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Module 5: Newtonian world and astrophysics

5.4 Gravitational fields

5.4.1

Point and spherical masses

(a) gravitational fields are due to objects having mass

Multiple Choice

Structured Questions

 

  

(b) modelling the mass of a spherical object as a point mass at its centre

  

(c) gravitational field lines to map gravitational fields

  

(d) gravitational field strength;

g = F/m

  

(e) the concept of gravitational fields as being one of a number of forms of field giving rise to a force.

 Learners will be expected to link this with
section 6.2

5.4.2

Newton's law of gravitation

(a) Newton's law of gravitation;

F = -GMm/r2 =- for the force between two point masses

   

(b) gravitational field strength

g = -GM/r2 for a point mass

   

(c) gravitational field strength is uniform close to the surface of the Earth and numerically equal to the acceleration of free fall.

    

5.4.3

Planetary motion

(a) Kepler's three laws of planetary motion

    

(b) the centripetal force on a planet is provided by the gravitational force between it and the Sun

   

(c) the equation

Learners will also be expected to derive this equation from first principles.

(d) the relationship for Kepler's third law T2 ∝ r3 applied to systems other than our solar system

 T2 ∝ r3  

(e) geostationary orbit; uses of geostationary satellites.

Predicting geostationary orbit using Newtonian laws.

    

5.4.4

Gravitational potential and energy

(a) gravitational potential at a point as the work done in bringing unit mass from infinity to that point;

gravitational potential is zero at infinity

    

(b) gravitational potential

Vg = - GM/r
at a distance r from a point mass M;

changes in gravitational potential

 Vg = - GM/r  

(c) force–distance graph for a point or spherical mass;

work done is area under graph

    

(d) gravitational potential energy

E =mVg = - GMm/r
at a distance r from a point mass M

E =mVg

E = - GMm/r

  

(e) escape velocity.

Predicting the escape velocity of atoms from the atmosphere of planets.