astronomical observations of our milky way galaxy indicate that it has a mass about 8.0 *10^13 times the mass of our sun. a star orbiting on the galaxy edge is about 6.0*10^4 light years a way from the galactic center what is the orbital period of that star in earth year
To determine the orbital period of a star on the edge of our Milky Way galaxy, we can use the concept of Kepler's third law of planetary motion. Kepler's third law states that the square of the orbital period (T) of a celestial object is directly proportional to the cube of its average distance (r) from the central object.
1. First, convert the distance from light-years to meters. We know that 1 light-year is approximately equal to 9.461 × 10^15 meters. Therefore, the distance of the star from the galactic center is:
Distance = 6.0 × 10^4 light years × (9.461 × 10^15 meters / 1 light year)
= 5.6766 × 10^20 meters
2. Next, calculate the orbital period using the mass of the Milky Way galaxy and the known value of the gravitational constant (G). The formula for calculating the orbital period is:
T^2 = (4π^2 / G) × r^3 / M
where T is the orbital period, r is the distance from the galactic center, G is the gravitational constant, and M is the mass of the Milky Way galaxy.
The mass of the Milky Way galaxy is given as 8.0 × 10^13 times the mass of our sun. The mass of the sun is approximately 1.989 × 10^30 kilograms. Therefore, the mass of the Milky Way galaxy is:
M = 8.0 × 10^13 × (1.989 × 10^30 kg)
= 1.5912 × 10^44 kg
The value of the gravitational constant (G) is approximately 6.67430 × 10^-11 m^3/(kg s^2).
3. Substituting the values into the formula, we get:
T^2 = (4π^2 / (6.67430 × 10^-11 m^3/(kg s^2))) × (5.6766 × 10^20 m)^3 / (1.5912 × 10^44 kg)
= 7.1137 × 10^38 s^2
4. Finally, to calculate the orbital period (T) in years, take the square root of the obtained value and divide it by the number of seconds in a year. The number of seconds in a year is approximately 3.154 × 10^7.
T = √(7.1137 × 10^38 s^2) / (3.154 × 10^7 s/year)
= 2.389 × 10^16 years
Therefore, the estimated orbital period of the star on the edge of our Milky Way galaxy is approximately 2.389 × 10^16 years.