Extension for Topic 9

What provides centripetal force for planets and satellites?

Key Words

Gravity; Masses; Centripetal force; Orbit

Gravity

We feel the pull of gravity on the Earth but why gravity should occur at all is something of a mystery.  With gravity Physicists know that:

• It occurs between any objects that have mass;

• It is a very tiny force;

• It has a very long range (infinite in fact);

• It is always attractive.

Gravity always pulls objects together.  It NEVER pushes them apart, so we say that it is an attractive force.  It is never repulsive.  Between objects of "normal" size the force is so small that you cannot feel it.  There is an attractive force between you and your neighbour in the computer lab as you read this.  However don't worry; you won't stick together!  Assuming you have a mass of 70 kg and are 1 metre from your neighbour, the force of gravity is 3 × 10-7 N, not a very big force.

Gravity is only felt where the objects are very large.  Planets are big objects.  The Earth has a mass of 6 × 1024 kg.  Being such a big object, the Earth has a gravity of 10 N/kg.

When we look at things like atoms, gravity is far too small.  The force of gravity between two hydrogen atoms is about 1.5 × 1036 times smaller than the electrical force between them.

Question 1  Give three properties of the force of gravity.  ANSWER

Gravity and the Universe

Many of the processes that occur in the universe happen because of the effect of gravity.  Although gravity is so tiny, its range is infinite.  This means that it is possible for tiny dust particles millions of kilometres apart to come together.  The forces involved may be tiny, but space is a friction-free environment.  This means that dust particles will accelerate towards each other.  The process will be slow, taking millions of years, but they will get there in the end.

Gravity decreases with distance.  If you double the distance, the force goes down by 4 times.  This is called an inverse square law.  You will do more about this at A level.

Stars form by gravity pulling dust together.  This picture shows clouds of dust coming together to form new stars.

Question 2.  Why can gravity attract dust particles many millions of kilometres apart?  ANSWER

Gravity has nothing to do whatever with magnetism.

Planets in Orbit

So far we have looked at how the gravity of one object makes another object come towards it.  The obvious thing is that they come together.  However that does not always happen.  Suppose an object, like a planet, has a forward velocity, but the gravity from a star is acting at 90 degrees.

Question 3  What do you think will happen? ANSWER

The planet will start to orbit the star.

The orbit tends to be a slightly squashed circle called an ellipse.  At some points in the orbit the planet is slightly close to the sun than at others.  The amount may be small, but there can be climatic effects on the planet.

Notice that the gravity forces act in pairs.  The gravity of the star pulls on the planet, and the gravity of the planet pulls on the star.  The gravitational pull by a planet on a star is sufficient to make it appear to wobble slightly.  The wobbling appears to be periodic.  This is how the existence of planets of stars other than the Sun has been found out.  Astronomers cannot see the planets; they are far too far away.  However the small movement of a star would suggest that it is being pulled by a planet.

Gravity provides the centripetal force to keep the planet in orbit.

Question 4  Which way does the centripetal force act?  ANSWER

Question 5  What would happen to the planet if the gravity were suddenly "switched off"?  ANSWER

The further out a planet is, the longer it takes to make an orbit of the star.  For example Mercury takes takes 88 days to orbit the Sun while the Earth takes 365 days.

Satellites in Orbit

Orbits occur because of gravity, not because there is no gravity.  Where satellites orbit the Earth, the acceleration due to gravity is between about 2 to 9 m/s2.  So there is still an appreciable pull.

An orbiting satellite is actually falling to the Earth all the time, except it misses it.  Let's look at this in more detail.

Imagine a large gun on a high mountain.  It fires a shell which travels a certain distance.

Question 6  What happens to the range if the shell is fired faster?  ANSWER

In fact the surface of the Earth is, of course, curved.  So the range is a little bit further still.

Now suppose we have a higher mountain and a more powerful gun.  This time the shell travels even further.  It follows the curvature of the Earth until it finally hits the ground.  Gravity is acting towards the centre of the Earth.  The gravity pulls the shell down until it eventually hits the ground, quite a long way from the gun.

If the gun is powerful enough, the shell will leave the barrel at such a speed that it never actually hits the ground.  It goes around the Earth in orbit.

Question 7  Which way does gravity act?  What angle does the force of gravity make with the path of the shell?  ANSWER

So an orbiting satellite is constantly falling to the Earth.  However it travels at such a speed that it always misses the Earth.  Since space is a vacuum, there is no friction, so the satellite does not slow down.

If the satellite is slowed down, by firing retro-rockets, it will fall to the Earth's surface.  This procedure is vital for getting cosmonauts back safely.

If a satellite is accelerated to a higher speed, it will move into a higher orbit.  At a high enough speed it will leave the orbit altogether.  Space controllers use the gravity of planets to accelerate space probes to very high speeds.

A common bear-trap is to say that for a satellite in orbit there is zero gravity.

Cosmonauts in satellites feel weightless.  This is because they are falling at the same rate as the satellite, not because there is no gravity.  They train for weightless conditions by being carried in a plane that dives in a parabolic path.  This is known as the "Vomit Comet".

Types of Orbit

The picture shows two common kinds of orbit.

Geostationary satellites have an orbit time equal to the rotational period of the Earth.

Question 8  (Easy) What is the rotational period of the Earth?  What is the direction of the orbit?  ANSWER

This means that relative to a point on the ground they appear stationary.

A common bear trap is to say that the orbital speed is zero.  It is about 7 km/s.

Geostationary satellites are used for communication.

Satellites in polar orbit are used for monitoring.  They orbit the Earth every 90 minutes and as they make each orbit, a new section of the Earth passes underneath.  This allows all the ground to be "swept".

Polar orbits are used by satellites that carry out monitoring, for example for weather and spying.

Have a go at the Crossword about circular motion.

 Summary Gravity holds planets and satellites in their orbits; Gravity is an attractive force Gravity provides the centripetal force; Orbits of planets are ellipses; An orbiting satellite is actually falling all the time; Satellites can be in geostationary orbit or polar orbit.

Now try the Topic Quiz

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