# Lunar and solar tides [closed]

I just read the following statement in a book:

If the diameter of the earth increased by 20%, both lunar and solar tides would be weakened with lunar tides weakening more than solar tides.

What does this mean? I basically don't know about solar tides and how lunar and solar tides are related.

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## closed as unclear what you're asking by Emilio Pisanty, Dilaton, Qmechanic♦Aug 26 '13 at 20:03

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Does the book say why they would be weakened? – Emilio Pisanty Aug 24 '13 at 14:52
if the diameter of earth increases by 20%.... – Rajath Krishna R Aug 24 '13 at 15:01
$\uparrow$ Which book? – Qmechanic Aug 26 '13 at 20:03

The tides happen because the side of the Earth facing the Moon is nearer to the Moon that the other side of the Earth, so the gravitational field of the Moon is stronger on one side of the Earth than the other. The tidal force is derived in the Wikipedia article on tidal force: I'll just quote the result:

$$F \approx \frac{G M_{Earth} M_{Moon} }{r^3} d$$

where $r$ is the distance from the centre of the Earth to the centre of the Moon, and $d$ is the diameter of the Earth. $F$ is the force stretching the Earth i.e. the difference between the forces on the near and far sides. The approximation assumes that the diameter of the Earth, $d$, is much less than the Earth Moon distance.

So firstly increasing the diameter of the Earth will increase the tidal force not decrease it, and secondly the tidal force is approximately proportional to the Earth's diameter, so an increase of 20% will increase the solar and luner tides by the same ratio of 20%.

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