a. The solar system travels about 188495.56 light years each year.
b. the solar system is circling the center of the galaxy at about 520000 mi/hr
a. Distance solar system travels each year.
The solar system travels about 188495.56 light years each year.
Since the distance the solar system travel around the milky way is a circular orbit. The distance travelled is the circumference of a circle.
So, the circumference C = 2πr where
- r = radius of circle = distance of solar system from center of milky wat = 30000 light years
So, C = 2πr
= 2π × 30000 light years
= 60000π light years
= 188495.56 light years
So, the solar system travels about 188495.56 light years each year.
b. Speed of solar system
The solar system is circling the center of the galaxy at about 520000 mi/hr
The speed of the solar system circling the milky way is given by v = rω where
- r = radius of orbit = 30000 light years = 30000 × 5.88 × 10¹² miles = 1.764 × 10¹⁷ miles and
- ω = angular velocity of solar system = 2.6 × 10⁻⁸ radians per year = 2.6 × 10⁻⁸ radians per year × 1year/365 days × 1 day/24 hours = 2.6 × 10⁻⁸ radians/8760 hour = 2.97 × 10⁻¹² radians per hour
So, substituting the values of the variables into the equation, we have
v = rω
v = 1.764 × 10¹⁷ miles × 2.97 × 10⁻¹² radians per hour
v = 5.23908 × 10⁵ miles/hour
v = 523908 miles/hour
v ≅ 520000 mi/hr to the nearest ten thousand
So, the solar system is circling the center of the galaxy at about 520000 mi/hr
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