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.

What Is a Satellite?

A satellite is an object that moves in an orbit around another, more massive object.

There are two main types of satellites:

• Natural satellites – naturally occurring objects that orbit planets or other bodies.
• Artificial satellites – human-made objects placed into orbit for a particular purpose.

The Moon is Earth's natural satellite. Earth also has thousands of artificial satellites and other spacecraft orbiting it.

 

 

 

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Natural Satellites

Natural satellites are usually called moons.

Examples include:

• Earth's Moon
• Phobos and Deimos orbiting Mars
• Europa and Ganymede orbiting Jupiter
• Titan orbiting Saturn

Natural satellites vary greatly in size, composition, and distance from their planets.

Artificial Satellites

Artificial satellites are machines launched into space and placed into specific orbits.

They can carry:

• Cameras
• Radio transmitters and receivers
• Scientific instruments
• Weather sensors
• Navigation equipment

Their orbit is chosen according to the job the satellite needs to perform.

Circular Orbits

A satellite in a circular orbit remains approximately the same distance from the object it is orbiting.

Gravity continuously pulls the satellite toward Earth. However, the satellite also has a large tangential velocity.

These two effects combine to produce an orbit.

 

 

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The gravitational force acts toward the centre of Earth and provides the centripetal force needed to keep the satellite moving in a circular path.

Without gravity, the satellite would move away along a path tangent to its orbit.

Orbital Speed

The speed required for a circular orbit depends on the satellite's distance from Earth.

For a circular orbit:

\( v = \sqrt[]{ \frac{GM}{r} } \)​

where:

• v = orbital speed
• G = gravitational constant
• M = mass of the object being orbited
• r = distance from the centre of that object

This relationship tells us:

Smaller orbital radius → greater orbital speed

Larger orbital radius → lower orbital speed

Geostationary Orbits

A geostationary satellite appears to remain above the same point on Earth's surface.

To do this, the satellite must:

• Orbit above the equator.
• Travel in the same direction as Earth's rotation.
• Have an orbital period equal to Earth's rotation period — approximately 24 hours.
• Be approximately 35,786 km above Earth's surface.

 

 

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The satellite is still moving rapidly through space. It only appears stationary because it moves around Earth at the same rate that Earth rotates.

Why Are Geostationary Satellites Useful?

Because they remain above approximately the same location, ground-based antennas can point continuously toward the same satellite.

This makes geostationary satellites particularly useful for:

• Television broadcasting
• Telecommunications
• Internet services
• Weather monitoring

Low Earth Orbit

Many artificial satellites operate in Low Earth Orbit (LEO), generally a few hundred to around 2,000 km above Earth's surface.

Satellites in LEO travel around Earth much faster than geostationary satellites.

For example, the International Space Station orbits roughly 400 km above Earth's surface and completes an orbit in about 90 minutes.

 

 

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LEO is commonly used for:

• Earth observation
• Scientific research
• Imaging
• Some communication systems
• Human spaceflight

Because LEO satellites are relatively close to Earth, they can provide detailed observations and lower communication delay.

Polar Orbits

A polar orbit carries a satellite over or near Earth's North and South Poles.

As the satellite orbits, Earth rotates underneath it. Over time, the satellite can observe much of Earth's surface.

 

 

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Polar and near-polar orbits are particularly useful for:

• Mapping
• Weather observations
• Environmental monitoring
• Measuring ice coverage
• Monitoring forests and oceans
• Earth imaging

Common Uses of Artificial Satellites

Artificial satellites have become an important part of modern technology.

Communication

Communication satellites transmit information between different parts of Earth.

They can carry:

• Television signals
• Telephone communications
• Internet data
• Emergency communications

Navigation

Navigation satellite systems allow receivers to determine their position on Earth.

Satellite navigation is used in:

• Smartphones
• Cars
• Aircraft
• Ships
• Surveying

Weather Forecasting

Weather satellites observe:

• Clouds
• Storm systems
• Atmospheric conditions
• Ocean temperatures

These observations help meteorologists track storms and produce weather forecasts.

Earth Observation

Satellites can repeatedly photograph and measure Earth's surface.

Scientists use them to study:

• Deforestation
• Agriculture
• Wildfires
• Pollution
• Glaciers
• Sea ice
• Natural disasters

What Affects Orbital Motion?

Several factors affect the motion of a satellite.

Orbital Radius

The distance between the satellite and the centre of the object it orbits affects both its speed and orbital period.

For circular Earth orbits:

Higher orbit → lower orbital speed → longer orbital period

Lower orbit → higher orbital speed → shorter orbital period

Mass of the Central Object

A more massive central object produces a stronger gravitational field.

For example, a satellite orbiting a very massive planet experiences different orbital conditions from one at the same orbital radius around a less massive planet.

Velocity

A satellite must have the correct velocity to maintain its desired orbit.

If its velocity changes, the shape or size of its orbit can change.

Spacecraft therefore use engines or thrusters to adjust their orbits when necessary.

Gravity

Gravity provides the inward force necessary for orbital motion.

A satellite can be thought of as continuously falling toward Earth while moving forward fast enough to keep missing it.

This continuous free fall produces an orbit.

Comparing Satellite Orbits

Example: Choosing an Orbit

A scientist wants to monitor changes in forests across the entire Earth.

A polar or near-polar orbit would be useful because the satellite can observe different areas as Earth rotates beneath it.

A television company wants to transmit signals continuously to the same region.

A geostationary orbit would be useful because the satellite remains above the same part of Earth.

Did You Know?

Satellites in orbit are still affected strongly by Earth's gravity. Astronauts do not appear weightless because there is no gravity in space.

Instead, astronauts and their spacecraft are falling together around Earth. This condition is called free fall and produces the experience of apparent weightlessness.

Key Terms

• Satellite – an object that orbits another object.
• Natural satellite – a naturally occurring satellite, such as a moon.
• Artificial satellite – a human-made object placed into orbit.
• Orbit – the path of an object around another object.
• Circular orbit – an orbit with approximately constant distance from the central object.
• Geostationary orbit – an orbit in which a satellite appears stationary above one point on Earth's equator.
• Polar orbit – an orbit that passes over or near Earth's poles.
• Low Earth Orbit (LEO) – an orbit relatively close to Earth's surface.
• Orbital speed – the speed of an object travelling through its orbit.
• Orbital period – the time required to complete one orbit.
• Centripetal force – the inward force required for circular motion.

Key Takeaways

• Satellites can be natural or artificial.
• The Moon is a natural satellite, while communication and weather satellites are artificial.
• Gravity provides the centripetal force that keeps satellites in orbit.
• Satellites in lower circular orbits move faster and have shorter orbital periods.
• Geostationary satellites orbit above the equator with a period of approximately 24 hours.
• Different satellite orbits are chosen for different purposes.
• LEO, polar, and geostationary orbits each have advantages for particular applications.

What Is Escape Velocity?

Imagine throwing a ball upward from Earth's surface.

If you throw it slowly, it rises a short distance and falls back to Earth. If you throw it faster, it travels higher before returning.

What if you could launch it fast enough that it never returned?

The minimum initial speed required for an object to escape from the gravitational influence of a planet or other astronomical body, without further propulsion, is called its escape velocity.

For Earth, the escape velocity from the surface is approximately:

v_e​ = 11.2 km/s​

That is approximately 40,300 km/h.

 

 

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What Does It Mean to Escape?

An object launched upward is constantly pulled back by gravity.

If it does not have enough energy, gravity eventually causes it to return.

At escape velocity, however, the object has enough initial kinetic energy to overcome the gravitational attraction of the planet and continue moving outward indefinitely.

Escape velocity does not mean that gravity suddenly disappears. Gravity becomes weaker with increasing distance but, theoretically, extends indefinitely.

The Escape Velocity Equation

For a spherical astronomical body, escape velocity can be calculated using:

\( v_e = \sqrt[]{ \frac{2GM}{r} } \)​​

where:

• v_e​ = escape velocity in m/s
• G = gravitational constant, 6.67×10⁻¹¹ N m²/kg²
• M = mass of the planet in kg
• R = distance from the planet's centre in m

This equation shows us that escape velocity depends mainly on two properties:

the mass of the planet and the distance from its centre.

How Does Planetary Mass Affect Escape Velocity?

Look again at the equation:

\( v_e = \sqrt[]{ \frac{2GM}{r} } \)​

If a planet has a greater mass, it produces a stronger gravitational field.

Therefore:

Greater planetary mass → stronger gravitational attraction → greater escape velocity

However, mass is not the only factor. The planet's radius also matters.

A very large planet may have a large mass, but its surface may also be much farther from its centre.

Therefore, escape velocity depends on the combination:

\( \frac{M}{R} \)​

This is why we cannot determine escape velocity from mass alone.

Comparing Escape Velocities

Different planets have different masses and radii, so they have different escape velocities.

 

 

 

Notice that Jupiter has a much greater escape velocity than Earth.

This is mainly because Jupiter is extremely massive. An object requires much more energy to escape from Jupiter's gravitational field.

The Moon, by comparison, has an escape velocity of only about 2.4 km/s because it has much less mass than Earth.

Escape Velocity and Energy

Escape velocity can also be understood using energy.

An object near a planet possesses gravitational potential energy because of its position in the planet's gravitational field.

It also possesses kinetic energy if it is moving.

Kinetic energy is:

\( E_K = \frac{1}{2}mv^2 \)

For escape to occur, the object must have enough initial kinetic energy to overcome the gravitational binding energy associated with the planet.

For an object of mass m at distance R from the centre of a planet:

\( U = - \frac{GMm}{R} \)​

The negative sign indicates that the object is gravitationally bound to the planet.

For the minimum escape condition:

\( \frac{1}{2}mv_e^2 = \frac{GMm}{R} \)​

Solving for ve​:

\( v_e^2 = \frac{2GM}{R} \)​

Therefore:

​\( v_e = \sqrt[]{ \frac{2GM}{r} } \)​

An important result appears here: the mass m of the escaping object cancels.

Does the Mass of the Spacecraft Matter?

Surprisingly, no.

Ignoring air resistance, the escape velocity is the same for a small rock, a satellite, and a massive spacecraft launched from the same location.

This is because a more massive object requires more energy to accelerate, but it also experiences proportionally greater gravitational attraction.

Therefore:

Escape velocity depends on the planet, not the mass of the escaping object.

Worked Example 1: Escape Velocity from Earth

Calculate Earth's escape velocity using:

M = 5.97×10²⁴ kg

R = 6.37×10⁶ m

G = 6.67×10⁻¹¹ N m²/kg²

Step 1: Write the equation

\( v_e = \sqrt[]{ \frac{2GM}{R} } \)​

Step 2: Substitute

\( v_e = \sqrt[]{ \frac{2(6.67 \cdot10^{-11})(5.97 \cdot10^{24}) }{6.37 \cdot10^6 } } \)​​

Step 3: Calculate

v_e ​≈ 11190 m/s

Step 4: Convert to km/s

v_e​ ≈ 11.2 km/s

Answer: Earth's escape velocity is approximately 11.2 km/s.

Worked Example 2: A Smaller Planet

A planet has:

M = 6.0×10²³ kg

and

R = 3.0×10⁶ m

Calculate its escape velocity.

Step 1

​\( v_e = \sqrt[]{ \frac{2GM}{R} } \)

Step 2

\( v_e = \sqrt[]{ \frac{2(6.67 \cdot10^{-11})(6.0 \cdot10^{23}) }{3.0 \cdot10^6 } } \)​

Step 3

v_e​ ≈ 5165 m/s

Therefore:

v_e​ ≈ 5.2 km/s​

Escape Velocity vs Orbital Velocity

Escape velocity should not be confused with orbital velocity.

An object in orbit is still gravitationally bound to the planet. It continually falls toward the planet while moving sideways.

An escaping object has enough energy to leave the planet's gravitational influence without returning.

 

 

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For the same distance from a planet:

\( v_{escape} = \sqrt[]{2}v_{orbit} \)​

So escape velocity is about 1.41 times the circular orbital velocity at the same radius.

Do Rockets Really Launch at 11.2 km/s?

A rocket does not normally need to reach 11.2 km/s immediately at Earth's surface.

The escape-velocity calculation assumes an object receives its speed at once and then travels without additional propulsion.

Real rockets:

• Accelerate over time.
• Continue producing thrust during flight.
• Travel through Earth's atmosphere.
• Experience air resistance.
• Often enter orbit before travelling farther into space.

Escape velocity is therefore best understood as an energy requirement, rather than simply a required speed that every rocket must immediately reach.

Did You Know?

Escape velocity becomes extremely large for very compact astronomical objects.

A black hole is an extreme example. Inside its event horizon, the escape speed required by the classical analogy would exceed the speed of light. In general relativity, the more precise explanation is that the geometry of spacetime prevents anything inside the event horizon from escaping.

Key Terms

• Escape velocity – the minimum initial speed required to escape a body's gravitational influence without further propulsion.
• Gravitational field – the region in which a mass experiences gravitational attraction.
• Kinetic energy – energy possessed by an object because of its motion.
• Gravitational potential energy – energy associated with an object's position in a gravitational field.
• Orbital velocity – the velocity required for an object to follow a particular orbit.
• Planetary mass – the total mass of a planet.
• Planetary radius – the distance from the centre of a planet to its surface.

Key Takeaways

• Escape velocity is the minimum initial speed required to escape a gravitational field without further propulsion.
• Earth's surface escape velocity is approximately 11.2 km/s.
• More massive planets generally have greater escape velocities.
• A planet's radius also affects escape velocity.
• Escape velocity can be understood through the relationship between kinetic energy and gravitational potential energy.
• The mass of the escaping object does not affect escape velocity.
• Escape velocity can be calculated using: \( v_e = \sqrt[]{ \frac{2GM}{R} } \)​​