In the autumn the apples on an apple tree ripen and, if they are not picked, they one by one detach themselves from the branches and drop to the ground. A force must be pulling them downwards.
When you throw a ball into the air, it travels up and over in an arc, but soon falls back to the ground. Again, a force must be pulling it downwards. This downwards force is gravity. It is the attraction, or pull, the Earth exerts on everything on or near it. All the other heavenly bodies exert gravity in a similar way. Gravity is literally what holds the universe together.
One of the first people to investigate the Earth's gravity was the Italian scientist Galileo, in the early 1600s. Galileo lived in Pisa at the time, and is supposed to have carried out an experiment from the top of the famous leaning tower there.
He dropped two weights from the tower, a light one and a heavy one. Scientists of the time believed that heavy objects fell faster than light ones. But when Galileo dropped his weights from the tower, they both hit the ground together.
Galileo proved in this experiment that, whatever their weight, bodies fall to the Earth at the same rate when they are dropped. Prove this for yourself by dropping a golf ball (heavy) and a ping-pong ball (light) from the same height.
If you dropped a pebble over a high cliff and were able to measure its speed as it fell, you would find that it would be travelling at a speed of about 9.8 metres per second after one second. After another second, it would be travelling 9.8 metres per second faster; and after another second, 9.8 metres per second faster still. And so on. You would find that its speed increased by 9.8 metres per second every second it was falling. In other words, the rate of increase in the pebble's speed - its acceleration - was 9.8 metres per second per second.
And every falling body accelerates at this rate because of the Earth's pull. We call this the acceleration due to gravity, or g. We saw in the golf and ping-pong ball experiment earlier that both balls hit the ground together. They fall at the same rate because gravity accelerates them equally, even though they have a different weight. And we would expect any objects to fall the ground together when they are dropped together.
But do they? Drop an orange and a balloon together. Do they hit the ground together? You find that they don't. The orange hits the ground before the balloon. So our theory that all objects fall to the ground at the same rate is upset.
Clearly another force is involved here besides gravity. And it is slowing down the balloon. This force is the resistance, or drag, of the air. Air resists the movement of anything travelling through it. And the bigger the object, the greater is the resistance acting upon it. So the balloon, which is much bigger than the orange, experiences greater air resistance and is slowed down more as it falls.
In the same way, a hammer and a feather should fall together when they are dropped, but don't because the air resistance affects the feather more. However, if you dropped the hammer and the feather on the Moon, they should fall together because there is no air and therefore no air resistance.
In fact one of the Apollo astronauts, David Scott, carried out just this experiment on the Apollo 15 mission in July 1971. He held up the geological hammer he had been working with and a feather he had brought from Earth, and let them go. Under the pull of the Moon's gravity, they both hit the ground together. "How about that," cried Scott, "Mr Galileo was correct!"
Galileo worked not only on falling bodies, but on swinging ones. It is said that, while in Pisa Cathedral, he observed the lamps swinging and, being a good scientist, timed their rate of swing. He found that, for a particular lamp, the rate of swing was constant, no matter how far they swung. But the rate of swing varied from lamp to lamp. It depended on the length of their supporting chain.
Galileo had discovered the principle of the pendulum. The swinging lamp was a kind of pendulum. In its simplest form a pendulum consists of a rod with a weight, or bob, attached to one end. It is supported at the other so that it can swing freely.
As Galileo found, the pendulum's rate of swing depends only on its length, not on the weight of the bob or on the amount it travels sideways when it swings. It is the pendulum's constant rate of swing that makes it suitable as a regulator in clocks.
The rate of swing of a pendulum does depend on something else, however. It depends on g, the acceleration due to gravity. Normally we regard g as constant. But this is not strictly true: g does vary slightly from place to place.
It is quite easy mathematically to work out a relationship that links T, the period of swing of a pendulum - the time in seconds it takes to return to the same point; l, the length in metres of the pendulum; and g, in metres per second per second. It is:
T =
where is a mathematical constant equal to about 3.14.
This formula gives us a simple way of measuring g. All you do is set up a pendulum and measure its length and period of swing. You can then work out g by rearranging the formula and squaring:
g =
Find out the value of g for yourself. Make a simple pendulum by tying a steel nut to one end of a piece of cotton, and tying the other end to a suitable support. Make your pendulum 1 metre long to simplify calculations later. Set your pendulum swinging, and time ten or twenty complete swings. Divide the time by the number of swings to get the period of swing. Now work out g from the formula above. You will be surprised how accurate your value of g is, even with your rough-and-ready pendulum.
Galileo died in 1642. By coincidence, this was the same year that another scientific genius was born, in England. He was Isaac Newton, whose theoretical and practical work transformed the natural sciences and mathematics. He is particularly remembered for his discovery of the laws of gravity, in a story that may or may not be true.
The story goes that one day he was sitting under an apple tree, when an apple fell to the ground near his feet. This set him wondering whether the force that pulled the apple to the ground - that is, gravity - was the same force that keeps the Moon circling endlessly around the Earth. He decided that it was.
The Moon is travelling through space. If no forces acted upon it, it would travel in a straight line. But in fact it circles around the Earth. So there must be a force connected with the Earth that attracts the Moon and makes it travel in a circle, in orbit around the Earth. This force must be the Earth's gravity.
You can see how gravity acts on the Moon by whirling a stone on a piece of string around your head. Make sure you are out in the open and there is nobody about! The stone keeps travelling in a circle because you are pulling on the string. If you let go of the string, the stone will shoot off in a straight line. And so it is with the Moon. Gravity (the inward pull) keeps the Moon (the stone) travelling in a circle. If gravity were suddenly to cease, the Moon would fly off into space in a straight line.
Newton realised that it was not only the Earth that had gravity, but every body in the universe. The gravity of the Sun holds the planets in their orbits in the solar system. Gravity binds stars into great star islands, or galaxies; and galaxies into clusters and superclusters. Gravity holds the whole universe together.
Newton summed up his ideas on gravity in his universal law of gravitation: Every bit of matter in the universe attracts every other bit of matter with a force that depends on their masses, and inversely on the square of the distance between them.
Expressing this mathematically: the force of gravity (F) between two bodies of mass m and m and distance d apart is
proportional to the product of their two masses (m m ) and 1 over d squared.
We can write this as: F _______
This shows that if you double one of the masses, you double the gravitational force. But if you double the distance between them, you reduce the force one quarter (one over two squared).
On the Earth, gravitational force - the force of gravity - exists between every object on the Earth's surface and the Earth itself. It acts to pull the object downwards to the surface.
It is the force we call weight.
From Newton's law of gravitation, we see that this force is proportional to an object's mass. The greater the mass of an object, the more the Earth attracts it, and the greater is its weight.
The terms 'mass' and 'weight' are often confused. But as you can see, they are different. 'Mass' is the amount of matter in an object. It never changes. 'Weight' is the force acting on an object because of gravity. It changes when the strength of gravity changes.
The force of gravity that attracts an object to the Earth depends, of course, not only on the object's mass but on the mass of the Earth which is attracting it. So we can say generally that for a given object, the force of gravity it experiences depends on the mass of the attracting body. Or in other words, the weight of an object depends on the mass of the attracting body.
For example, the Moon is much smaller and has much less mass than the Earth. So its gravity is much weaker - only about one-sixth that of the Earth. This means that objects on the Moon weigh only one-sixth what they do on Earth.
On the other hand, the planet Jupiter is much bigger and more massive than the Earth. So its gravity is much greater - over two and a half times greater. This means that objects on Jupiter would weigh over two and a half times more than they do on Earth.
So we see that a particular object would have a different weight on the Earth, the Moon and Jupiter. But it would still have the same mass. Its mass is fixed. Its weight varies according to the strength of gravity.
Coming back to Earth, and looking again at Newton's law, we see that the force of gravity on an object also depends on distance (d in the formula). This is the distance between the object and the Earth's centre (its centre of mass).
So as you climb above the surface, gravity gets less. But the change is very gradual. Only when you soar hundreds of kilometres
into space does gravity weaken markedly. And the higher you go, the weaker it becomes. This explains why satellites orbiting higher up do not have to travel so fast to stay in orbit.
In their orbiting spacecraft, we talk of astronauts being in a state of zero-g (meaning no gravity). But of course this is not true. Gravity still acts in orbit. If it didn't, the spacecraft would fly off into space.
We also call the 'zero-g' condition 'weightlessness', because nothing in orbit appears to have any weight. Weight is the downwards pull acting on an object because of gravity. And because gravity is still present in orbit, objects are still being pulled downwards. They are falling towards the Earth. But you can't measure their weight - the downwards pull on them - with a pair of scales, because the scales will be falling too!.
