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.

Answer 1

Answer:

The time period of the solar system's orbit is $2.05\times10^{8}\ year$

Explanation:

Given that,

Distance = 25000 light year

Speed of light $c=3\times10^{8}\ m/s$

Speed of astronomers = 230 m/s

Suppose the orbit is circular, we need to find the time period of the solar system's orbit.

We need to calculate the time period

Using formula of time period

$t = \dfrac{d}{v}$

$t = \dfrac{2\pi r}{v}$

r = distance

t = time

v = speed

Put the value into the formula

$t=\dfrac{2\pi\times25000\times9.46\times10^{15}}{230\times10^{3}}$

$t=6.460\times10^{15}\ sec$

Time in years

$t=\dfrac{6.460\times10^{15}}{3.15\times10^{7}}$

$t=2.05\times10^{8}\ year$

Hence, The time period of the solar system's orbit is $2.05\times10^{8}\ year$