Gravity and Orbital Motion

Gravity Is a Universal Force

Gravity is the attractive force that acts between any two objects that have mass.

Every object with mass attracts every other object with mass. This means that gravity acts between:

• you and Earth
• Earth and the Moon
• Earth and the Sun
• stars within a galaxy
• galaxies within clusters

For small everyday objects, gravitational attraction is extremely weak. However, planets, stars, and other astronomical objects have enormous masses, so the gravitational forces between them can be very large.

Gravity is one of the most important forces in astronomy because it controls much of the large-scale structure and motion of the universe.

 

 

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Newton's Law of Universal Gravitation

In 1687, Isaac Newton described gravity mathematically. His Law of Universal Gravitation states:

Every two masses in the universe attract each other with a force that depends on their masses and the distance between them.

\( F = G \frac{m_1m_2}{r^2} \)

Where:

• F = gravitational force, measured in newtons (N)
• G = universal gravitational constant
• m₁ = mass of the first object, measured in kilograms (kg)
• m₂ = mass of the second object, measured in kilograms (kg)
• r = distance between the centres of the two objects, measured in metres (m)

The gravitational constant is:

G = 6.67×10⁻¹¹ N m²/kg²

The very small value of G helps explain why gravitational attraction between ordinary objects is difficult to notice.

How Mass Affects Gravity

The gravitational force becomes stronger when the masses of the objects increase.

From Newton's equation:

F α m_1​m₂​

For example:

• If m₁​ doubles, the gravitational force doubles.
• If m₂​ triples, the gravitational force triples.
• If both masses double, the force becomes four times greater.

This is one reason gravity is so important in astronomy. Stars and planets contain enormous amounts of mass.

The Sun, for example, has much more mass than any planet in the Solar System. Its enormous mass produces the gravitational attraction that governs the motion of the planets.

How Distance Affects Gravity

Distance has an especially important effect on gravitational force.

Newton's equation contains:

r²

This means gravity follows an inverse-square relationship:

\( F \alpha \frac{1}{r^2} \)​

Therefore:

For example, if two objects move from 1 million km apart to 2 million km apart, their gravitational attraction does not simply halve. It becomes one-quarter as strong.

Gravity and Celestial Motion

Gravity explains why astronomical objects follow curved paths and orbits.

A planet moving through space has a tendency to continue moving in a straight line because of its inertia. At the same time, the Sun's gravity continuously pulls the planet toward the Sun.

The combination of these effects produces an orbit.

The planet is continually falling toward the Sun, but its sideways motion prevents it from falling directly into the Sun.

 

 

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This same principle explains:

• planets orbiting stars
• moons orbiting planets
• artificial satellites orbiting Earth
• stars orbiting the centres of galaxies

Gravity provides the centripetal force required to keep an orbiting object moving along its curved path.

Comparing Gravitational Forces

The strength of gravity between astronomical bodies depends on both mass and distance.

Consider these situations:

Two very massive stars

Their enormous masses can produce a very strong gravitational attraction, even when they are separated by large distances.

Earth and the Moon

Both objects have large masses, so there is significant gravitational attraction between them. This force keeps the Moon in orbit around Earth.

Two asteroids

Their masses are much smaller, so their gravitational attraction is normally much weaker.

However, mass alone does not determine gravitational force. Distance must always be considered as well.

A very massive object that is extremely far away may exert less gravitational force than a smaller object that is nearby.

Why Gravity Dominates Astronomical Systems

Gravity is actually the weakest of the four fundamental interactions. However, it dominates the behaviour of planets, stars, galaxies, and other large astronomical systems.

There are several reasons for this.

Gravity Has an Unlimited Range

Gravity becomes weaker with distance, but it never completely disappears.

The Sun's gravity therefore extends far beyond the planets.

Gravity Is Always Attractive

Masses always attract each other gravitationally.

Unlike electric forces, there is no negative mass that can cancel gravitational attraction in the same way that positive and negative electric charges can cancel each other.

Astronomical Objects Have Enormous Masses

Stars, planets, and galaxies contain tremendous amounts of matter.

The Sun has a mass of approximately:

1.99×10³⁰ kg

Earth has a mass of approximately:

5.97×10²⁴ kg

These enormous masses make gravitational effects extremely important.

Large Objects Are Usually Electrically Neutral

Electromagnetic forces can be much stronger than gravity, but large astronomical objects usually contain approximately equal amounts of positive and negative charge.

Their overall electric forces therefore tend to cancel.

Gravity does not cancel in this way, allowing it to dominate on astronomical scales.

Worked Example: Earth and a Satellite

A satellite has a mass of 500 kg. It is 7.0×10⁶ m from the centre of Earth.

Calculate the gravitational force between Earth and the satellite.

Given:

m₁​ = 5.97×10²⁴ kg

m₂​ = 500 kg

r = 7.0×10⁶ m

G = 6.67×10⁻¹¹

Substitute into the equation:

\( F = (6.67 \cdot10^{-11}) \frac{(5.97 \cdot10^{24})(500) }{(7.0 \cdot10^6)^2 } \approx 4.1 \cdot10^3 N \)​

Answer:

F ≈ 4.1×103 N​

Earth therefore pulls on the satellite with a gravitational force of approximately 4100 N.

The satellite also pulls on Earth with exactly the same magnitude of force in the opposite direction, according to Newton's Third Law.

Worked Example: Changing the Distance

Two objects experience a gravitational force of 800 N.

If the distance between their centres doubles, what is the new gravitational force?

Because:

\( F \alpha \frac{1}{r^2} \)​

doubling the distance gives:

\( F_{new} = \frac{800}{2^2} = \frac{800}{4} = 200N \)​

The gravitational force becomes one-quarter of its original value.

Gravity Shapes the Universe

Gravity operates on scales far larger than individual planetary systems.

It causes clouds of gas and dust to collapse and form stars. Gravity holds stars together in galaxies and helps organize galaxies into enormous groups and clusters.

 

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Gravity therefore helps explain structures ranging from moons orbiting planets to some of the largest structures observed in the universe.

Did You Know?

You are gravitationally attracted to every other person on Earth. However, because human masses are relatively small, this gravitational force is far too weak for us to notice.

Earth's enormous mass produces a much stronger gravitational attraction, which is why Earth's gravity has such an obvious effect on us.

Key Vocabulary

• Gravity – the attractive force between objects with mass.
• Gravitational force – the force of attraction produced by gravity.
• Universal gravitational constant (G) – the constant used in Newton's Law of Universal Gravitation.
• Inverse-square law – a relationship in which a quantity decreases according to the square of the distance.
• Orbit – the curved path of one object around another due to gravity.
• Celestial body – a natural object in space, such as a planet, moon, star, or asteroid.
• Centripetal force – a force directed toward the centre of a circular or curved path.
• Inertia – the tendency of an object to resist changes in its motion.

Key Takeaways

• Every object with mass attracts every other object with mass.
• Greater masses produce stronger gravitational forces.
• Increasing distance greatly reduces gravitational force because gravity follows an inverse-square law.
• Gravity provides the centripetal force that keeps planets, moons, and satellites in orbit.
• Gravity dominates astronomical systems because it has an unlimited range, is always attractive, and acts on objects with enormous masses.
• Newton's Law of Universal Gravitation can be used to calculate the gravitational force between two objects.
• Gravitational forces always occur as equal and opposite forces between the interacting objects.