Orbital Motion and Gravity

This lesson covers orbital motion, gravitational force, and how gravity keeps planets, moons, and satellites in orbit, as required by the AQA GCSE Physics specification (4.8.1). This is a Physics-only topic. You need to understand how gravity provides the centripetal force for orbital motion, how orbital speed and radius are related, and the difference between circular and elliptical orbits.

---

Gravity and Gravitational Fields

Gravity is a non-contact force of attraction between any two objects that have mass. Every object with mass exerts a gravitational pull on every other object with mass. The strength of the gravitational force depends on:

1. The masses of the two objects — greater masses produce a stronger gravitational force.
2. The distance between the centres of the two objects — the force decreases as the distance increases.

A gravitational field is the region around a mass where another mass would experience a gravitational force. The gravitational field of a planet or star extends to infinity, but it becomes weaker with distance.

Gravitational Field Strength

The gravitational field strength (g) at a point is the force per unit mass acting on an object at that point:

g = F / m

where:

• g = gravitational field strength (N/kg)
• F = gravitational force (weight) in newtons (N)
• m = mass in kilograms (kg)

Location	Gravitational Field Strength (N/kg)
Earth (surface)	9.8
Moon (surface)	1.6
Mars (surface)	3.7
Jupiter (surface)	24.8
Sun (surface)	274

Exam Tip: On Earth, g = 9.8 N/kg (often rounded to 10 N/kg in calculations). This means that every kilogram of mass experiences a gravitational force (weight) of 9.8 N. Weight = mass x gravitational field strength (W = mg). Do not confuse mass (kg) with weight (N).

---

Weight and Mass

It is essential to distinguish between mass and weight:

Quantity	Definition	Unit	Changes with location?
Mass	The amount of matter in an object	kg	No — mass is the same everywhere
Weight	The gravitational force acting on an object	N	Yes — depends on gravitational field strength

The equation linking weight, mass, and gravitational field strength is:

W = m x g

For example, an astronaut with a mass of 80 kg:

• On Earth: W = 80 x 9.8 = 784 N
• On the Moon: W = 80 x 1.6 = 128 N
• On Jupiter: W = 80 x 24.8 = 1,984 N

The astronaut's mass is always 80 kg, but their weight changes depending on the gravitational field strength at their location.

---

Orbital Motion

An orbit is the path of one object around another due to gravity. For example:

• Planets orbit the Sun.
• Moons orbit planets.
• Artificial satellites orbit Earth (or other bodies).

Why Do Objects Stay in Orbit?

An orbiting object is constantly falling towards the larger body due to gravitational attraction. However, it also has a velocity at right angles to the direction of the gravitational force. The combination of:

• The object's forward velocity (tangential velocity)
• The gravitational pull towards the central body

produces a curved path — an orbit.

If the object were moving in a straight line, it would fly off into space. If it had no tangential velocity, it would fall straight towards the central body. The balance between these two produces the circular (or elliptical) orbital path.

Exam Tip: Gravity provides the centripetal force needed for orbital motion. A common exam question asks: "What provides the centripetal force for a planet orbiting the Sun?" The answer is: the gravitational attraction between the Sun and the planet. Do not say "centripetal force" as if it is a separate force — it is gravity acting as the centripetal force.

---

Gravity as the Centripetal Force

For an object moving in a circular orbit, a centripetal force is needed to keep it moving in a circle. This centripetal force is directed towards the centre of the circle (towards the larger body).

In the case of orbital motion:

• For a planet orbiting the Sun, the centripetal force is the gravitational attraction between the Sun and the planet.
• For a moon orbiting a planet, the centripetal force is the gravitational attraction between the planet and the moon.
• For an artificial satellite orbiting Earth, the centripetal force is the gravitational attraction between Earth and the satellite.

graph TD
    A["Central Body (e.g. Sun)"] --- B["Gravitational Force (centripetal force)"]
    B --- C["Orbiting Body (e.g. Planet)"]
    C --- D["Tangential Velocity"]
    D --- E["Curved Orbital Path"]

    style A fill:#f39c12,color:#fff
    style C fill:#3498db,color:#fff
    style B fill:#e74c3c,color:#fff

---

Orbital Speed, Radius, and Period

There is a clear relationship between the orbital speed, orbital radius, and orbital period of an orbiting object.

Key Relationships

• An object in a smaller orbit (closer to the central body) moves faster and has a shorter orbital period.
• An object in a larger orbit (further from the central body) moves slower and has a longer orbital period.

This is because:

• Closer objects experience a stronger gravitational pull (gravity is stronger at shorter distances).
• This stronger pull requires a higher speed to maintain a stable orbit.

Planet	Average Distance from Sun (AU)	Orbital Period (years)	Average Orbital Speed (km/s)
Mercury	0.39	0.24	47.4
Venus	0.72	0.62	35.0
Earth	1.00	1.00	29.8
Mars	1.52	1.88	24.1
Jupiter	5.20	11.86	13.1
Saturn	9.54	29.46	9.7
Uranus	19.19	84.01	6.8
Neptune	30.07	164.8	5.4

Exam Tip: Notice the pattern: as the distance from the Sun increases, the orbital period increases and the orbital speed decreases. If asked to explain why, state that at greater distances the gravitational force is weaker, so a lower speed is needed to maintain a stable orbit. Conversely, at shorter distances, the stronger gravitational pull requires a faster orbital speed.

---

Circular and Elliptical Orbits

Circular Orbits

In a perfectly circular orbit, the distance between the orbiting object and the central body is constant. The orbital speed is also constant. While no real orbit is perfectly circular, many planetary orbits are very nearly circular (Earth's orbit has an eccentricity of only about 0.017).

For a circular orbit:

• The gravitational force is always perpendicular to the velocity of the orbiting object.
• The speed is constant, but the direction changes continuously — so the velocity changes continuously.
• Because the velocity is changing (direction is changing), the object is accelerating — even though its speed is constant.

Elliptical Orbits

An elliptical orbit is an elongated, oval-shaped orbit. In an elliptical orbit:

• The distance between the orbiting object and the central body changes during the orbit.
• The speed of the orbiting object varies — it moves faster when closer to the central body (at perihelion for orbits around the Sun) and slower when further away (at aphelion).
• Comets have highly elliptical orbits — they spend most of their time far from the Sun, moving slowly, and speed up dramatically as they approach the Sun.