (E) No forces act on the ball.

A ball that is tossed straight up from the surface of a small, spherical asteroid with no

atmosphere. The ball rises to a height equal to the asteroid's radius and then falls straight down toward the

surface of the asteroid. The acceleration of the ball at the top of its path is

• (A) at its maximum value for the ball's flight

• (B) equal to the acceleration at the surface of the asteroid

• (C) equal to one-half the acceleration at the surface of the asteroid

• (D) equal to one-fourth the acceleration at the surface of the asteroid

• (E) zero

A satellite of mass M moves in a circular orbit of radius R with constant speed v. True statements about this satellite include which of the following? I. Its angular speed is v/R. II. Its tangential acceleration is zero. III. The magnitude of its centripetal acceleration is constant.

• (A) I only

• (B) II only

• (C) I and III only

• (D) II and III only

• (E) I, II, and III

Two identical stars, a fixed distance D apart, revolve in a circle about their mutual center of mass, as shown above. Each star has mass M and speed v. G is the universal gravitational constant. Which of the following is a correct relationship among these quantities?

• (A) v^2 = GMD

• (B) v^3 = GM2D

• (C) v^2 = GMD^2

• (D) v^2 = MGD

• (E) v^2 = 2GM/D