A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is 5.7 x 1020 m, and the angular speed of the star is 5.4 x 10-15 rad/s. How long (in years) does it take for the star to make one revolution around the center? (b) Number Units Vp

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Text Transcription:**

A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is \(5.7 \times 10^{20}\) m, and the angular speed of the star is \(5.4 \times 10^{-15}\) rad/s. How long (in years) does it take for the star to make one revolution around the center?

(b) [Input box]

Units [Dropdown menu]

**Diagram Explanation:**

The diagram shows a spiral galaxy with a highlighted path indicating the circular orbit of a star. The orbit is marked as a dashed circle around the center of the galaxy. The diagram includes:

- An outer circular path, labeled as "r" (radius).
- A red arrow indicating the direction of the star's motion along the circular orbit.
- The spiral arms of the galaxy are depicted in a light blue color, winding towards the center.
- A central point representing the center of the galaxy.

This visual illustrates the star's orbit in relation to the galactic structure.
Transcribed Image Text:**Text Transcription:** A star rotates in a circular orbit about the center of its galaxy. The radius of the orbit is \(5.7 \times 10^{20}\) m, and the angular speed of the star is \(5.4 \times 10^{-15}\) rad/s. How long (in years) does it take for the star to make one revolution around the center? (b) [Input box] Units [Dropdown menu] **Diagram Explanation:** The diagram shows a spiral galaxy with a highlighted path indicating the circular orbit of a star. The orbit is marked as a dashed circle around the center of the galaxy. The diagram includes: - An outer circular path, labeled as "r" (radius). - A red arrow indicating the direction of the star's motion along the circular orbit. - The spiral arms of the galaxy are depicted in a light blue color, winding towards the center. - A central point representing the center of the galaxy. This visual illustrates the star's orbit in relation to the galactic structure.
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