Final answer:
To find the mass of the Milky Way galaxy, we apply a version of Kepler's Third Law using the orbital period and radius of the Sun's orbit. We convert units to meters and seconds, calculate the Sun's orbital velocity, and use this alongside the gravitational constant to estimate the galaxy's mass within the Sun's orbit.
Step-by-step explanation:
To determine the mass of the Milky Way galaxy using the information given, we can refer to a version of Kepler's Third Law tailored for galactic scales, which allows us to estimate the mass of the galaxy based on the orbital period and radius of an orbiting object—in this case, our Sun. The version of the law used in galactic dynamics is:
M = (v^2 x R) / G
where M is the mass of the galaxy within the Sun's orbit, v is the orbital speed of the Sun, R is the radius of the Sun's orbit, and G is the gravitational constant.
Calculation Steps:
First, we need to convert the orbital period from million years to seconds, as follows: 230 million years x (365.25 days/year) x (24 hours/day) x (3600 seconds/hour).
Next, convert the radius of the Sun's orbit from light-years to meters using the fact that one light-year is approximately 9.461 x 10^15 meters.
Now, we can calculate the orbital velocity of the Sun using the circumference of its orbit (2 x π x R) and the orbital period found in step 1 to obtain v = (2 x π x R) / period.
Finally, apply Kepler's Third Law to find the mass M using the velocity v from step 3, the radius R from step 2, and the known value of the gravitational constant G.
Performing these calculations would result in an estimate for the Milky Way's mass within the Sun's orbit.
Important Note
It is critical to understand that these calculations only provide the mass within the Sun's orbit. There is additional mass outside the Sun's orbit, much of which is thought to be dark matter, that is not accounted for in this simple model.