Gravitational Feilds Flashcards
Define gravitational field.
This is a region of space
Which a mass experiences a force
Due to gravitational attraction of another mass.
Formula for force of a gravitational field.
F ∝ m1, m2
F ∝ 1/r²
F = (m1 m2) / r²
[K = G]
G > universal gravitational constant
G= 6.67x10⁻¹¹ Nm²/Kg²
Newton law of gravitation.
This states that the gravitational force of attraction between two point masses is proportional to the products of the masses and inversely proportional to the square of their separation distance
What happens to the force due to gravity when the masses are twice as far away ?
It reduces
Formula for gravitational field strength
Gs = Fg/m (N/ kg)
Fg = force due to gravity or weight
First law of Keplers
The planet revolves in an elliptical orbit
Second law of Keplers
Each planet revolves in such a way that the imaginary line joining it to the sun sweeps out equal areas unequal times
Third law of Keplers
The square of the periods of revolution of the planets are proportional to the cubes of their mean distances from the sun.
T² ∝ r³
Prove T² ∝ r³
Proof = Fg = Fc
(G me ms)/ r² = (ms v²) / r
Once they are set equal, ms and Ms cancel each other. r cancels one r
(G me) / r = v²
Since v = 2πr/T
(2πr/T)² = (Gme/r)
4 π² r² / T² = Gme / r
Cross multiply with the intention of isolating T²
4 π² r² (r) = Gme (T²)
4 π² r³ = Gme (T³)
Divide both side by Gme
T³ = (4 π² r³) / Gme
Since k = (4 π²) / Gme
T² = Kr³
T² ∝ r³
Define artificial satellites
It is a huge body that moves around a planet in an orbit due to the force of gravitational attraction
Define parking orbit
A parking orbit is a path in space of the satellite which makes it appear to be in the same position, relative to the observer at a point.
Uses of parking orbit
1) many geostationary satellites are required for efficient broadcasting
2) communication can only occur provided, there is no obstruction between the transmitter and the receiver
