Whizzing stars

Classical Mechanics Level 3

The star S2 orbits the central region of our galaxy extremely quickly. The star has an orbital period of 15.5 years. The orbit is an ellipse, and the point of closest approach of S2 to the center of our galaxy is 17 light-hours, or \(1.84 \times 10^{13}~m\). To get an idea about how close this is in astronomical terms, this is about four times as far as the distance from the sun to Neptune.

Since the orbit is an ellipse the velocity of the star is not constant. However, we can get a rough estimate of the average speed by treating the orbit as a perfect circle. If the orbit of S2 was a perfect circle of radius 17 light-hours, what fraction of the speed of light is S2 going on average, i.e. what is \(v_{S2}/v_{light}\)?

Details and assumptions

  • The speed of light is \(3 \times 10^8~m/s\).
  • There are \(3.15 \times 10^7\) seconds in a year.

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