Does every planet have a law of gravitation?

The law of gravitation is not a question of any planet or star. It is a universal law. It is equally and strictly true of every particle of matter everywhere, and applied strictly between that particle of matter and every other particle, whether near or far. For us on the Earth, the most important kind of gravitation is the Earth’s gravitation; that is simply because the Earth is so near. But a book, which rests on a table under the pull of the Earth, is also being pulled towards the Sun, and the Moon, and every star in the sky. Only the Earth has the advantage of pulling the book downward since the Earth is nearer to it. This downward pull is better known as gravitation force.
In the case of any of the heavenly bodies, the gravitation force depends upon its mass. If we could exist on the surface of the Sun, we should find the downward pull vastly greater than that of Earth; on Mars less than that of Earth; on the Moon still less, and so on. Be it greater of weaker, the gravitation force is present everywhere in the universe.

Additional reading:
Newton’s law of universal gravitation (Wikipedia)

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