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Why is the Moon a satellite?

Short answer

Because it orbits a planet. For NASA, a satellite is any object that circles a planet, a star, or a moon, and the Moon circles Earth: it's its only natural satellite. It does so at an average distance of 384,400 km and completes one orbit in 27 Earth days, the same time it takes to rotate.

Why is the Moon a satellite?
International Space Station Full Moon Transit

What it means to be a satellite

For NASA, a satellite is any object that orbits a planet, a star, or a moon. The word says nothing about size or origin: there are natural satellites, such as the Moon or Earth itself relative to the Sun, and thousands of artificial satellites circling our planet. What defines the status is the mechanics: a body stays in orbit when its velocity is balanced by the gravitational pull of the central object. Without that balance, it would either fly off in a straight line into space or fall onto it.

Earth's only moon

The Moon is Earth's only natural satellite. It orbits at an average distance of 384,400 km (238,855 miles) and has a radius of about 1,740 km. It completes one orbit in 27 Earth days, although from the surface its cycle appears to repeat every 29 days, because while the Moon orbits, Earth also moves around the Sun. That mismatch is what separates the orbital month from the month of phases.

One face, and no air

The Moon rotates in the same time it takes to orbit Earth once. This is synchronous rotation, a result of tidal locking between the two bodies, and the reason we always see the same hemisphere. It also lacks an atmosphere in the usual sense, having instead a very thin exosphere that isn't breathable, doesn't cushion impacts, and offers no protection against solar radiation. Its origin, according to NASA, lies in the collision of a Mars-sized body with Earth billions of years ago: the satellite formed from the debris of that impact, rather than being captured afterward.

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Why is the Moon a satellite? | Above Ten Thousand