Gravitational forces

Mass

The mass of an object is the amount of matter or ‘stuff’ it contains. The more matter an object contains, the greater its mass. For example, an elephant contains more matter than a mouse, so it has a greater mass. As planets and stars are so big, they have a huge amount of mass. Mass is measured in units such as kilograms (kg). A 100 kg object has a greater mass than a 5 kg object. The mass of an object always remains constant regardless of its position in space. For example, an object with a mass of 5 kg on Earth will also have a mass of 5 kg on the Moon.

Gravitational field strength (g)

All objects are attracted towards each other by a force called gravity. Gravitational field strength is a measure of the force of gravity, measured in Newtons (N), exerted per kilogram (kg) mass of substance. The units for gravitational field strength are N/kg. Gravitational field strength is given the symbol g. Do not confuse this with the unit symbol for grams(g). Any object with mass exerts the force of gravity, and the higher the mass, the higher the force of gravity exerted. The larger the planet and the higher its mass, the higher the gravitational field strength is.

Weight

The weight of an object is the force acting on it due to gravity. An object’s weight depends on the mass of the object and the strength of the gravitational field surrounding it. The equation used to calculate the weight of an object is:

Weight is measured in Newtons (N)

Mass is measured in kilograms (kg)

Gravitational field strength is measured in Newtons per kilogram (N/kg)

Mass and weight

The weight and mass of an object are not equal. Mass is a measure of how much stuff is in an object but weight is a measure of the force acting on that stuff.  Weight depends upon the mass of the object and the gravitational field strength of the surroundings. This means that your mass would always be the same regardless of whether you were on Earth, on the Moon or on Jupiter. Gravitational field strength differs on other planets and the Moon from that on Earth. If you were to calculate your weight on Earth, on the Moon and on other planets, it would be different.

In space there is no gravitational field so you would have the same mass but no weight. This is why the feeling of floating is described as ‘weightlessness’. Similarly, if you were on a very large planet, your mass would be the same but your weight would increase.

For example, the Earth has a gravitational field strength of 10 N/kg. This means that for every 1 kg of mass, the force of gravity is 10 N. For an object with a mass of 1.6 kg, its weight on Earth is calculated as:

The Moon is much smaller than the Earth and has a lower mass. The gravitational field strength is lower on the Moon at 1.6 N/kg and we would therefore expect the force of gravity or weight to be lower on the Moon. We can prove this by calculating the weight for the same 1.6 kg object on the Moon:

Jupiter is much larger than the Earth and has a higher gravitational field strength of 26 N/kg. If the 1.6 kg object was placed on Jupiter, we would expect the weight to be greater. We can again prove this by using the weight calculation:

• • Weight is measured in Newtons (N)
  • Mass is measured in kilograms (kg)
  • The gravitational field strength is measured in Newtons per kilogram (N/kg)

Gravity and the solar system

There are artificial satellites in space which are used to transmit information back to Earth. The mass of these satellites is tiny compared to the mass of Earth, so Earth exerts a force of gravity on them. As the satellites are constantly accelerating, they are moving in a continuous circle. This gravitational force prevents them from accelerating off into space and keeps them orbiting the Earth.

The larger an object is, the more gravitational strength it has, so objects are always attracted to the largest object they are near. The Sun is much larger than the planets and has a much higher mass. Its gravitational field strength is much higher than that of any of the planets and so it is able to exert a large force of gravity.

The gravitational force exerted by the Sun is so great that it causes all of the planets to orbit around itself. One orbit is the time taken for the planet to move around the Sun once. Diagrams of the solar system and the orbits of planets are often misleading. They tend to suggest that the orbits of the planets are extreme ellipses but they are usually drawn in this way to show distances between the planets.

The orbits of the planets around the Sun are actually almost circular but with some slight squashing of the circles. We describe them as elliptical because they are not perfect circles. It would be more accurate to say that the orbits of the planets are slightly elliptical in shape.

As the planets orbit the Sun, the distance between them does not significantly change. This means that the planets do not move towards or away from the Sun during their orbit. The speed at which the planets orbit the Sun does not alter.

The length of time taken for any planet to orbit the Sun depends on the distance between the Sun and that plant. Planets which are further from the Sun move more slowly and take more time to complete an orbit. For example, Mercury, the closest planet to the Sun, takes just eight Earth days to complete one orbit. Earth takes one year to orbit the Sun, and Neptune, which is the furthest planet from the Sun, takes 164 Earth years to complete an orbit.

Moons are smaller than planets, so the planets are able to exert gravitational forces on the moons. This gravitational force keeps these moons moving in orbit around the planet and prevents them from drifting off into space. The orbit of the moons around planets is elliptical in shape. As the moons orbit the planets, the distance between them does not significantly change. This means that the moons do not move towards or away from the planet during their orbit. The speed at which the moons orbit the planet does not alter during the orbit.

Comets are made of dust and ice and are found orbiting many of the stars and planets in space. The shapes of their orbits are extreme ellipses. The distance between the comet and the star changes greatly during the orbit as does the speed at which the comet is orbiting. As the comet moves very far away from the star it slows down but when it starts to move towards the star its speed increases. This acceleration occurs because the force of gravity becomes stronger the closer the comet gets to the star, and as gravity increases, the acceleration also increases.

The extreme heat produced by the star causes the comet to burn up as it gets close to the star. When we see comets in the sky from Earth it is often the trail of ice and dust being burned off from the tail of the comet when the comet moves close to the Sun.

Orbital speeds

Orbital speed is a measure of the speed at which one object orbits another. The orbital speed of a planet is dependent upon the distance between the planet and the Sun. Orbital speed will vary depending on the distance one object is from another, as gravitational strength weakens with distance. The further away the planet is from the Sun, the bigger its orbit is and the less the force of gravity affects the acceleration. The planets furthest away from the Sun move more slowly and therefore take more time to complete one orbit. The orbital speed of an object can be calculated using the equation:

Orbital speed may be given in metres per second (m/s) or kilometres per hour (km/hr).

Orbital radius may be given in metres (m) or kilometres (km).

Time may be given in seconds (s) or hours (h).

You must always use the units provided in the exam question.

This equation takes 2 x π x orbital radius to get the length of the orbit. This is the same as using 2πr to find the circumference of a circle. The length of the orbit is then divided by the time taken to complete the orbit to calculate the speed. The time period is the time that it takes for the planet to do one full rotation and get back to the same place as it started. This is one complete orbit.

Example

The Earth has a time period of one year, meaning that it takes one full year to orbit the Sun. The orbital radius of Earth is 149.6 million kilometres.

Calculate the orbital speed in kilometres per hour (km/h).

Firstly, we need to convert one year into hours. The number of hours in a year can be calculated by multiplying the number of days in a year by the number of hours in a day. One day has 24 hours and one year has 365 days. Therefore, number of hours in a year 365 x 24 = 8760 hours. We can substitute this number, along with the orbital radius of 149,600,000 km, into our equation: