Universal Gravitational Constant Value is,

G = 6. 6743 x 10^-11 N.m².kg ^-2 or 6.6743×10^-8 Dyn.cm².g^-2

Universal Gravitational Constant is a physical constant involved in the calculations of gravitational effects. It is the gravitational force acting between two bodies of unit mass. The Universal Gravitational Constant is used in different formulas of Gravitation.

In this article, we will look into the Universal Gravitational Constant, Universal Gravitational Constant Dimension, Universal gravitational constant Value, and others in detail.

What is a Universal Gravitational Constant?

The Universal Gravitational Constant, also known as the gravitational constant, is a fundamental physical constant involved in the calculation of gravitational effects in Sir Isaac Newton’s law of universal gravitation and in Albert Einstein’s theory of general relativity. It is denoted by the capital letter “G” and has a value of approximately.

Value of Universal Gravitational Constant

The value of the Universal Gravitational constant G is given below:

Universal Gravitational Constant Value:

G = 6. 6743 x 10^-11 N.m².kg ^-2 or 6.6743×10^-8 Dyn.cm².g^-2

Learn more about, Gravitational Force

Newton’s Universal Gravitation Law

Newton’s law of universal gravitation states that the attractive force between two objects is equal to G times the product of their masses. It is inversely proportional to the square of the distance between them, directed along the line connecting their centers of mass.

Learn more about, Newton’s Universal Law of Gravitation

Universal Gravitational Constant Mathematical Representation

The mathematical representation of the Universal Gravitational Constant, denoted by “G,” is given by the formula:

F = G (m₁m₂/r²)

where,

• F is the gravitational force between two objects
• G is the Universal Gravitational Constant
• m₁ and m₂ are Masses of the Two Objects
• r is Distance between two Objects

This formula is derived from Newton’s law of universal gravitation, which states that the attractive force between two objects is equal to G times the product of their masses, inversely proportional to the square of the distance between them, directed along the line connecting their centers of mass.

S I Units of Universal Gravitational Constant

SI units of G are N·m²·kg^-2

CGS unit of Universal Gravitational Constant is dyn·cm²·g^-2.

Universal Gravitational Constant Dimensional Formula

The dimensional formula of the Universal Gravitational Constant, denoted by “G,” is

[M^-1L³T^-2]

Learn more about Universal law of Gravitation

Application of Universal Gravitational Constant

Here are some examples of how the Universal Gravitational Constant is used in various situations:

Calculating the gravitational force between two objects: Using the formula

F = Gm₁m₂/r²

We can calculate the gravitational force between two objects with masses m1​ and m2​ and a distance r between them. For example, if m₁​ is 1 kg, m_2​ is 2 kg, and r is 3 m, the gravitational force between them would be:

F= G 1kg × 2kg/ 3m = 0.002N

Measuring Mass of Celestial Objects: The gravitational constant can be used to measure the mass of celestial objects, such as stars, planets, or galaxies, by observing their gravitational effects on nearby objects. For example, the mass of our planet can be calculated using the gravitational constant and the acceleration due to gravity on Earth.

Testing Equivalence Principle in General Relativity: The gravitational constant plays a crucial role in testing the equivalence principle, which states that the laws of physics are the same in all inertial frames. By measuring the gravitational force between objects in different frames, scientists can verify the consistency of the laws of gravity.

Studying Motion of Celestial Bodies: The gravitational constant is used in the analysis of the motion of celestial bodies, such as planets and moons, under the influence of gravity. By knowing the masses of the objects and the distance between them, scientists can calculate the gravitational force acting on them and predict their motion.

Related Resources,

• Kepler’s Law of Planetary Motion
• Law of Inertia
• Centripetal and Centrifugal Force

Examples on Universal Gravitational Constant

Example 1: Two particles of equal mass “m” go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their center of mass is

• (A) √Gm/R
• (B) √Gm/4R
• (C) √Gm/3R
• (D) √Gm/2R

Solution:

Option (B) is Correct

Gm²/4R² = mV²/R

V = √Gm/4R

Example 2: A simple pendulum has a time period T₁ when on the earth’s surface, and T₂ when taken to a height R above the earth’s surface, where R is the radius of the earth. The value of T₂/T₁ is

• (a) 1
• (b) 3
• (c) 4
• (d) 2

Solution:

Option (d) is Correct

Time period of a simple pendulum = 2π√l/g

On the surface of earth g₁ = GM/R²

At a height R above the earth g₂ = GM/(2R)²(g₁/g₂) = (4/1)T = 2π√(l/g)

Time period on the surface of the earth T₁ = 2π√l(R)²/GM

Time period on the surface of the earth T₂ = 2π√l(2R)²/GMT₂/T₁ = 2

Example 3: The mass of a spaceship is 1000 kg. It is to be launched from the earth’s surface out into free space. The value of ‘g’ and ‘R’ (radius of the earth) is 10 m/s2 and 6400 km respectively. The required energy for this work will be

• (a) 6.4 x 1010 Joules
• (b) 6.4 x 1011 Joules
• (c) 6.4 x 108 Joules
• (d) 6.4 x 109 Joules

Solution:

Option (a) is Correct

Energy required is given by = GMm/R

= gR² ×m/R (∵g = GM/R²)

= mgR = 1000 × 10 × 6400 × 103= 64 × 109 J= 6.4 × 1010 J

Practice Questions on Universal Gravitational Constant

Q1. The mass of a spaceship is 2000 kg. It is to be launched from the earth’s surface out into free space. The value of ‘g’ and ‘R’ (radius of the earth) is 20 m/s² and 8000 km respectively. The required energy for this work will be?

Q2. Two particles of masses “4m” and 2m respectively go around a circle of radius R under the action of their mutual gravitational attraction. The speed of each particle with respect to their centre of mass is?

Q3. What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius R in a circular orbit at an altitude of 4R?

Universal Gravitational Constant-FAQs

1. What is the Use of Universal Gravitational Constant?

Universal Gravitational Constant (G) is used in Newton’s Law of Universal Gravitation to calculate the gravitational force between two objects with mass.

2. What is the SI unit of the Universal Gravitational Constant?

The SI unit of the Universal Gravitational Constant is Newton meter squared per kilogram squared (N·m²/kg²).

3. What is the Dimension of Universal Gravitational Constant?

The dimension of the Universal Gravitational Constant is [M^-1L³T^-2].

4. What is the Formula using Universal Gravitational Constant?

Gravitational force (F) between two masses (m₁ and m₂) at a distance (r) is given by the formula:

F= G⋅m₁⋅m₂/r²

5. What is the Value of Universal Gravitational Constant?

Value of the Universal Gravitational Constant (G) is 6.674×10⁻¹¹ N\m²/kg²