H2 Physics - Gravitational Fields

State Newton’s Law of Gravitation

It states that two point masses attract each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them

State the constant G

6.67 x 10⁻¹¹ N m² kg⁻²

State the formula for magnitude of gravitational force between 2 masses

F = GMm/r²

Define a gravitational field

It is the region of space in which a mass placed in that region experiences a gravitational force

Define gravitational field strength at a point in space

It is the gravitational force experienced per unit mass at that point

State the 2 formulae for gravitational field strength

• g = F/m

• g = GM/r²

State whether gravitational field strength is a vector or scalar quantity

Vector quantity

State how gravitational field strength can be determined in a system with many masses

It is the vector sum of the individual gravitational field strengths due to each mass at that point

Describe how g varies inside and outside a uniform sphere

• Inside the sphere, g increases linearly from 0 to its maximum from the centre to the edge of the sphere (g = Gρvπr)

• Outside the sphere, g decreases at a decreasing rate since g is inversely proportional to r²

Define gravitational potential energy

It is the work done by an external force in bringing the mass from infinity to that point

State the 2 formulae for GPE

U = mgh (close to earth)

U = -GMm/r (can be used in any case)

Define gravitational potential

It is the work done per unit mass by an external force in bringing a small test mass from infinity to that point

State the 2 formulae for gravitational potential

• Φ = U/m

• Φ = -GM/r

State the gravitational potential at infinity

Zero

State whether gravitational potential is a scalar or vector quantity

Scalar quantity

State how the gravitational potential can be found with multiple masses in a system

It can be found by adding the individual potentials at that point due to each mass

State the formula which relates gravitational field strength and gravitational potential

g = -dΦ/dr

Describe how the escape velocity formula can be derived

• At infinity, U, Eₖ = 0 so by the conservation of energy Eₜ = U + Eₖ = 0

• Sub in the respective formula for both U and Eₖ and solve for v (escape velocity)

State the formula for escape velocity

vₘᵢₙ = √(2GM/R)

Describe why free fall acceleration is not the same as g at all parts of the Earth

• At the geographic poles, free fall acceleration will be equal to g

• However, at any point of the earth, some of the acceleration due to gravity is used to provide the centripetal acceleration so the free fall acceleration decreases closer to the equator (a_f = g - a꜀)

Describe 2 factors which lead to non uniform gravitational field strength of earth

• The earth is not a perfect sphere so there will be parts of the Earth which are further from the centre

• The earth does not have a uniform density so different parts of earth have different masses

State Kepler’s third law

The square of the periods of revolution of the planets are directly proportional to the cubes of their mean distances from the sun

State the formula for the kinetic energy of a satellite

Eₖ = ½GMm/r

State the formula for the total energy of a satellite

Eₜ = -½GMm/r

State the relationship between the total energy of a body and whether it will be bound to the earth

• Eₜ < 0: bounded

• Eₜ = 0: just reaches infinity

• Eₜ > 0: goes past infinity

Define a geostationary satellite

It is a satellite which remains at a fixed position in the sky as viewed from any location on the Earth’s surface

State the 3 conditions that a geostationary satellite must satisfy

• Orbital period is the same as that of the Earth around its axis of rotation (24h)

• Direction of rotation is the same as that of the Earth about its axis of rotation (west to east)

• Plane of orbit lies in the same plane as the equator (satellite is above the equator)

State the 3 advantages of the geostationary satellite

• There is continuous surveillance of the region under it

• It is easy to communicate with it since the transmitters and receivers can point in fixed positions (good for communication purposes)

• The satellite can transmit and receive signals over a large area (due to its high altitude)

State the 3 disadvantages of geostationary satellites

Since they are usually very high up this leads to:

• A significant loss in signal strength

• Poorer resolution in imaging satellites

• Time-lag in telecommunication