An earthlike planet- in january 2006 astronomers reported the discovery of a planet, comparable in size to the earth, orbiting another star and having a mass about 5.5 times the earth’s mass. it is believed to consist of a mixture of rock andice, similar to neptune. if this planet has the same density as neptune (1.76 g/cm3), what is its radius expressed (a) inkilometers and (b) as a multiple of earth’s radius? consult appendix f for astronomical data.

To solve this problem we will begin by applying the given relations of density in terms of mass and volume, and from this last value we will take its geometric measurement for a sphere (Approximation of a planet) From there we will find the radius of the planet. Finally we will make a comparison between the radius of the new planet and the radius of the earth to understand its proportion.

Defining the Volume variables we have to

Here

V= Volume

m = mass

=Density

For a spherical object the Volume is

PART A)

Equation we have

In this case the mass of new planet is 5.5times the mass of Earth,

Then,

The mass of the Earth is kg and the density is ,

Replacing we have that,

Therefore the radius of this new planet is

PART B) The value of radius of the Earth is

Then the relation between them is

Therefore the radius of the new planet in terms of radius of the Earth is

where are the vectors ?