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If you lift an object, for example your pencil, then let it go, the pencil falls down towards the ground. The force which pulls your pencil towards the ground is gravity. Earth pulls everything towards it using gravity, including pencils, people and even huge objects like the Moon. Earth pulls on the Moon with gravity, which causes the Moon to orbit around Earth, so that we see the Moon each night. Similarly, all the planets in the Solar system (including Earth) orbit around the Sun because the Sun is pulling the planets with gravity.
Our understanding of how things move and why they move has changed greatly over time. For centuries, people thought that the motion of the stars and planets were governed by different laws from those which described the motion of objects on Earth. This way of thinking was changed completely in the 17th century by Isaac Newton. He understood that objects fall to Earth due to the force of gravity, pulling them towards Earth. He also realised that the motion of the planets could be explained using these same laws, and that the reason why the planets orbit the Sun is also because of gravity, with the Sun’s enormous mass exerting a gravitational pull on the planets and causing them to orbit around it.
What does space do? Until just over 100 years ago, the answer to this question would have been something like “nothing really”. Space was considered as little more than a set of axes e.g. x,y,z with which an object’s position could be described using a set of coordinates. Similarly time was considered to be something which did nothing more than tick forward regularly at the same rate, no matter where you happened to measure it. This was entirely sufficient for Newton’s laws of gravity, discovered in the 17th century, and based on the idea that two masses exert an attractive force on each other. Newton’s laws had been used very successfully to describe gravitational effects on Earth and beyond e.g. the motion of the planets around the Sun.