# 11.2.4. Newton’s Universal Gravitation Law

Given that a planet's mass and diameter are 4 and 8 times those of the Earth respectively, calculate the ratio between the acceleration due to gravity on that planet and that on the Earth.

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### Example

Given that a planet's mass and diameter are 4 and 8 times those of the Earth respectively, calculate the ratio between the acceleration due to gravity on that planet and that on the Earth.

### Solution

The relation between acceleration, mass, and radii of two planets can be written as

Given that the planet is 4 times the mass of the Earth, let the Earth have a mass of

Given that the planet has a diameter 8 times the length of the Earth, let the Earth have a radius of

Let the planet have an acceleration due to gravity

The ratio between the acceleration due to gravity on that planet and that on the Earth is