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

t = 2.05 x 10⁸ years

Step-by-step 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 = (1.486 * 10^(21))/(230 * 10^3)`

t = 6.47 x 10¹⁵ sec

`t = (6.47* 10^(15))/(60* 60* 24 * 365)`

t = 2.05 x 10⁸ years