Dimensional Analysis Problem: Mass of the Solar System Excluding Planets and Sun

[HSuzuki]

Homework Statement

Assume that in interplanetary space within the solar system there is one hydrogen atom per cubic centimeter, and that the mass of such an atom is 1.67 x 10^-27 kg. In addition, take the radius of the solar system to be 4.0 light-hours. For the sake of this calculation, take the solar system to be spherical in shape. Note that we are not including the masses of the planets and the sun. Based on this set of assumptions, what is the mass of the solar system excluding discrete bodies such as the planets and the sun? Use for the speed of light 3.00 x 10^8 m/s and assume there are 3.15 x 10^7 seconds in a year.

Thanks for your attempt and help!

Homework Equations

The Attempt at a Solution

 

[Nathanael]

Homework Statement

Assume that in interplanetary space within the solar system there is one hydrogen atom per cubic centimeter, and that the mass of such an atom is 1.67 x 10^-27 kg. In addition, take the radius of the solar system to be 4.0 light-hours. For the sake of this calculation, take the solar system to be spherical in shape. Note that we are not including the masses of the planets and the sun. Based on this set of assumptions, what is the mass of the solar system excluding discrete bodies such as the planets and the sun? Use for the speed of light 3.00 x 10^8 m/s and assume there are 3.15 x 10^7 seconds in a year.

Thanks for your attempt and help!

Have you tried to solve it? An attempted solution would be nice to see so that we can help you where you need it.