# Consider a planet in some solar system which has a mass double

## Homework Statement

Consider a planet in some solar system which has a mass double the mass of earth and same density as of earth . What is the weight of object on the planet in terms of 'W' , where 'W' is weight of object on Earth

## Homework Equations

W=mg ... density = M / V . .... g=GM/R2

## The Attempt at a Solution

since they both have same density..
i equated their M/V ratios and it gets me the ratio of their radii ..
but it still gets me nowhere

Pengwuino
Gold Member

Letting 'D' indicate the information you know for the double sized planet, you know

$M_{D} = 2M_{Earth}$

and you know $R_{D} = X R_{Earth}$ where X is whatever you determined the ratio between the radii are. So simply find what the gravitational acceleration on this new planet will be with $g = {{GM}\over{R^2}}$. The trick will be being able to write 'g' as $g = Y \times {{GM_{Earth}}\over{R_{Earth}^2}}$ where you have some constant, 'Y', multiplying the original values known for the Earth. Those known values you know gives $g_{Earth} = 9.8 m/s$.

You'll have some multiplicative value in front that will tell you how many times stronger or weaker the gravity is.

Letting 'D' indicate the information you know for the double sized planet, you know

$M_{D} = 2M_{Earth}$

and you know $R_{D} = X R_{Earth}$ where X is whatever you determined the ratio between the radii are. So simply find what the gravitational acceleration on this new planet will be with $g = {{GM}\over{R^2}}$. The trick will be being able to write 'g' as $g = Y \times {{GM_{Earth}}\over{R_{Earth}^2}}$ where you have some constant, 'Y', multiplying the original values known for the Earth. Those known values you know gives $g_{Earth} = 9.8 m/s$.

You'll have some multiplicative value in front that will tell you how many times stronger or weaker the gravity is.

thanks , got it