Calculating Angular Distance on a Circular Track with Given Radius and Distance

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In summary, simple angular distance is a measure of the angle between two points on a circle or sphere and is commonly used in fields such as astronomy and navigation. It can be calculated by dividing the arc length between two points on a circle by the radius of the circle and can be expressed in various units such as degrees, radians, or arcminutes/arcseconds. It differs from great circle distance, which measures the shortest distance between two points on the surface of a sphere. Some practical applications of simple angular distance include astronomy, navigation, surveying, and cartography.
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eshock202
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Homework Statement


running on a circular track w/ radius of .450 km and runs a distance of 2.54 km. what is the angular distance in radians.


Homework Equations


theta = s/r


The Attempt at a Solution


I assume the 2.54 km would be the arc length? so would the answer just be 2.54/.450 = 5.65 rad?
 
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FAQ: Calculating Angular Distance on a Circular Track with Given Radius and Distance

What is simple angular distance?

Simple angular distance is a measure of the angle between two points on a circle or sphere. It is often used in astronomy and navigation to determine the position of celestial bodies.

How is simple angular distance calculated?

Simple angular distance is calculated by dividing the arc length between two points on a circle by the radius of the circle. This can be expressed as a fraction, decimal, or in degrees, minutes, and seconds.

What units are used to measure simple angular distance?

Simple angular distance can be measured in degrees, radians, or arcminutes/arcseconds. Radians are the most commonly used unit in scientific calculations, while degrees are more commonly used in everyday life.

How is simple angular distance different from great circle distance?

Simple angular distance is a measure of the angle between two points on a circle or sphere, while great circle distance is a measure of the shortest distance between two points on the surface of a sphere. Simple angular distance takes into account the curvature of the circle or sphere, while great circle distance does not.

What are some practical applications of simple angular distance?

Simple angular distance is used in a variety of fields, including astronomy, navigation, surveying, and cartography. It is also used in calculations for satellite orbits, telescope pointing, and determining the position of stars and planets in the sky.

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