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a) Determining Angular Size from Distance and Diameter You can approximate the actual size of small objects on the sky by using the following ratio: (1) 57.3 x Object's diameter de Object's distance Small object's angular size (in degrees) Note that the object's distance and diameter must both be measured in the same linear units, like miles or light years. You must "compare apples with apples", and you could not use this formula with an object's size given in feet and its distance in miles. Instead, you would convert the diameter's measurement in feet into miles, or convert its distance measurement into feet.

a) Determining Angular Size from Distance and Diameter You can approximate the actual size of small objects on the sky by using the following ratio: (1) 57.3 x Object's diameter de Object's distance Small object's angular size (in degrees) Note that the object's distance and diameter must both be measured in the same linear units, like miles or light years. You must "compare apples with apples", and you could not use this formula with an object's size given in feet and its distance in miles. Instead, you would convert the diameter's measurement in feet into miles, or convert its distance measurement into feet.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
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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a) Determining Angular Size from Distance and Diameter You can approximate the actual size of small objects on the sky by using the following ratio: (1) Small object's angular size (in degrees) 57.3 x Object's diameter Object's distance Note that the object's distance and diameter must both be measured in the same linear units, like miles or light years. You must "compare apples with apples", and you could not use this formula with an object's size given in feet and its distance in miles. Instead, you would convert the diameter's measurement in feet into miles, or convert its distance measurement into feet.
Transcribed Image Text:a) Determining Angular Size from Distance and Diameter You can approximate the actual size of small objects on the sky by using the following ratio: (1) Small object's angular size (in degrees) 57.3 x Object's diameter Object's distance Note that the object's distance and diameter must both be measured in the same linear units, like miles or light years. You must "compare apples with apples", and you could not use this formula with an object's size given in feet and its distance in miles. Instead, you would convert the diameter's measurement in feet into miles, or convert its distance measurement into feet.
2. a) Use Equation (1) to determine: the angular size of a person 5.5 feet tall standing 5.0 x 10¹ feet (50 ft) away. Use 5.5 feet as the diameter of the "object" in the equation; be sure to include the proper unit and proper number of significant digits.) b) the angular size of a person 5.5 feet tall standing 5.0 x 10² feet (500 ft) away. Answer: Measure/Research This: Determine This: Answer: c) the angular size of a dime seen from 1 mile away. To do this, you must first measure or research the size of a dime, and then be sure you use the same units for diameter and distance in the equation. Use the following conversion factors (assumed to be exact) to help you calculate this quantity: 1 mile = 5280 feet 1 foot 12 inches 1 inch = 2.54 cm Diameter of a dime = Distance of 1 mile = Calculate the angular size of a dime seen from 1 mile: Unit: Answer: Unit: centimeters centimeters Unit:
Transcribed Image Text:2. a) Use Equation (1) to determine: the angular size of a person 5.5 feet tall standing 5.0 x 10¹ feet (50 ft) away. Use 5.5 feet as the diameter of the "object" in the equation; be sure to include the proper unit and proper number of significant digits.) b) the angular size of a person 5.5 feet tall standing 5.0 x 10² feet (500 ft) away. Answer: Measure/Research This: Determine This: Answer: c) the angular size of a dime seen from 1 mile away. To do this, you must first measure or research the size of a dime, and then be sure you use the same units for diameter and distance in the equation. Use the following conversion factors (assumed to be exact) to help you calculate this quantity: 1 mile = 5280 feet 1 foot 12 inches 1 inch = 2.54 cm Diameter of a dime = Distance of 1 mile = Calculate the angular size of a dime seen from 1 mile: Unit: Answer: Unit: centimeters centimeters Unit:
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