The sun is a star and shines all the time, just like every other star. The difference between the sun and other stars is that the sun is the closest star to the earth. It is 93 million (9.3 x 106) miles away from us, and the next nearest star, Proxima Centauri, is 2.47 x 1013 miles away from us. That means that Proxima Centauri is roughly 10 million times farther from earth than the sun is. This helps explain why the sun appears much larger and brighter than other stars, as well as why we don't see the sun and other stars at the same time.
Since earth is (approximately) spherical and rotates on its axis, we have daytime--when our part of earth is facing the sun and the sunlight (which is in fact starlight) is so much brighter than any other star's light that we can't see other stars in the sky--and nighttime--when our part of earth is facing away from the sun and we don't have interference from its bright light, so we can see all the other stars in the sky.
Remember, there is always a part of the earth that is facing the sun, so that the opposite side of earth that is facing away from the sun. Here in California, when we face the sun, the country of Egypt is facing directly away from the sun because Egypt is approximately 12 hours ahead of us. Likewise, when it is night time in California, it is daytime in Egypt. We created time zones in order to keep track of this! If you're having trouble picturing it, make yourself a model: a lamp can be the sun, and a basketball can be the earth (the model is not to scale). But if you find the air hole on the basketball, where you'd attach a pump in order to inflate the ball, you can keep track of that spot as you turn the ball to simulate the rotation of the earth. When the air hole is facing the lamp, that is like daytime, when the only star we can see is the sun (the lamp). When the air hole is facing away from the lamp, that is like nighttime. But remember, the sun has not disappeared; it is just making daytime for the other side of the basketball.
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