# What is the acceleration due to gravity on the surface of a planet that has twice the mass of the Earth and half its radius?

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#### Explanation

#### Explanation:

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The mass increases linearly but radius decreases exponentially, so the result is

#### Explanation:

Let's first look at the equation for the force of gravity:

which is often simplified for working with objects on the surface of the Earth (since we know the gravitational constant and the mass of the Earth) to

where M is the mass experiencing Earth's gravity.

So what happens when we double the mass of the Earth and reduce its radius to 1/2? Let's multiply

then make the substitutions:

So the numerator increases linearly (

The force of gravity on Earth is roughly

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