Gravitational Fields (HL IB Physics)

The gravitational force between two identical uniform spheres of mass M is F when the distance between them d.

If the radius of each sphere is x, what is the correct expression for mass, M?

A satellite of mass m is placed in a geostationary orbit. If the Earth’s angular velocity is ω rad s^–1, what is the circumference of the satellite’s orbit?

A spherical planet of uniform density has two times the mass of the Earth and three times the average radius. The magnitude of the gravitational field strength at the surface of the Earth is g. What is the gravitational field strength at the surface of the planet?

The inverse square law means that halving the radius of a planet results in quadrupling the gravitational field strength at its surface.

The centres of two planets are separated by a distance R. The gravitational force between the two planets is F. What will the force between the planets be when their separation increases to 4R?

A mass at point P gives rise to a gravitational field strength g at point X as shown.

An identical mass is placed at point Q as shown.

What is the resultant gravitational field strength at X in this new situation?

A spacecraft travels away from Earth in a straight line with its motors shut down. At one instant, the speed of the spacecraft is 5.7 km s^-1. After a time of 1000 s, the speed is 5.2 km s^-1.

What is the gravitational field strength acting on the spacecraft during this time interval?

Which of the following statements about uniform gravitational fields is incorrect?

A test mass m moves between position A and B as shown, in the presence of a source mass M. 

Which of the following statements is correct? 

A positive charge Q is deposited on the surface of a small sphere. The dotted lines represent equipotentials.

A small positive point charge is moved from point P closer to the sphere along two different paths X and Y. What is the best comparison of the work done along X and Y, W_X and W_Y?

Equipotential surfaces corresponding to lines of constant gravitational potential are conventionally drawn so that the difference in potential between any two adjacent surfaces is the same. 

Consider the equipotential surfaces for a spherical mass M. Which of the following statements is incorrect? 

Which of the following statements about gravitational fields is correct?

The mass of Jupiter is m_J and the mass of its moon Europa is m_E. 

If their radii is given by r_J and r_E respectively, what is the ratio ?

A satellite of mass 2000 kg is in the Earth’s gravitational field. It moves radially from a point where the gravitational potential is –40 MJ kg^–1 to a point where the gravitational potential is –10 MJ kg^–1. What is the direction of movement of the satellite and the change in its gravitational potential energy?

Which graph shows how the kinetic energy E_K, the potential energy E_P and the total energy E of the international space station varies with distance x from the centre of Earth?

A probe is launched from the surface of the Earth, which has a radius R, at half the required escape velocity. 

What is the maximum height from the surface the probe will reach, before returning to the ground (with a bang)? 

The graph shows the variation of gravitational potential V with distance r from the centre of a spherical planet of mass M and radius R₀. 

Which statement best describes how to determine the gravitational field strength at a distance r = R from the planet?

The gravitational field strength is g and the gravitational potential is V at the surface of Earth, which has a radius of r.  

Which row in the table gives the correct value of the gravitational field strength and the gravitational potential at a height of 2r from Earth's surface? 

The shape of equipotential surfaces in the gravitational field depends on perspective. 

The image below shows equipotential surfaces (represented by dotted lines) due to the Earth’s gravitational field in a ‘local’ frame of reference (close to the Earth’s surface) and in a ‘non–local’ frame of reference (far from the Earth’s surface):

Which line, A to D, in the table shows the variation of gravitational potential V with radial distance r from the Earth’s surface?

You may assume each dotted line represents equal changes in potential ΔV and that r_E represents the radius of the Earth.

The relative positions of a binary star system is shown below:

The line XY joins the surface of the star of mass m to the surface of the star of mass M > m. Assume the stars have the same diameter.

Which graph correctly represents the variation of the gravitational potential ϕ along the line XY? 

Planet Z, with centre O, is shown in the figure below.

The radial distances OP is equal to the OX, and OQ is equal to OY, such that PX and QY are loci of Planet Z.

Which of the following statements is incorrect?

Two objects X and Y of equal mass, m and distance, D apart move with a constant speed v in circular orbit about their common centre of mass CM. X has a charge of +6.0 nC and Y has a charge of –6.0 nC.

Which graphs shows the electric potential, V and gravitational potential, φ,  against position along the straight-line joining X and Y?

The Earth has radius, r and mass M. Which expression could be used to calculate the minimum time, T of one Earth-day for the material at the equator to just remain on the surface?

A space probe with mass m is launched from the surface of the Earth’s equator into orbit. The total energy E_t given to the space probe is:

where G is the gravitational constant and M and r_E are the mass and radius of Earth.

What is the height of the space probe’s orbit above the Earth’s surface?

Two satellites, X and Y, of equal mass, orbit a planet at radii R and 2R respectively.

Which one of the following statements is correct?

Observations are made on two separate planetary system's suns of mass M₁ and mass M₂.

Their orbiting planets, P₁ and P₂ have masses of m₁ and m₂, and are observed to have identical orbits in shape and magnitude. P₁ completes an orbit in a quarter of the time taken by P₂.

Which statement can astronomers reasonably deduce?