That is a very good question!
Actually no, planets within the solar system are not getting further apart with time. And the same is true for atoms within your body, our galaxy, and all the galaxies on our local group (there is about 40 of them, and they are very close to us – for example the Andromeda Galaxy is moving towards us! )
None of these things are getting further away form each other due to the expansion of the Universe. This is because these things are in a state called ‘gravitationally bound’. It means that they are so close to each other that the attractive force of gravity pulling these things together is stronger than the overall expansion of the Universe, so they stay close together.
This means that the expansion of the Universe is no excuse for my cat to be getting fat 😛
No, the planets are kept in place by the force of Gravity, which keeps them orbiting around the Sun. In the same way, the Sun is orbiting around the centre of our Galaxy. Even other Galaxies are kept close by the force of gravity they experience from our Galaxy and others nearby.
The expansion of the Universe only affects the space in between these big groups of things that are kept together by gravity, like very, very distant galaxies. These are the ones that we use to prove that the Universe is expanding.
Imagine that gravity is a piece of string, and the closer you are to a massive (something with a lot of mass) object, the thicker that string gets. Planets, stars, and even satalitte galaxies have a thick enough piece of string between each other that they dont drift apart with the expansion of space.
However, galaxies that are so far away from other galaxies have string is very thin – enough that they can “feel” each other, but not enough to stop them moving with the expanding space.
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