Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

5.1.2Astrophysics

Gravitational Field Strength

5 min read 9 parts Lesson 3 of 13 1 quiz

0%read

Section 1 of 9Gravity and gravitational fields

Every object with mass attracts every other object with mass.

Gravity
This attraction, the force of gravity, is always attractive.
For everyday objects it is far too small to notice, but for something the size of a planet or star it is very large.
Gravitational field
The region around a mass where another mass experiences a force is called a gravitational field.

The gravitational field strength, g, at a point is the force per unit mass on a small object placed there:

g = W ÷ m

where W is the weight (N), m is the mass (kg) and g is measured in newtons per kilogram (N kg−1). Rearranged, this is the familiar equation W = mg. On the surface of the Earth g = 9.8 N kg−1, meaning each kilogram of mass feels a pull of 9.8 N.

Section 2 of 9Mass and weight

Mass is the amount of matter in an object; it is measured in kilograms and is the same wherever the object is. Weight is the force of gravity on the object, measured in newtons, and it depends on the gravitational field strength at the location.

Mass and weight
Astronauts have the same mass on the Moon as on Earth but a much smaller weight, because g is smaller there.
Mass is measured by a balance; weight is measured by a newton meter (a spring balance).

Section 3 of 9Values of g on different bodies

Bodyg (N kg−1)
Moon1.6
Mercury and Mars3.7
Venus8.9
Earth9.8
Saturn10.4
Jupiter24.8
Sunabout 274

The field strength at the surface depends on two things: the mass of the planet (more mass, stronger field) and the radius (the further from the centre, the weaker the field).

Values of g on different bodies
Jupiter is massive, so g is large; the Moon is small and light, so g is small.
Far from any planet, g is small but never exactly zero, falling with distance according to an inverse-square pattern.

Section 4 of 9Free fall and g as acceleration

An object that is falling freely, with no air resistance, has only its weight acting, so its acceleration a = F ÷ m = mg ÷ m = g.

Free fall and g as acceleration
Therefore the gravitational field strength in N kg−1 is numerically equal to the free-fall acceleration in m s−2.
On the Moon a hammer and a feather dropped together fall at the same rate and hit the ground together,
  • because there is no air there and all objects accelerate at 1.6 m s−2.

The field strength also appears in the equation for gravitational potential energy, GPE = mgh: on a planet with a weaker field it takes less energy to lift an object through the same height.

What the symbols mean: Ep = gravitational potential energy gained (J) · m = mass (kg) · g = 9.81 N kg−1 · h = change in height (m)

Section 5 of 9Gravity and the Solar System

The Sun’s gravitational field keeps the planets in orbit and gets weaker with distance, so planets far from the Sun feel a weaker pull and take longer to orbit it.

Gravity and the Solar System
Gravity from the Moon, and to a lesser extent the Sun, causes tides on Earth.
In the next lessons gravity is the force that provides the centripetal force for orbits, and it determines the orbital period.

Section 6 of 9Using g in calculations

When answering calculation questions, first decide whether you need mass or weight.

1
If the question gives a mass in kilograms and asks for a force, multiply by g.
2
If it gives a weight in newtons and asks for a mass, divide by g.
3
Always check the planet: the same astronaut equipment has different weights on different bodies.
4
A useful check is to compare with Earth: on the Moon the weight is about one sixth, on Mars about 38%, and on Jupiter about 2.5 times the Earth value.
5
The mass in kilograms never changes with location,
  • which is why mass is the property used when working out the acceleration produced by a given force, F = ma, anywhere in the Universe.

Section 7 of 9Worked examples

  1. A rover has a mass of 180 kg. Calculate its weight on Mars (g = 3.7 N kg−1) and on Earth (g = 9.8 N kg−1).

  2. An astronaut weighs 120 N on the Moon where g = 1.6 N kg−1. Find the astronaut’s mass and weight on Earth.

  3. How much gravitational potential energy does a 2.0 kg tool gain when lifted through 5.0 m on the Moon (g = 1.6 N kg−1)? Compare with Earth.

Section 8 of 9Key terms

TermMeaning
Gravitational fieldRegion where a mass experiences a force due to another mass.
Gravitational field strength (g)Force per unit mass at a point, in N kg−1.
WeightThe force of gravity on an object, W = mg, measured in newtons.
MassAmount of matter in an object; measured in kilograms and unchanged by location.
Free fallMotion under the action of gravity alone.

Section 9 of 9Exam technique

1
Saying mass changes on the Moon. Mass stays the same; only weight changes.
2
Using kg as the unit of weight. Weight is a force in newtons.
3
Using g = 10 N/kg or 9.8 m/s without checking which value the question gives.
4
Thinking there is no gravity in space. Astronauts in orbit still experience gravity of about 90% of that at the surface; they only seem weightless because they are in free fall.
5
Forgetting that g depends on both the mass and the radius of the planet.
\n