Given that the Sun moves in a circular orbit of radius 8 kpc...

Given that the Sun moves in a circular orbit of radius 8 kpc around the center of the Milky Way, and its orbital speed is $220 \mathrm{km} / \mathrm{sec},$ work out how long it takes the Sun to complete one orbit of the Galaxy.

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Key Concepts

Circular Motion

Circular motion involves the movement of an object along a circular path with a constant radius. The key aspect in calculating orbital characteristics, such as the orbital period, is understanding that the distance traveled in one complete orbit is given by the circumference of the circle, which is 2? times the radius.

Orbital Period Calculation

The orbital period is computed by dividing the distance of one complete orbit (the circumference) by the orbital speed. This basic relation, period = distance/speed, is fundamental to understanding motion in gravitational fields where orbits are approximately circular.

Unit Conversion

Unit conversion is crucial in astronomy to maintain consistency across measurements. When working with distances expressed in kiloparsecs (kpc) and speeds in kilometers per second (km/s), it is necessary to convert these to compatible units, and often to transform the final result into more comprehensible units like years.

Galactic Scale

Understanding galactic scales involves comprehending the vast distances and time periods that are typical within a galaxy. Recognizing the scale at which these measurements occur helps in contextualizing the motion of stars and the structure of galaxies.

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