Throughout history, people have been awed and alarmed by comets. Some felt that they were omens, whether good or bad. Today we know that comets aren't messages from the gods but chunks of rock and ice orbiting the sun in elliptical orbits. Either way, comets still awe us with their beauty every time they make their visit to the inner solar system.
One of the earliest and most important discoveries about comets was made by Edmond Halley. He was an English astronomer in early seventeen hundreds who noticed that every 76 years historical records mentioned the appearance of a particularly bright comet. He realized that these appearances must have been made by just one comet coming every 76 years. Halley predicted that the comet would return in late 1758, which it did. Because of his discovery, the comet was named after him and Halley's comet still visits us every 76 years.
Since then, it has been discovered that comets orbit the sun in highly elliptical orbits. This means that instead of being a constant distance from the sun, like the Earth, a comet goes far away from the sun and then comes back, as shown by the following animation.

This animation also disproves a common misconception: The tail of the comet is not left behind it like a trail of dust or smoke. The tail is produced when solar energy heats the comet and the vaporized particles are blown into space. This means that the tail will always point away from the sun, not away from the direction that the comet is traveling in.
The comet's trip around the sun can take any where from 50 years to 30 million years. During this time, the comet leaves the Oort Cloud. This is a cloud of icy and rocky debris orbiting far outside the solar system. Comets are debris from the Oort cloud which have been knocked out of their stable circular orbit. As the comet gets closer and closer to the sun, the tail forms, becoming brighter and longer. Then the comet passes around the sun, heading back towards the Oort Cloud and the tail fades away.
As you can see, comets are not an everyday experience. Many "new" comets are just comets that have orbits of many thousands of years, or even millions. The appearance of a comet is certainly something which is worthwhile to observe, no matter how cold it is outside.
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