Question 1. In class this week, you learned about Newton's version of Kepler's third law. This equation uses the period, P, of an orbit (how long an object takes to complete one orbit around another) and the average distance, a, between the two objects to estimate the mass of a system, (m1 + m2). In astronomy we use this equation to calculate masses of planets, stars, and even galaxies or black holes. Let's find out if Eris is really more deserving of being called a planet than Pluto by calculating the mass of Eris and comparing our result to the mass of Pluto. Newton's equation is:

Equation (1):

From the observations of Dysnomia, Mike Brown and his team were able to see that Dysnomia has an almost-circular orbit with an average distance, a, to Eris of 37,350 km and an orbital period, P, of 15.774 days. Using these orbital parameters, what would the combined mass of the system be?

You will need:

p = 3.1415

G (gravitational constant) = 6.67384 10^-11 m³ kg^-1 s^-2

Watch your units!

The gravitational constant, G, is given in meters, m, and the average distance, a, in km. You will need to change the average distance to meters before you use it in the equation.

a [km]	x 1000 [m/km]	= a [m]

• The gravitational constant, G, also has units of seconds, s, and the period of Dysnomia is given in days. You will need to change the period to seconds before you use it in the equation.

P [days]	x 24 [hr/day]	x 60 [min/hr]	x 60 [s/min]	= P [s]

Now we are ready to calculate the mass of the system

4p2	x a3	/G	/P2	= (m1+m2)

I'm looking to understand the breakdown of the gravitational constant.