Let us assume that our galaxy consists of $2.5 \times 10^{11}$ stars, each of one solar mass. How long will a star at a distance of $50,000 \; ly$ from the galactic centre take to complete one revolution? Take the diameter of the Milky Way to be $10^{5} \; ly$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Mass of our galaxy, $M = 2.5 \times 10^{11} \times (2.0 \times 10^{30} \; kg) = 5 \times 10^{41} \; kg$.
Radius of the orbit, $r = 50,000 \; ly = 5 \times 10^{4} \times 9.46 \times 10^{15} \; m = 4.73 \times 10^{20} \; m$.
Using Kepler's Third Law for the time period $T$ of a star revolving around the galactic centre:
$T = \sqrt{\frac{4 \pi^{2} r^{3}}{G M}}$.
Substituting the values:
$T = \sqrt{\frac{4 \times (3.14)^{2} \times (4.73 \times 10^{20})^{3}}{6.67 \times 10^{-11} \times 5 \times 10^{41}}}$.
$T = \sqrt{\frac{39.48 \times 105.82 \times 10^{60}}{33.35 \times 10^{30}}} = \sqrt{125.27 \times 10^{30}} \approx 1.12 \times 10^{16} \; s$.
Converting seconds to years:
$T = \frac{1.12 \times 10^{16}}{365.25 \times 24 \times 3600} \approx 3.55 \times 10^{8} \; \text{years}$.

Explore More

Similar Questions

The orbital period of a geostationary satellite is (in $\,h$)

Which one of the following statements regarding an artificial satellite of the earth is incorrect?

Assuming that the earth is revolving around the sun in a circular orbit of radius $R$,the angular momentum is directly proportional to $R^{n}$. The value of $n$ is

Two satellites revolve around a planet in coplanar circular orbits in an anticlockwise direction. Their periods of revolution are $1\, h$ and $8\, h$ respectively. The radius of the orbit of the nearer satellite is $2 \times 10^{3}\, km$. The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is $\frac{\pi}{x}\, rad\, h^{-1}$ where $x$ is ..... .

$A$ satellite of mass $1000 \ kg$ is launched to revolve around the earth in an orbit at a height of $270 \ km$ from the earth's surface. Kinetic energy of the satellite in this orbit is . . . . . . $\times 10^{10} \ J$. (Mass of earth $= 6 \times 10^{24} \ kg$,Radius of earth $= 6.4 \times 10^6 \ m$,Gravitational constant $= 6.67 \times 10^{-11} \ Nm^2 \ kg^{-2}$)

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo