Gravitational fields (chapter 2)

• Field of Force: Region of space where there is force acting on an object
• Line of force: An imaginary line which represents the direction and the strength of a field
• Newton's Law of Gravitation: It states that the gravitational force between two points is equal to the product of their masses and is inversely proportional to the square of their separation (remember that the separation is to be taken from the centers of the respective masses).

F ∝ m₁m₂/r²

F=Gm₁m₂/r²

(G is the universal Gravitational Constant)

note: objects are considered as point masses when the seperation between them is very large than their relative sizes.

• Gravitational field strength: Gravitational field strength is defined as force per unit mass.

GMm/r² ÷ M = Gm/r²

Graphs representing the variation of gravitational field strength relative to the separation from Earth's surface

Graph representing the gravitational field strength between 2 planets

• Gravitational potential: It is the work done per unit mass in bringing an object from infinity to that point. Its unit is J/kg and the symbol used to represent it is Ф. 

Ф= -Gm/r

Gravitational potential energy is negative because gravitational forces are all attractive.

Graph representing the variation in gravitational potential relative to the separation

Graph representing the gravitational potential between 2 planets

the graph shows that more energy is required to escape from the larger planet as it has greater gravitational field strength.

• Gravitational potential energy at a point: It is the work done by the whole body to move it from infinity to that point.

Relating the linear motion of a particle towards the center of the planet with law of conservation of energy

ΔK.E = ΔP.E

1/2mv²- 0 = 0 - (-GMm/r)
v² = 2Gm/r
v² = 2Ф

• Geostationary satellites: Geostationary satellites are satellites that appear to be above a certain point on earth all the time. It is because the geostationary satellites have the same period as the period of the Earth's rotation. The following are their properties:

1. They are launched from the equator. (they have equatorial orbits)
2. Their rotation is from West to east.
3. Their altitude above the surface of earth is 3600 km.

Finding the Linear speed of satellite

since the gravitational force provides the satellite with centripetal force:

Gravitational force = centripetal force

GMm/r² = mv²/r

v² = GM/r