CIE AS & A Level Physics 9702: Topic 13: Gravitational fields- Unit : 13.1 Gravitational field Study Notes

Defining Gravitational Field

•  There is a force of attraction between all masses
• This force is known as the ‘force due to gravity’ or the weight
• The Earth’s gravitational field is responsible for the weight of all objects on Earth
•  A gravitational field is defined as:
• A region of space where a mass experiences a force due to the gravitational attraction of another mass
• The direction of the gravitational field is always towards the centre of the mass

• • Gravitational forces cannot be repulsive

•  The strength of this gravitational field $(g)$ at a point is the force $\left(F_g\right)$ per unit mass $(m)$ of an object at that point:

                                                                                            $
                                                                                       \mathrm{g}=\frac{F_g}{m}
                                                                                              $

• Where:

• • $\mathrm{g}=$ gravitational field strength $\left(\mathrm{N} \mathrm{kg}^{-1}\right)$
  •  $F_g=$ force due to gravity, or weight (N)
  •  $\mathrm{m}=$ mass $(\mathrm{kg})$

• This equations tells us:

• • On planets with a large value of $g$, the gravitational force per unit mass is greater than on planets with a smaller value of $g$

• On such planets such as Jupiter, an object’s mass remains the same at all points in space. However, their weight will be a lot greater meaning for example, a human will be unable to fully stand up

                     A person’s weight on Jupiter would be so large a human would be unable to fully stand up

• The direction of a gravitational field is represented by gravitational field lines
•  The gravitational field lines around a point mass are radially inwards
• The gravitational field lines of a uniform field, where the field strength is the same at all points, is represented by equally spaced parallel lines

• • For example, the fields lines on the Earth’s surface

Gravitational field lines for a point mass and a uniform gravitational field

•  Radial fields are considered non-uniform fields

• • The gravitational field strength $g$ is different depending on how far you are from the centre

•  Parallel field lines on the Earth’s surface are considered a uniform field

• •  The gravitational field strength $g$ is the same throughout

Exam Tip
Always label the arrows on the field lines! Gravitational forces are attractive only. Remember:

• For a radial field: it is towards the centre of the sphere or point charge
• For a uniform field: towards the surface of the object e.g. Earth