91Ó°ÊÓ

The distance covered by the object in a circular path of radius\(r\)for completing one revolution is given by,

\(d = 2\pi r\)

If the speed of the revolution is\(v\), then the time for one revolution is

\(T = \frac{{2\pi r}}{v}\)

We then can calculate the time using the formula as:

\(\begin{aligned}{}T & = \frac{s}{v}\\ & = \frac{{2r\,\pi }}{v}\end{aligned}\)

On substituting the values in the above equation,

\(\begin{aligned}{}T & = \frac{{2\pi \left( {3.00 \times {{10}^4}\,{\rm{ly}}} \right)}}{{250\,{\rm{km/s}}}}\\ & = \frac{{2\pi \left( {3.00 \times {{10}^4}\,{\rm{ly}}} \right)\left( {9.460 \times {{10}^{12}}\,{\rm{km/ly}}} \right)}}{{250\,{\rm{km/s}}}}\\ & = 7.1327 \times {10^{15}}\,{\rm{s}}\end{aligned}\)

Converts the seconds to the years,

\(\begin{aligned}{}T & = \left( {7.1327 \times {{10}^{15}}\,{\rm{s}}} \right)\left( {\frac{{1{\rm{y}}}}{{3.156 \times {{10}^7}\,{\rm{s}}}}} \right)\\ & = 2.26 \times {10^8}\,{\rm{y}}\end{aligned}\)

Therefore, the time taken by the solar system to revolve around the milky way is approximately \(2.26 \times {10^8}\,\)years.