January 16, 2025
Exploring Gravitation: Laws, Formulas, and Theories
Gravitation or gravity means the attracting force acting between any two quantities. Every object in the universe tends to force every other object with a particular force, though in many circumstances the force cannot be measured because of the very vast distance between them. Besides, the range of gravity is sort of infinite, but the impact will gradually decrease with distance.
Describe Newton’s Laws of Gravitation
Newton's law of universal gravitation states that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula that represents Newton’s laws of gravitation:
F = Gm1m2/r2
Where,
F is the gravitational force between two objects.
G is the universal gravitational constant with a value of 6.674 × 10-11 Nm2kg-2.
m1 is the mass of one massive body measured in kg.
m2 is the mass of the second body measured in kg.
r is the distance of separation between them measured in kilometre (Km).
What do you mean by Acceleration due to gravity?
Acceleration due to gravity is defined as the magnitude of acceleration obtained by an object due to the presence of gravitational force. Its SI unit is m/s2. Acceleration due to gravity is a vector quantity as it has both magnitude and direction. It is represented by g. The standard value of g on the surface of the earth at sea level is 9.8 m/s2.
f = GmM/(R+h)2
Where
f = Force between two bodies
G = Universal gravitational constant that is equal to 6.67 × 10 -11 Nm 2 kg -2
m = Mass of the object
M = Mass of the earth
R = Radius of the earth
h = The distance of the body from the surface of the earth
Since h (h<<R) is smaller than the radius of the Earth, it can be rewritten as
f = GMm/r2 —---(i)
As you all know, Force acting on a body due to gravity is given by the formula
f = mg —--(ii)
Equating both (i) and (ii), we get the formula for acceleration due to gravity as
g = GM/r2
Factors affecting the value of acceleration due to gravity g:
- Effect of altitude above the Earth surface
- Effect of depth below the surface of the Earth
- The shape of the Earth
- Earth’s rotational motion about its own axis.
Gravitational Potential
The work done in placing a unit test mass from infinity into the gravitational field of source mass is referred to as gravitational potential.
It is denoted by Ug.
- Gravitational potential is represented by the formula, Ug = – GM / r
- Gravitational potential is a scalar quantity and its SI unit is J/Kg.
- Gravitational Potential is always negative.
Gravitational Potential Energy
Potential energy of any object at any point of gravitational field is the amount of work done in taking an object from an infinite distance to that point. It is denoted by U.
Gravitational Potential Energy is defined by the formula= – GMm / r
The negative sign indicates that the gravitational potential energy decreases as the distance increases.
Gravitational potential energy at height h from surface of earth is given by the formula:
Uh = – GMm / (R + h) = mgR2 / (R+h)
Kepler’s Laws of Planetary Motion
- The law of orbit: Every planet moves in an elliptical orbit with the Sun at one of the two foci.
- The Law of Area: The radius vector of a planet drawing from the sun, describes equal areas in equal time intervals, that is, the rate of areal increase is constant.
- The Law of Period: The square of the time period of revolution of the planet around the sun is in directly proportion to the cube of semi-major axis of its elliptical orbit.
What do you understand by the term weightlessness?
Weightlessness is defined as the state or situation when a body experiences little to no gravitational force. Weightlessness is experienced by a body when the net force acting on an object is zero, thereby making it experience zero gravity. This can occur under various situations:
- When an object is in a free fall state.
- During a parabolic flight which is used to train astronauts.
- Inside a satellite.
What do you mean by Escape Velocity?
Escape velocity is defined as the minimum amount of velocity that is required if a body has to be vertically projected upwards from the surface of the earth in such a way that it just crosses the Earth’s gravitational field and never returns back to the Earth.
Escape velocity is calculated by:
ve = √(2GM / R)
= √2gR
NOTE: Escape velocity of the Earth is 11.2 km/s.
Describe Binding Energy
The energy which is used in order to pull a satellite from its orbit around the earth (planet) to infinity is called binding energy of a satellite.
The binding energy of satellite with the mass m is given by:
BE = + GMm / 2r
Define orbital velocity
Orbital velocity is the speed with which a body moves in its orbit around the other body. The objects which are in uniform circular motion around the earth are said to be in orbit. This velocity of the object depends on the distance of the particular object from the centre of the earth.
This velocity is usually provided to the artificial satellites such that they orbit around any specific planet.
Orbital velocity is defined by the formula,
vo = √GM / r = R √g / (R + h)
where, M = mass of the planet, R = radius of the planet, and h = height of the satellite from planet surface.
FAQS:
1. What is the formula with which I can define Gravitational force?
The formula to represent gravitational force is:
F = Gm1m2/r2
where F is the force of gravitation, G is the Universal Gravitational constant, m1 is the mass of one body, m2 is the mass of the second body and r is the distance of separation between them.
2. What is the formula of Gravitational Potential Energy?
Gravitational Potential Energy is defined by the formula= – GMm / r
3. What do you mean by Earth Satellites?
Earth satellites are objects that are in a circular motion around the Earth. Their motion is very much like the rotation of the different planets around the sun and therefore Kepler laws of planetary motion can be applied to them.
