Final answer:
Our solar system orbits the center of the Milky Way Galaxy, taking approximately 230 million years to complete one revolution with an orbital speed of 250 km/s and a radius of 30,000 light-years.
Step-by-step explanation:
The solar system orbits the center of the Milky Way Galaxy approximately every 230 million years (the duration of one galactic year). With an assumed circular orbit and a radius of 30,000 light-years, our solar system's speed in this orbit is about 250 kilometers per second. To calculate the period of orbit, we can use the formula for the circumference of a circle (C = 2πr) and then divide by the speed to find the time. Given a radius (r) of 30,000 light-years and knowing that 1 light-year is approximately 9.461×1012 kilometers, we first convert the orbital radius into kilometers and then calculate the circumference. Dividing this by the constant speed of 250 km/s gives us the time for one complete revolution around the Milky Way's center.
The orbital distance traveled by the solar system in one galactic year can be calculated as (2π × 30,000 ly × 9.461×1012 km/ly), which equals approximately 5.66×1017 km. Dividing this distance by the orbital speed (250 km/s) results in approximately 2.26×1015 seconds. To convert this into years, we divide by the number of seconds in a year (31,536,000 s/year), which gives us approximately 230 million years.