Gravitational Fields
Gravitational fields and gravitational field strength
● All objects with mass create a gravitational field around them
● This field extends to infinity but gets weaker as the distance from the center of
mass of the object increases, becoming negligible at long distances
● Any other object with mass placed in a gravitational field will experience an
attractive force towards the center of mass of the object creating the field
○ For objects on Earth, we call this gravitational attraction the object’s weight
● The gravitational field strength at a point within a gravitational field is defined as
the gravitational force exerted per unit mass on a small object placed at that point
within the field
𝐹
○ g= 𝑚
○ Unit is Newtons per kilogram, the same as the unit for acceleration
● F = mg is the same as F = ma
○ Therefore, gravitational field strength at a point is the same as the
acceleration of free fall of an object at that point
○ g=a
● Gravitational field strength is a vector quantity and always points towards the
center of mass of the object, creating
the gravitational field
● Gravitational field lines help us
map the gravitational field pattern
around an object
○ These lines don’t cross
○ The arrows show the
direction of the force on a mass at that
point in the field
● Since gravitational force is
always attractive, te direction of the
gravitational field is always towards the center of mass of the object producing the
field
○ A stronger field is represented by field lines that are closer together
● The field lines around a spherical mass from a radial
field
● The gravitational field strength decreases with
distance from the center of the mass, as shown by
the field lines getting further apart
● The radial fields for a spherical mass and a single
point mass are similar
, ○ Therefore a star or
planet can be modelled as a point
mass, with field lines converging
at the center of mass of the object
● If the field lines are parallel
and equidistant, the field is a
uniform gravitational field
● In a uniform field, the
gravitational field strength does
not change
Newton’s law of
gravitation
● It describes the forces
between any objects that have
mass
● Can be used to explain both
the motion of the planets around the Sun and why objects near the surface of the
Earth fall towards the ground
● Consider 2 objects of mass M and m separated from each other by a distance r
○ Each objects creates its own gravitational field and the
interaction of these fields gives rise to forces between the
objects
○ According to Newton’s 3rd Law, the 2 objects must
experience a force of the same magnitude but in opposite
directions
● Newton’s law of gravitation states the force between 2 point
masses is:
○ Directly proportional to the product of the masses F ∝ Mm
○ Inversely proportional to the square of their separation or
1
distance F ∝ 𝑟2
● We can write this as an equation using the gravitational constant
G
○ The minus sign shows that the gravitational force is an attractive force
𝐺𝑀𝑚
○ F = - 𝑟2
● The value for G is 6.67 x 10-11 N m2 kg-2
● The attractive force F between objects decreases with distance in an
inverse-square relationship
○ Double the distance, and the force between objects will decrease by a
factor of 4
Gravitational fields and gravitational field strength
● All objects with mass create a gravitational field around them
● This field extends to infinity but gets weaker as the distance from the center of
mass of the object increases, becoming negligible at long distances
● Any other object with mass placed in a gravitational field will experience an
attractive force towards the center of mass of the object creating the field
○ For objects on Earth, we call this gravitational attraction the object’s weight
● The gravitational field strength at a point within a gravitational field is defined as
the gravitational force exerted per unit mass on a small object placed at that point
within the field
𝐹
○ g= 𝑚
○ Unit is Newtons per kilogram, the same as the unit for acceleration
● F = mg is the same as F = ma
○ Therefore, gravitational field strength at a point is the same as the
acceleration of free fall of an object at that point
○ g=a
● Gravitational field strength is a vector quantity and always points towards the
center of mass of the object, creating
the gravitational field
● Gravitational field lines help us
map the gravitational field pattern
around an object
○ These lines don’t cross
○ The arrows show the
direction of the force on a mass at that
point in the field
● Since gravitational force is
always attractive, te direction of the
gravitational field is always towards the center of mass of the object producing the
field
○ A stronger field is represented by field lines that are closer together
● The field lines around a spherical mass from a radial
field
● The gravitational field strength decreases with
distance from the center of the mass, as shown by
the field lines getting further apart
● The radial fields for a spherical mass and a single
point mass are similar
, ○ Therefore a star or
planet can be modelled as a point
mass, with field lines converging
at the center of mass of the object
● If the field lines are parallel
and equidistant, the field is a
uniform gravitational field
● In a uniform field, the
gravitational field strength does
not change
Newton’s law of
gravitation
● It describes the forces
between any objects that have
mass
● Can be used to explain both
the motion of the planets around the Sun and why objects near the surface of the
Earth fall towards the ground
● Consider 2 objects of mass M and m separated from each other by a distance r
○ Each objects creates its own gravitational field and the
interaction of these fields gives rise to forces between the
objects
○ According to Newton’s 3rd Law, the 2 objects must
experience a force of the same magnitude but in opposite
directions
● Newton’s law of gravitation states the force between 2 point
masses is:
○ Directly proportional to the product of the masses F ∝ Mm
○ Inversely proportional to the square of their separation or
1
distance F ∝ 𝑟2
● We can write this as an equation using the gravitational constant
G
○ The minus sign shows that the gravitational force is an attractive force
𝐺𝑀𝑚
○ F = - 𝑟2
● The value for G is 6.67 x 10-11 N m2 kg-2
● The attractive force F between objects decreases with distance in an
inverse-square relationship
○ Double the distance, and the force between objects will decrease by a
factor of 4
