Question

The solar system is 25,000 light years from the center of our Milky Way galaxy. One light year is the distance light travels in one year at a speed of 3.0×108m/s. Astronomers have determined that the solar system is orbiting the center of the galaxy at a speed of 230 km/s.
Assuming the orbit is circular, what is the period of the solar system's orbit?

Answer 1

Answer:

t = 2.05 x 10⁸ years

Explanation:

given,

solar system distance from milky way galaxy =  25,000 light years

Speed of light = 3.0×10⁸ m/s

orbiting speed of solar system = 230 Km/s

time period of solar system = ?

1 light year  = 9.461 x 10¹⁵ m

Distance(r) = 25,000 x 9.461 x 10¹⁵ m

              =2.365 x 10²⁰ m

Circumference(r) = 2 π r

                            = 2 x π x 2.365 x 10²⁰

                            = 1.486 x 10²¹ m

distance = speed x time

$t = \dfrac{1.486 \times 10^{21}}{230 \times 10^3}$

t = 6.47 x 10¹⁵ sec

$t = \dfrac{6.47\times 10^{15}}{60\times 60\times 24 \times 365}$

t = 2.05 x 10⁸ years