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A red giant is a big giant star that weighs about one-half to ten times as much as our Sun. Red giants get their name because they appear to be colored red and they are very large. Many red giants could fit thousands and thousands of suns like ours inside of them. Mira, Aldebaran, Arcturus and Gamma Crucis are red giants.
Right now, our Sun is a main-sequence star, not a red giant. However, five billion years from now, scientists believe our sun will become a red giant. It will be about 200 times wider than it is now. It will become so big it will swallow up Mercury, Venus and even the Earth.
How a star becomes a red giant
All new stars change hydrogen to helium through nuclear fusion. This makes a lot of energy (e.g. light and heat). In a normal star, like our Sun and all other main-sequence stars, this change happens at the very center of the star. Sooner or later, almost all of the hydrogen at the center has changed to helium. This causes the nuclear reaction to stop. The center will start to get smaller due to the star's gravity. This makes the layer just outside the center get hotter. This layer still has hydrogen. This hydrogen will fuse to make helium.
The outer layers of the star will get much, much bigger. The star will get brighter, sometimes as much as ten thousand times as bright as it was at first. Since the outside of the star will get bigger, the energy will be spread over a much larger area. Because of this, the temperature of the surface will go down and the color will change to red or orange.
Sometime later, red giants will start to fuse helium to make other elements like carbon, nitrogen and oxygen. Some of their outer layers will blow away, leaving interstellar gas and dust circling the star. In time, most red giants will become white dwarfs. Very large red giants become neutron stars or black holes.