How Orbits and Gravitational Fields Work

Gravity is the force that keeps planets in orbit around the Sun and moons in orbit around planets. It acts as the centripetal force for circular (or near-circular) orbital motion.

Gravitational force and orbits

• Every object with mass attracts every other object with mass.
• The gravitational force between two objects increases with their masses and decreases with the square of the distance between them.
• For a planet orbiting the Sun, the gravitational force provides the centripetal force needed for circular motion.

Orbital speed and radius

For a stable circular orbit:

• An object closer to the central body orbits faster and has a shorter orbital period.
• An object further away orbits more slowly and has a longer period.

Example: Mercury (closest to the Sun) has the shortest orbital period (88 days). Neptune (furthest) has the longest (165 years).

Gravitational field

A gravitational field is a region in which a mass experiences a force. The gravitational field strength $g$ at a point is the force per unit mass:

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

On Earth’s surface, $g \approx 9.8$ N/kg. This value decreases with altitude.

Gravitational field patterns

The field lines around a spherical mass (like a planet) point radially inward toward the centre. The lines are closer together near the surface (stronger field) and spread out further away (weaker field).

Common errors and how to correct them

Saying there is “no gravity in space.” Gravity extends to infinity; it just gets weaker with distance. Astronauts in orbit feel weightless because they are in free fall, not because gravity is zero.

Confusing $g$ as gravitational field strength and $g$ as acceleration due to gravity. They are numerically equal: $g = 9.8$ N/kg = $9.8$ m/s$^2$. The units differ depending on context.

How to apply this in an exam

State that gravity provides the centripetal force for orbital motion. For gravitational field strength, use $g = F/m$ and state the unit (N/kg). Know that closer orbits are faster with shorter periods.