Problem 56323. Air Mass to Star for an Observer at Mean Sea Level

Created by Meg Noah

Solve Later

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<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 281px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 140.5px; transform-origin: 407px 140.5px; vertical-align: baseline; "><div style="block-size: 63px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 31.5px; text-align: left; transform-origin: 384px 31.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 375.5px 8px; transform-origin: 375.5px 8px; unicode-bidi: normal; "><span style="">Air mass is a measure of how much atmosphere light from a source above the atmosphere (eg sun, planet, star) has to travel through to reach an observation point on the Earth surface. It’s measured as a ratio of the amount of atmosphere relative to the amount of atmosphere for an overhead (nadir) line-of-sight.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 239.5px 8px; transform-origin: 239.5px 8px; unicode-bidi: normal; "><span style="">To calculate air mass, divide the value of 1 by the cosine of the zenith angle.</span></span></div><div style="block-size: 37px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.5px; text-align: left; transform-origin: 384px 18.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-17px"><img 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style="width: 129.5px; height: 37px;" width="129.5" height="37"></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 261.5px 8px; transform-origin: 261.5px 8px; unicode-bidi: normal; "><span style="">The elevation angle of a star is given with respect to the local astronomical horizon:</span></span></div><div style="block-size: 22px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11px; text-align: left; transform-origin: 384px 11px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-6px"><img src="data:image/png;base64,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" style="width: 137px; height: 21px;" width="137" height="21"></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 378px 8px; transform-origin: 378px 8px; unicode-bidi: normal; "><span style="">Write a function to calculate the Air Mass a star's light passes through from the line-of-sight elevation angle in degrees.  Allow the function to compute air mass for an array of line-of-sight elevation angles.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 8px; transform-origin: 0px 8px; unicode-bidi: normal; "><span style=""></span></span></div></div></div>

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Solution 10159707

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Sebastian Szymczyk on 15 Dec 2022

It would be nice if the specifications of the problem were stated more clearly, as while making the function suitable for processing vectors is easy to do, it should have been stated as a requirement that the function must be able to process vectors.

Dyuman Joshi on 16 Dec 2022

@Sebastian, that is left to the solver to go through all the test cases and is not considered a special requirement on Cody.

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Problem 56323. Air Mass to Star for an Observer at Mean Sea Level

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Problem 56323. Air Mass to Star for an Observer at Mean Sea Level

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