### Re: what would happen to the solar sytem's structure if the earth was destroyed

Date: Thu May 18 16:06:46 2000
Posted By: Erika Gibb, Grad student, Physics & Astronomy/Origins of Life, RPI
Area of science: Astronomy
ID: 958431000.As
Message:

Hello Ly Tran!
Every body in the solar system (and indeed the Universe) attracts gravitationally every other body. This principle is known as Newton's Theory of Universal Gravitation. Newton deduced that the strength of the attraction (or the force) between two objects (like 2 planets or stars) depends on both their masses and the distance between them.* The bigger the masses or the smaller the distance between them, the stronger they attract each other. For example, if you have two stars which are attracting one another, and you replace one of them with a star which has twice the mass, the attractive force between the two stars is doubled. Similarly, if you have two stars attracting each other and you double the distance between them, the force of attraction is 1/4 what it was.

We can use Newton's Theory of Universal Gravitation to calculate the effect of Earth's gravity on other planets in the solar system. If we calculate the force of gravity between Earth and Venus when Venus is at its closest point to Earth (and therefore when the gravitational attraction between Earth and Venus is strongest), we find that the attraction between Earth and Venus is almost 50,000 times weaker than the attraction between Venus and the Sun! Using the same equations, the gravitational pull between Earth and Jupiter is found to be more than 200,000 times weaker than the pull of gravity between Jupiter and the Sun!

The Sun is so much more massive than every other body in the solar system that its gravitational force dominates the motion of the planets, overwhelming the contribution of a small planet like Earth. The only body in the solar system for which Earth's gravitational attraction is close to that of the Sun is the Moon because the Moon is so close to the Earth.

So if the Earth were suddenly to disappear entirely, the structure of the solar system would be essentially the same (minus the Earth, of course). [Also, the Moon's orbit would change substantially, though it would remain at about the same distance from the Sun and continue to orbit the Sun. Moderator]

* Newton's Gravitational Law can be written mathematically as

```                    GMm
F = ---
r^2
```

where `F` is the force, `G` is what is known as the gravitational constant, `M` and `m` are the masses of the two bodies, and `r` is the distance between them. [`r^2` means that one squares the value of `r` or multiplies it by itself.]

Erika

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