Universal Law of Gravitation - Formula, Application, FAQs
Gravity is one of the fundamental forces of nature that governs the motion of planets, stars, satellites, and everyday objects on Earth. Newton’s Law of Universal Gravitation explains how every mass attracts every other mass with a force that depends on their masses and the distance between them. This universal law not only defines gravitational force but also helps in understanding concepts like gravitational constant (G), acceleration due to gravity (g), weight, and the difference between mass and weight. From predicting satellite motion to explaining tides and eclipses, gravitation plays a crucial role in physics. In this article, we will explore Newton’s universal law of gravitation, its formula, applications, importance, and key differences between gravitational force and weight in a clear and concise manner.
This Story also Contains
- Newton's Law of Universal Gravitation
- Gravitational constant
- Weight and Gravitational Force
- Difference Between Gravitational Force and Weight
- Also Read:
- Application of universal law of gravitation-
- What is the Importance of Universal Law of Gravitation
Newton's Law of Universal Gravitation
Every particle in the universe attracts every other particle with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This force acts along the line joining the centres of the two particles.
$
\begin{aligned}
F & \propto m_1 m_2 \\
F & \propto \frac{1}{r^2}
\end{aligned}
$
Combining both proportionalities,
$
F=G \frac{m_1 m_2}{r^2}
$
where $G$ is the universal gravitational constant.
Also read -
Gravitational constant
The gravitational constant $G$ is defined as the gravitational force between two unit masses placed at a unit distance apart in vacuum.
$
G=6.67 \times 10^{-11} \mathrm{~N} \mathrm{~m}^2 \mathrm{~kg}^{-2}
$
SI Unit: $\mathrm{N} \mathrm{~m}^2 \mathrm{~kg}^{-2}$
Weight and Gravitational Force
Weight
The weight of a body is the gravitational force exerted by the Earth on that body.
If a body of mass $m$ is near the surface of the Earth (mass $M$, radius $R$ ), then:
$
W=G \frac{M m}{R^2}
$
Since,
$
g=G \frac{M}{R^2}
$
Therefore,
$
W=m g
$
Where:
- $W=$ weight of the body
- $m$ = mass of the body
- $g=$ acceleration due to gravity
Difference Between Gravitational Force and Weight
| Gravitational Force | Weight |
| Force between any two masses | Force exerted by Earth on a body |
| Given by $(F = G \frac{m_1 m_2}{r^2})$ | Given by (W = mg) |
| Acts between all objects | Acts only when body is under Earth’s gravity |
| Universal | Depends on value of (g) |
Also Read:
Application of universal law of gravitation-
Newton's law of gravitation applies to both large and small objects.
When the distance between two bodies is less than 10^-9 meters, it fails.
Newton's law has a number of applications, two of which are described below:
- This formula proven to be extremely accurate in predicting the orbits and time periods of current artificial satellites.
- This law proved to be quite accurate in predicting solar and lunar eclipses.
What is the Importance of Universal Law of Gravitation
- The earth's gravitational force binds terrestrial objects to it.
- This law explains the attractive force that exists between any two mass objects.
- The force of attraction between the moon and the ocean water causes tides to form in the ocean.
- With the sun, all planets make an elliptical revolution.
Also check-
- NCERT Exemplar Class 11th Physics Solutions
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NCERT Physics Notes:
Frequently Asked Questions (FAQs)
Newton’s law of universal gravitation which states that every particle in universe attracts every particle (other) by force that is directly proportional to the product of their masses as well as the square of their distance inversely.
Gravity is all around us. Planetary orbits, the solar system, and even galaxies are shaped by it. The Sun's gravity stretches all the way to the farthest regions of the solar system, holding the planets in their orbits. The Moon and human-made satellites are kept in orbit by Earth's gravity.
On the surface of the moon, the acceleration due to gravity is 1.625 m/s^2.
No, the value of g varies depending on where you are on the planet's surface. At the equator, gravity's acceleration is smaller than at the poles. This is due to the fact that g is inversely related to radius, and the earth's radius is smaller near the poles and bigger at the equator.
Objects move toward one another, according to Einstein, because of the curvatures in space-time, not because of the force of attraction between them.
