To start with, we need to understand why planets have moons in the first place. Moons start out as astronomical bodies moving through space that get pulled in by the gravity of a larger object, such as a planet. For there to be an orbit, the velocity of the body through space has to be balanced with the gravity of the planet. If the gravity is greater, the object will be pulled down to the planet and crash; if the velocity is greater, the object will be able to escape that planet’s gravitational pull and continue traveling through space. When the gravity of the planet and the velocity of the object are balanced, the forces are continuously “tugging” the object both forward in space and closer to the planet – forming an orbit.
So in order for a planet to have a moon, it needs two things – it needs to encounter an astronomical body traveling nearby, and it has to exert enough of a gravitational pressure (ie it has to be large enough) to pull the body into orbit.
All of the planets are big enough to exert that gravitational pressure, so that’s not a problem. However, Mercury and Venus are close to the sun. Even if they were able to exert gravitational pull on an object, the pull of the giant sun would be much greater – so neither of them have moons, because the gravity of the sun would pull any potential moons away from them.
Mars is far enough away from the sun, and also near an asteroid belt – it has two moons. Earth’s moon is sort of a fluke – it’s believed that an object collided with the Earth, causing chunks of debris to fly out into orbit and coalesce into our moon.
Jupiter, Saturn, Uranus, and Neptune are huge – they managed to attract many moons into their orbit. If you still count Pluto as a planet – even though it’s small, it’s near another belt of objects (the Kuiper belt), so it was able to attract five astronomical bodies into its orbit.
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