Answer:
The time period of the solar system's orbit is [tex]2.05\times10^{8}\ year[/tex]
Explanation:
Given that,
Distance = 25000 light year
Speed of light [tex]c=3\times10^{8}\ m/s[/tex]
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
[tex]t = \dfrac{d}{v}[/tex]
[tex]t = \dfrac{2\pi r}{v}[/tex]
r = distance
t = time
v = speed
Put the value into the formula
[tex]t=\dfrac{2\pi\times25000\times9.46\times10^{15}}{230\times10^{3}}[/tex]
[tex]t=6.460\times10^{15}\ sec[/tex]
Time in years
[tex]t=\dfrac{6.460\times10^{15}}{3.15\times10^{7}}[/tex]
[tex]t=2.05\times10^{8}\ year[/tex]
Hence, The time period of the solar system's orbit is [tex]2.05\times10^{8}\ year[/tex]
