What is the Gravitational Constant?

The gravitational constant, represented by the symbol G, is a fundamental constant of nature that determines the strength of the gravitational force between two masses.

It appears in Newton's Law of Universal Gravitation, allowing scientists to calculate the gravitational attraction between any two objects.

The value of the gravitational constant is:

$\boxed{G=6.67\times10^{-11}\text{ N·m}^2\text{/kg}^2}$G=6.67×10−11 N\cdotpm2/kg2​

This value is the same everywhere in the universe.

Whether calculating the attraction between two apples, Earth and the Moon, or distant stars, the same value of G is always used.

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Why is G Called a Constant?

A constant is a quantity whose value never changes.

Unlike mass or distance, which vary from one situation to another, the gravitational constant has the same value:

• On Earth
• On the Moon
• Throughout the Solar System
• In distant galaxies

Because G is universal, Newton's Law can be applied anywhere in the universe.

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The Role of G in Newton's Law

Newton's Law of Universal Gravitation is written as:

where:

• F = gravitational force (N)
• G = gravitational constant
• m₁ = first mass (kg)
• m₂ = second mass (kg)
• r = distance between the centres of the masses (m)

The gravitational constant acts as the proportionality constant that links the masses and their separation to the resulting gravitational force.

Without G, the equation would not produce the correct value for the force.

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Units of the Gravitational Constant

The SI units of G are:

$\boxed{\text{N·m}^2\text{/kg}^2}$N\cdotpm2/kg2​

These units ensure that when:

• Mass is measured in kilograms (kg),
• Distance is measured in metres (m),

the calculated force is expressed in newtons (N).

Remember:

• Mass → kilograms (kg)
• Distance → metres (m)
• Force → newtons (N)

Using consistent SI units is essential for obtaining the correct answer.

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Why is the Value of G So Small?

The value of G is extremely small:

$6.67\times10^{-11}$

This tiny number means that gravity is an inherently weak force between small objects.

For example:

Two students standing one metre apart attract each other gravitationally, but the force is far too small to be felt.

Other forces, such as friction and electromagnetic forces, completely dominate everyday situations.

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Gravity is Weak—but Important

Although gravity is the weakest of the four fundamental forces, it becomes the dominant force on astronomical scales.

Why?

Because gravity has two unique properties:

• It acts between all objects with mass.
• It is always attractive.

Unlike electric forces, which can both attract and repel, gravitational forces always add together.

When enormous masses such as planets and stars are involved, gravity becomes incredibly strong.

For example:

• Earth's gravity holds the atmosphere in place.
• The Sun's gravity keeps the planets in orbit.
• Gravity binds galaxies together.

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Using G in Calculations

Whenever Newton's Law of Gravitation is used, G must be included.

Worked Example

Question

Calculate the gravitational force between two masses.

Mass 1 = 500 kg

Mass 2 = 800 kg

Distance between centres = 10 m

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Step 1

Write the equation.

$F=G\frac{m_1m_2}{r^2}$

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Step 2

Substitute the values.

$F= 6.67\times10^{-11} \frac{(500)(800)}{10^2}$

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Step 3

Calculate.

First calculate the masses:

$500\times800=400\,000$

Then divide by:

$10^2=100$$\frac{400\,000}{100}=4000$

Finally:

$F= 6.67\times10^{-11}\times4000$$F=2.67\times10^{-7}\text{ N}$

Answer

$\boxed{F=2.67\times10^{-7}\text{ N}}$F=2.67×10−7 N​

Although these masses are quite large, the force remains extremely small because the value of G is so tiny.

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Measuring G

The gravitational constant was first measured experimentally by the English scientist Henry Cavendish in 1798.

He used a very sensitive device called a torsion balance.

The experiment measured the tiny gravitational attraction between large lead spheres.

Cavendish's work allowed scientists to:

• Calculate Earth's mass.
• Better understand planetary motion.
• Improve gravitational calculations throughout astronomy.

His experiment is often described as "weighing the Earth."

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Comparing Gravity with Other Forces

Gravity is much weaker than the other three fundamental forces.

For example:

• A small refrigerator magnet can easily lift a paperclip against the pull of the entire Earth.

This happens because the magnetic force between the magnet and the paperclip is much stronger than the gravitational force acting on the paperclip.

Although gravity dominates the motion of planets and stars, it is usually insignificant when dealing with atoms and molecules.

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Why Scientists Still Study G

Although G has been known for more than 200 years, measuring it precisely remains surprisingly difficult.

Gravity between laboratory-sized objects is extremely weak.

Modern scientists continue improving measurements of G because accurate values are important for:

• Astronomy
• Satellite navigation
• Planetary science
• Cosmology
• Tests of fundamental physics

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Key Terms

Gravitational Constant (G) — The universal constant that determines the strength of gravitational attraction between masses.

Universal Constant — A physical constant that has the same value everywhere in the universe.

Proportionality Constant — A constant that relates quantities in a mathematical equation.

Torsion Balance — A sensitive instrument used by Henry Cavendish to measure the gravitational constant.

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Key Takeaways

• G is the universal gravitational constant.

• Its value is:

  $6.67\times10^{-11}\text{ N·m}^2\text{/kg}^2$6.67×10−11 N\cdotpm2/kg2
• G appears in Newton's Law of Universal Gravitation.
• The very small value of G explains why gravity is much weaker than the other fundamental forces.
• Gravity only becomes dominant when extremely large masses, such as planets and stars, are involved.
• Scientists use G to calculate gravitational forces throughout the universe.

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Suggested Images

Suggested placement:

1. After "Measuring G" – Illustration or historical drawing of Henry Cavendish's torsion balance experiment.
2. After "The Role of G in Newton's Law" – Diagram of two masses separated by a distance with force arrows and the gravitation equation.
3. After "Comparing Gravity with Other Forces" – Photo of a magnet lifting a paperclip to illustrate how electromagnetic forces can easily overcome gravity.
4. After "Gravity is Weak—but Important" – Earth–Moon system showing gravitational attraction acting between two massive bodies.