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Gravitational Field Region around a mass where gravitational forces are experienced
Gravitational Field Strength Force per unit mass, (g) → (acceleration)
Equipotential lines : all horizontal lines have the same G.P. (ϕ)
F = w = mg
g = (^) mw [constant]
Measured in ms− Gravitational Potential Energy
G. P. E. = mgh
Gravitational Constant (G) = 6.67 × 10−
F = G
mM
r^2
m Mass of object 1 M Mass of object 2 r Distance between the 2 masses
Gravitational Field Strength
w = mg
g = G
M
r^2
Gravitational Potential G.P.) ( ϕ ) Gravitational Potential Energy G.P.E per unit mass work = F × distance
Gravitational Fields & Circular Motion
Gravitational Fields
Uniform Fields
Force
Gravitational Field Strength
Radial Fields
G. P. E = −G
M
r
d dx (Graviational P otential) =^ Gravitational F ield Strength d dx (−G^ M r ) =^ G^ M r^2
At ∞ G.P.E. is 0 Work is being done on the mass by the field The force is Attraction Force reducing the distance between the 2 masses Note : as you approach infinity the G.P.E. becomes more positive
Radian : angle subtended between 2 radii where the length of the arc equals the radius
Objects in circular motion have constant speed but changing velocity Objects in circular motion are not at equilibrium, they are affected by a net centripetal force
Displacement (S)
S = θr
θ Angle in radians
Angular Velocity / Frequency ( ω )
t
or ω =
T
T Periodic Time
Velocity (v)
v = ωr
Acceleration (a)
a =
v^2
r
or ω²r
Force (F)
F =
mv^2
r
or mω²r
F = G mMr 2 mv r 2 = G mM r^2
v = √^ GMr
Note The orbiting velocity is independent of the mass of the satallite
Polar satellites
conditions rotates around the poles period time between 90 and 105
Why is G.P.E always negative
Circular Motion
Orbits
Orbiting Speed
