Unit 1 Mechanics

1.4 Gravitation

Learning Outcomes

  1. State the inverse square law of gravitation F = GMm/r2
  2. Carry out calculations using the relationship in 1
  3. Define Gravitational field strength
  4. Sketch gravitational field lines for an isolated point mass and for two point masses
  5. State that the graviational potential at a point in a gravitational field is the work done by external forces in bringing unit mass from infinity to that point.
  6. State that the zero of gravitational potential is taken to be zero at infinity
  7. State the expression for the gravitational potential -GM/r at a distance r from mass m
  8. Explain what is meant by a conservative field
  9. Explain the terms 'escape velocity'
  10. State that the motion of photons is affected by gravitational fields
  11. State that within a certain distance of a sufficiently dense body, the escape velocity is greater than c, hence nothing can escape from such a body, eg a black hole
  12. Carry out calculations involving orbital speed, period of rotation and radius of orbit of satellites

Aids to Understanding

Homework Due Friday

Suggested Homework..Try this for Friday 14th October

Suppose we wish to put a spacecraft in a geo-stationary orbit around the Earth. The Earth's mass is 6.0 x 1024 kg, the Earth's radius is 6.3 x 106 m and the height of a geo-stationary orbit is 3.6 x 107 m.
1. (it might be a good idea to draw the situation roughly to scale)

i) Calculate the gravitational field strength at this point.
ii) Calculate the force on the spacecraft, of mass 1000 kg, at this point.
iii) Calculate the gravitational potential at this point.
iv) Calculate the gravitational potential energy of a spacecraft at this point.
v) Calculate the speed of the spacecraft at this point.
vi) Calculate the kinetic energy of the spacecraft at this point.
vii) Calculate the total energy of the spacecraft at this point.
viii) By what factor is the answer to vi) larger than v)?
ix) Suppose the spacecraft wishes to leave the Earth and travel to the outer reaches of the solar system to take some pictures. What minimum speed will the spacecraft need to reach?
x) By what factor is the answer to ix) larger than your answer to v)?


Homework problem

Advanced Higher Physics .. Unit 1 Mechanics .. 1.4 Gravitation .. BR (2011)