Calculating Mass and Weight of a Planet

[whereisccguys]

2 part question

The density of a certain planet varies with radial distance as: D(r) = Do*[1-(a*r/Ro)], where Ro= 3.1623×106 m is the radius of the planet, Do = 3160 kg/m3 is its central density, and a = 0.160. Calculate the total mass of this planet.

Calculate the weight of a one kilogram mass located on the surface of the planet.

i tried integrating D(r) with and plugin in the radius of the planet but it doesn't work

i know this question has somethin to do with integrating through shell method but I'm not sure how to do it

can any1 help me?

 

[Hootenanny]

Why doesn't it work?

~H

 

[nrqed]

2 part question

The density of a certain planet varies with radial distance as: D(r) = Do*[1-(a*r/Ro)], where Ro= 3.1623×106 m is the radius of the planet, Do = 3160 kg/m3 is its central density, and a = 0.160. Calculate the total mass of this planet.

Calculate the weight of a one kilogram mass located on the surface of the planet.

i tried integrating D(r) with and plugin in the radius of the planet but it doesn't work

i know this question has somethin to do with integrating through shell method but I'm not sure how to do it

can any1 help me?

I am not sure what you integrated exactly but here are some thoughts:

First, you must determined the total massof the planet, right? This is given by the integral of $D(r) dV = D(r) r^2 sin(\theta) dr d\theta d\phi$. The angular integrals are trivial and give $4 \pi$. The radial integral is straightforward.

Then, you must use this in the universal law of gravitation to determine the *weight* of 1 kg at the surface of the planet, $F= {G m M \over r^2}$.

Patrick