Weight - a force downwards due to gravity
Large bodies such as the Sun, the Moon and the Earth all have very large masses.
Due to the large mass each body has a gravitational field that attracts smaller masses to it.
Mass (\(m\)) is a measure of the quantity of matter that makes up an object. It is measured in kilograms (\(kg\)). The mass of an object can only change if some mass is added or taken away.
Weight (\(W\)) is a force, measured in newtons (\(N\)). Weight is caused by the pull of gravity acting on a mass, usually near the surface of a planet. The weight of an object can change if it is on a different planet, with a different Force per unit mass. Measured in newtons per kilogram (N/kg)., \(g\).
The bigger the body, the greater the gravitational field strength (\(g\)) measured in Newtons per kilogram (\(Nkg^{-1} \)).
For example, we are attracted to the Earth.
The Moon is attracted to the Earth, which is why it stays in orbit around the Earth.
The Earth is attracted to the Sun and so the Earth stays in orbit around the Sun.
The gravitational field strengths of different objects in our solar system are shown in the table.
| Object in our solar system | Gravitational field strength on the surface in \(Nkg^{-1} \) |
| Earth | 9∙8 |
| Jupiter | 23 |
| Mars | 3∙7 |
| Mercury | 3∙7 |
| Moon | 1∙6 |
| Neptune | 11 |
| Saturn | 9∙0 |
| Sun | 270 |
| Uranus | 8∙7 |
| Venus | 8∙9 |
| Object in our solar system | Earth |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 9∙8 |
| Object in our solar system | Jupiter |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 23 |
| Object in our solar system | Mars |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 3∙7 |
| Object in our solar system | Mercury |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 3∙7 |
| Object in our solar system | Moon |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 1∙6 |
| Object in our solar system | Neptune |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 11 |
| Object in our solar system | Saturn |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 9∙0 |
| Object in our solar system | Sun |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 270 |
| Object in our solar system | Uranus |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 8∙7 |
| Object in our solar system | Venus |
|---|---|
| Gravitational field strength on the surface in \(Nkg^{-1} \) | 8∙9 |
The gravitational field strength for a planet (or satellite – like the Moon) indicates the force on a \(1 kg\) mass on the planet or moon’s surface.
The force that holds you on the Earth – on the seat you are sitting on now – is known as your weight.
Weight can be calculated as:
\(Weight = mass \times gravitational\,field\,strength\)
\(W = m \times g\)
Weight and gravitational field strength
Example
Question
The lunar rover used by the Apollo 15 astronauts has a mass of \(120kg\).
Q1: What is the weight of the rover on the Earth?
Q2: What is the weight of the rover on the Moon?
Remember that wherever you go, your mass will remain the same.
Answer one
\(W = m \times g\)
\(= 120 \times 9.8\)
\(= 1176N\)
Answer two
\(W = m \times g\)
\(= 120 \times 1.6\)
\(= 192N\)
