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Shooting stars are actually meteors falling down on the surface of earth. How come some of them appear shooting up and not down?

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Shooting stars are indeed meteors falling down, but consider this: meteors which are part of a meteor shower actually appear to come from a point in the sky called the radiant point: google image

Since you're looking upwards, you may be looking straight at the radiant point, and therefore the meteors are 'radiating' away from that point in all directions; not only 'downwards' towards the horizon, but 'upwards' from your point of view.

You can see that, even for a meteor which is not part of a shower, it's just as likely for a meteor to be going 'upwards' across the sky, as it is to be going 'downwards'.

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