3.0 INTRODUCTION
A gravitational field is a region of space around a mass where another mass experiences a force of gravitational attraction.
GRAVITATIONAL POTENTIAL: Gravitational potential (V) at a distance (r) from a mass (M) is defined as the work done in bringing a unit mass from infinity to that point.
3.1 NEWTON’S LAW OF GRAVITATION
Newton’s Law of Gravitation states that every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres.
MATHEMATICAL EXPRESSION – The law can be Expressed Mathematically as:
F = G * (m₁ * m₂ / r²)
Where;
- F is the gravitational force between the two masses,
- G is the gravitational constant (approximately 6.674 × 10⁻¹¹ Nm2/kg2).
- m₁ and m₂ are the masses of the two objects,
- r is the distance between the centres of the two masses.
3.2 GRAVITATIONAL FIELD STRENGTH (g)
Gravitational field strength (often represented by the symbol ‘g’) is the strength of the gravitational field at a particular point, defined as the gravitational force per unit mass.
CHARACTERISTICS OF GRAVITATIONAL FIELD STRENGTH (g)
- It is a vector quantity (has direction).
- It is approximately 9.81m/s² at Earth’s surface; it varies with location.
- Its unit is N/kg.
- It describes the force experienced by an object in a gravitational field.
3.3 GRAVITATIONAL CONSTANT (G)
A proportionality constant in Newton’s law of gravitation.
CHARACTERISTICS OF THE GRAVITATIONAL CONSTANT (G)
- It is a scalar quantity (no direction).
- It is approximately 6.674 × 10⁻¹¹ Nm2/kg2.
- Its unit is Nm2/kg2.
- It is used to calculate the gravitational force between two masses.
3.4 ESCAPE VELOCITY
It is the minimum speed an object must reach to break free from a celestial body’s gravitational pull without any additional propulsion.
Mathematically, escape velocity is given as:
v = √(2GM/R)
Where:
G = Gravitational constant (6.674 × 10⁻¹¹ Nm2/kg2),
M = Mass of the celestial body,
R = Radius of the celestial body.
3.5 DIFFERENCES BETWEEN MASS AND WEIGHT
- Mass: Amount of matter (kg), Weight: Force of gravity on an object (N).
- Mass: Scalar quantity: constant, Weight: Vector quantity; varies with gravity.
- Weight: W = mg (mass × gravitational acceleration).
- Mass: Measured in Kilograms (kg), Weight: Measured in Newtons (N).
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