Gravitational Fields

Gravity is a force of ATTRACTION. It exists between any two masses. It is negligible if the masses are small.

• Mass of an object creates a force field around itself

• any other mass placed in this field is attracted towards the object

• the second mass will also have a force field around itself, so it pulls on the first mass with an equal and opposite force

• Force field = Gravitational field

If small test mass is close to a massive body - the small mass and the big mass attract each other with an equal and opposite force, but the force is too small to move the massive body by a noticeable amount. The small mass will be pulled by the large mass, following the field line.

• Field lines show direction of force (always towards the centre of the body for gravity)

g is the force per unit mass on a small test mass placed in the field

g = F/m

Free fall

• Weight = force of gravity acting on the object

• acceleration = g

Field Patterns

• Radial Fields - gravitational force directed to a central point (like the spokes of a wheel)

• Uniform Fields - gravitational field strength is always constant in magnitude and direction throughout the field - so field lines are parallel and equally spaced

• When looking at a planet from a zoomed out view, the field lines present radially. When looking at a planet zoomed in, the field lines appear uniform.

Gravitational Potential

• Increase distance from centre of the planet = decrease g

• GPE = energy of an object due to its position in a gravitational field.

• 0 GPE at infinity

• GPotential (V) = the GPE per unit mass of a small test mass (The work done per unit mass to move a small object from infinity to that point)

• 0 V at infinity

V = W/m or W = mΔV

ΔV = V2-V1

Potential Gradients

• Equipotential = surfaces of constant potential

• No work needs to be done to move along an equipotential line

• The closer the equopotentials, the greater the potential gradient, and the stronger the field.

• Further away from the Earth’s surface, the equipotentials for equal increases of potential are spaced further apart

• Near the surface of a small region of a planet, the equipotentials are horizontal (parallel to the ground) - as gravitational field around a small region is uniform.

• POTENTIAL GRADIENT IS THE CHANGE OF POTENTIAL PER METRE AT A POINT

g = ΔV/Δr (here, g is the potential gradient, and is the NEGATIVE VALUE OF THE FIELD STRENGTH)

Planetary Fields

• As the distance from the surface of the planet increases to the Radius of the planet (r=R), then the g and distance are directly proportional (as distance increases, the gravitational field strength increases

• when the distance exceeds the Radius of the planet (r>R), then it follows an inverse square relationship with g’

Escape velocity = minimum velocity an object must be given to escape from the planet when projected vertically from the surface.

v = sqroot(2GM/R)