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Imagine a giant ruler at the planet's distance that is 1 arcsecond across in your image. Given this angular length, and this distance to the ruler in AU, you can calculate the physical length of the ruler in AU. This then allow you to convert your measurement of the semi-major axis from arcseconds to AU. 0/ 360° - length / circumference (of big circle) 360° 0 = angular length = 1 arcsecond length

Imagine a giant ruler at the planet's distance that is 1 arcsecond across in your image. Given this angular length, and this distance to the ruler in AU, you can calculate the physical length of the ruler in AU. This then allow you to convert your measurement of the semi-major axis from arcseconds to AU. 0/ 360° - length / circumference (of big circle) 360° 0 = angular length = 1 arcsecond length

Stars and Galaxies (MindTap Course List)
Stars and Galaxies (MindTap Course List)
10th Edition
ISBN:9781337399944
Author:Michael A. Seeds
Publisher:Michael A. Seeds
Chapter4: Origins Of Modern Astronomy
Section: Chapter Questions
Problem 9P
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Imagine a giant ruler at the planet's distance that is 1 arcsecond across in your image. Given this angular length, and this distance to the ruler in AU, you can calculate the physical length of the ruler in AU. This will then allow you to convert your measurement of the semi-major axis from arcseconds to AU. 0/ 360° - length / circumference (of big circle) 360° 0 = angular length =1 arcsecond length
Transcribed Image Text:Imagine a giant ruler at the planet's distance that is 1 arcsecond across in your image. Given this angular length, and this distance to the ruler in AU, you can calculate the physical length of the ruler in AU. This will then allow you to convert your measurement of the semi-major axis from arcseconds to AU. 0/ 360° - length / circumference (of big circle) 360° 0 = angular length =1 arcsecond length
The physical length of the ruler as a fraction of the circumference of the big circle is the same as the angular length of the ruler as a fraction of 360°: length circumference %3D 360° Since circumference = 2n x radius and the radius of the big circle is the distance to the ruler/planet: length 2n x distance 360° Solving for the physical length of the ruler yields: length = 2n x distance 360° Question: Use this equation to determine a conversion factor from 1 arcsecond to AU at the planet's distance. You will need to convert e = 1 arcsecond to degrees first. AU Show your work for this calculation.
Transcribed Image Text:The physical length of the ruler as a fraction of the circumference of the big circle is the same as the angular length of the ruler as a fraction of 360°: length circumference %3D 360° Since circumference = 2n x radius and the radius of the big circle is the distance to the ruler/planet: length 2n x distance 360° Solving for the physical length of the ruler yields: length = 2n x distance 360° Question: Use this equation to determine a conversion factor from 1 arcsecond to AU at the planet's distance. You will need to convert e = 1 arcsecond to degrees first. AU Show your work for this calculation.
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