Gravitational Fields 🌍

students, have you ever wondered why a dropped phone falls straight down instead of drifting sideways, or why the Moon keeps orbiting Earth instead of flying away? The answer is gravitational fields. In this lesson, you will learn what a gravitational field is, how to describe it, and how to use IB Physics SL reasoning to solve problems involving gravity. By the end, you should be able to explain the key ideas, connect them to the wider topic of fields, and apply the main equations accurately.

What is a gravitational field?

A gravitational field is the region around a mass where another mass experiences a force. In simple terms, mass creates a gravitational influence in the space around it. If another object enters that space, it feels attraction toward the source mass. This is why Earth pulls objects toward its center and why planets orbit the Sun. 🌍☀️

The size of the gravitational field at a point is called the gravitational field strength, written as $g$. It tells us the force per unit mass acting on a small test mass:

$$g = \frac{F}{m}$$

Here, $F$ is the gravitational force on the test mass and $m$ is the mass of the object experiencing the force. The unit of $g$ is $\text{N kg}^{-1}$, which is equivalent to $\text{m s}^{-2}$.

Near Earth’s surface, $g$ is approximately $9.81\,\text{m s}^{-2}$, often rounded to $9.8\,\text{m s}^{-2}$. This means that every kilogram of mass experiences about $9.8\,\text{N}$ of gravitational force near the surface of Earth.

A useful idea in IB Physics SL is that fields are not physical “lines” in space, but a way to model an influence acting at a distance. Gravitational fields help us describe motion without needing direct contact between objects.

Newton’s law of universal gravitation

The force between two masses is given by Newton’s law of universal gravitation:

$$F = G\frac{m_1 m_2}{r^2}$$

In this equation, $G$ is the gravitational constant, $m_1$ and $m_2$ are the masses, and $r$ is the distance between their centers.

This equation shows two important patterns:

If either mass increases, the force increases.
If the distance between the masses increases, the force decreases with the square of the distance.

The inverse-square relationship is a major feature of gravitational fields. If the distance is doubled, the force becomes one quarter as large. If the distance is tripled, the force becomes one ninth as large.

Example: if two objects are separated by $r$, and then moved to $2r$, the new force is

$$F' = G\frac{m_1 m_2}{(2r)^2} = \frac{1}{4}F$$

This inverse-square behavior is important across fields in physics, including electric fields and light intensity. It shows how spreading influence over a larger spherical surface reduces strength with distance.

Gravitational field strength and field lines

Gravitational field strength can also be described as the force per unit mass at a point in space. This makes it a vector quantity, which means it has both magnitude and direction.

For a mass like Earth, the gravitational field points toward the center of the mass. Near a spherical planet, the field lines are radial and directed inward. At any point, the field line shows the direction of the force on a small test mass. 📍

Important field-line rules:

Field lines point in the direction of the force on a positive test mass.
Field lines closer together represent a stronger field.
Gravitational field lines never cross.
Around a spherical mass, field lines are symmetric and point toward the center.

Near Earth’s surface, field lines are often drawn as parallel lines because over small height changes, the field is nearly uniform. A uniform field means the field strength is constant in the region. This is a useful approximation for many school-level problems.

Example: when you drop a ball from a small height, the field around it is treated as uniform, so the acceleration is approximately constant at $g$.

Gravitational potential energy and work

Gravitational fields are closely linked to energy. When an object moves in a gravitational field, work may be done, changing gravitational potential energy.

Near Earth’s surface, the change in gravitational potential energy is

$$\Delta E_p = mg\Delta h$$

where $\Delta h$ is the change in height.

If an object rises, $\Delta E_p$ is positive because energy must be supplied to move it upward. If it falls, $\Delta E_p$ decreases and the lost potential energy becomes kinetic energy, ignoring air resistance.

Example: lifting a $2\,\text{kg}$ backpack by $1.5\,\text{m}$ changes its potential energy by

$$\Delta E_p = (2)(9.8)(1.5) = 29.4\,\text{J}$$

This means $29.4\,\text{J}$ of work is done against gravity.

For objects far from Earth, or for problems involving planets and satellites, the gravitational potential energy formula near the surface is not enough. In those cases, the more general relationship is needed:

$$E_p = -\frac{GMm}{r}$$

This formula shows that gravitational potential energy becomes less negative as $r$ increases. The zero point is usually chosen at infinity, which is standard in physics.

Motion in gravitational fields

Gravitational fields affect motion by producing acceleration. On Earth, the force of gravity causes free-fall motion. If air resistance is ignored, all objects fall with the same acceleration $g$, regardless of mass.

This is a very important idea in physics. A heavier object does not fall faster just because it has more mass. The gravitational force is larger for a larger mass, but the acceleration is still the same because $a = F/m$.

Using Newton’s second law and weight:

$$F = mg$$

This is the weight of an object near Earth’s surface. Weight is a force, measured in newtons, while mass is measured in kilograms.

Example: a student with mass $60\,\text{kg}$ has weight

$$F = (60)(9.8) = 588\,\text{N}$$

If the student drops a ball, the ball accelerates downward at approximately $9.8\,\text{m s}^{-2}$. In free fall, the only force acting is gravity, so the motion is uniformly accelerated.

In orbital motion, gravity provides the centripetal force needed to keep satellites moving in a curved path. For a satellite in circular orbit,

$$G\frac{Mm}{r^2} = \frac{mv^2}{r}$$

This relationship helps explain why satellites do not simply fall straight down. They are constantly falling toward Earth, but they also have enough sideways speed to keep missing the surface. 🛰️

Gravitational fields in the wider topic of fields

Gravitational fields are one of the three field types in this topic, along with electric and magnetic fields. They are similar in the way they describe action at a distance, but they differ in the source and the force they produce.

Main comparisons:

Gravitational fields are caused by mass.
Electric fields are caused by charge.
Magnetic fields are caused by moving charges and magnets.

All three can be represented with field lines and can be used to predict the motion of objects. Gravitational and electric fields both follow inverse-square laws in many situations, which is why these two fields are often compared together in IB Physics SL.

Gravitational fields are always attractive because mass is always positive in ordinary physics. Electric fields can attract or repel depending on the type of charge. Magnetic fields act differently again, especially because magnetic forces often depend on motion.

Understanding gravitational fields gives you a foundation for the rest of the Fields topic because it introduces the field idea, vector field strength, inverse-square laws, and energy changes in a clear and familiar context.

Worked example and exam-style reasoning

Suppose students is asked: “A $5.0\,\text{kg}$ object is lifted vertically through $3.0\,\text{m}$ near Earth’s surface. Calculate the change in gravitational potential energy.”

Use:

$$\Delta E_p = mg\Delta h$$

Substitute the values:

$$\Delta E_p = (5.0)(9.8)(3.0)$$

$$\Delta E_p = 147\,\text{J}$$

So the gravitational potential energy increases by $147\,\text{J}$.

If the question asks for reasoning, say that the object is moved against the gravitational field, so work must be done by an external force. That work is stored as gravitational potential energy.

Another common exam-style question may ask about the effect of increasing distance in a gravitational field. If the distance from the source mass is doubled, the field strength becomes one quarter because

$$g \propto \frac{1}{r^2}$$

This is the key relationship to remember for inverse-square fields.

Conclusion

Gravitational fields describe how masses interact across space. They explain why objects fall, why planets orbit, and why energy changes when objects move up or down in height. The main ideas are the gravitational field strength $g$, Newton’s law of gravitation, inverse-square behavior, and gravitational potential energy. In IB Physics SL, students should be able to use these ideas to interpret field diagrams, solve numerical problems, and connect gravity to electric and magnetic fields as part of the broader Fields topic.

Study Notes

A gravitational field is the region around a mass where another mass experiences a force.
Gravitational field strength is $g = \frac{F}{m}$ and has units of $\text{N kg}^{-1}$ or $\text{m s}^{-2}$.
Near Earth’s surface, $g \approx 9.8\,\text{m s}^{-2}$.
Newton’s law of gravitation is $F = G\frac{m_1m_2}{r^2}$.
Gravitational fields obey the inverse-square law, so doubling $r$ makes the force one quarter as large.
Field lines point toward the mass and show the direction of the force on a test mass.
Field lines closer together mean a stronger field.
Near Earth’s surface, the field is often treated as uniform.
Weight is given by $F = mg$.
Near Earth’s surface, gravitational potential energy change is $\Delta E_p = mg\Delta h$.
For larger-scale problems, gravitational potential energy can be written as $E_p = -\frac{GMm}{r}$.
In orbit, gravity provides the centripetal force.
Gravitational fields are attractive and are caused by mass.
Gravitational fields connect to electric and magnetic fields through the broader idea of fields.