Gravitational Fields

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Gravitational fields lines

arrows show direction of g force on mass placed in field

spacing - the closer the bigger the strength

From Earth the field lines are radial

Uniform - field lines are equally spaced, parallel ...

Newton's law of gravitation

Any 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 their separation.

Force ∝ 1/distance^2 or Force ∝ 1/r^2

Force ∝ Mm (product of masses)

Therefore:

F ∝ Mm/r^2

F=-GMm/r^2 G=6.67*10^-11

greater mass - greater force

greater distance - weaker pull

-sign means force is attractive

g=9.81ms^-2

g - gravitational field strength is the force per unit mass

g=F/m F=-GMm/r^2

g=-GM/r^2

Orbiting under gravity

Gravity provides the centripetal force keeping it in orbit. The satellite follows a circular path because the gravitational force is at right angles to its velocity.

F=mv^2/r F=GMm/r^2

mv^2/r = GMm/r^2

v^2 = GM/r (speed at which satellite must travel to stay in circular orbit)

Orbital period

v=2π/T

v^2=GM/r

(2πr/T)^2 = GM/r

T^2 = (4π^2*r^3)/GM

T^2 ∝ r^3