Gravitational field

Gravitational field

Space/field in which mass experiences a force

• Force per unit mass (g = Gm/r²) or grav force/mass

Grav. Field lines

Closer together = stronger field

Newton’s law of gravitation

Two point masses attract each other with force directly proportional to product of masses, and inversely proportional to square of their separation

Equation for force between two masses (gravitational force)

F = GMm/r²

Gravitational field strength

At a point in gravitational field, force exerted per unit mass

Equation for gravitational field strength

W = mg (W = F)

mg = GMm/r²

• g = GM/r²

Why g is constant for small changes in height near earths surface

Change in r is almost insignificant (relative to radius of earth)

What causes circular orbit

Object experiences gravitational force (gravitational field strength), which is/ provides the centripetal force of an object (inwards)

Equation for circular orbit (given w/omega)

GMm/r² = mw²r

Equation for circular orbit (given v/speed of satellite)

GMm/r² = mv²/r

Equation for period of circular orbit

• w = 2pi/T

• Substitute into GMm/r² = mw²r

• T² = 4piR³/GM

Conditions for geostationary orbit

• Circular orbit

• 24 hr. Orbit

• Orbit above equator

• Orbit from west to east

Gravitational potential

Work done per unit mass in bringing mass from infinity to a point

• -GM/r

Gravitational potential energy

Work done in moving mass from infinity to a point

• -GMm/r

• Grav. Potential energy = Gravitational potential x mass

Why gravitational potential near to a point mass is negative

• GP = 0 at infinity

• Work done is lost to move mass to infinity

• Gravitational forces are always attractive