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,iVBORw0KGgoAAAANSUhEUgAAARIAAAAqCAYAAAB/adRXAAAL0klEQVR4Xu2cXahtVRXH9V0x86mQiupB6ctIKwijog+IJExSe4lLyk0DkSijIuISUlJGRJAlKRcfvFdDRYpAiwrFiylBYVEPFRVhT2aR7zl+1/U//Z1nrI999tn7rL3PWDDY56w11/wYc4z/HB9zrjPPqKs4UBwoDizJgTOXfL9eLw4UB4oDZxSQlBAUB4oDS3OggGRpFlYFxYHiQAFJyUBxoDiwNAcKSJZmYVVQHCgOFJCUDBQHigNLc6CAZGkWVgXFgeJAAUnJQHFgfznwmqjuyqAPd9U+Er+3BP1rf5uZV20FJPOaj7n25pLo2GeDXtl18HXxeyrozqB7Rjr90nj++aB3duXO6X6PTXh3rvzo69d18eAbQT8J+mIHKF+N338GvX6bwaSAZNNEdf39/UI0iTKgGF/rmgccbusU5Vfx+/aebgFAPw/6bxAr9JNdORSO9/8YdOH6h7SSFr8ftR4NujfoegMNxn5WBzCfW0nLM6i0gGQGkzDjLgwpPGDyu6CXdcpzVTMOnv+tU6Kr47e1XB6Ke+8PejjoA/Yu753onnH79qBPzphHdE18wvK4NOjP1t/H4++3BW0TaO6ajgKSmUvoAXbPgQBzPVtNZa3QzbcGyeLgf4CDWAHK9fJkHFgrT3T3ARIAhQvFw3W6NujVQVhDfe0fIHt2mgYMAUWuDDAFJDzfWn3b2oHNQcI2vA9aZRmGK7oPy8EAk15WCQHHP3UF/X7LEpn97h79Lwq5FYIiEleZowvkVhlj+GBQG1R1IDkveb7hYvJC9wtItmIaVzIIWRRU3lob3iCKz/Vc0Nnd326peGyl7WimZH/ogIPgJIBEjIXgZes6rWTQC1b69Sh/U/dOZo3wiPFc0JUpIFmQwVV88zngSj4EJLIqGPFrg4gPTH03U0QFaAlQchFb+FBX75y4Csj9Joh+0sd3BGUpXgdasl5bmQaeYpHAMPxj0nf/CVLq70vxNz4xzxUM+3X8PZYOnJMwVF/6OeBg0Ofa8HYGGk/HfYKwXEMg5EDSxkGIPXApdjK3ufK+91lduD7PdB0/1MFWMQsmfLwDDl8xWIEIhhFUw7R9T1dmbpO+6f3xgN4yYxlyM9p6lc7k/lCwMwMSrcKLAEmbvVlmnOt4N7PE2nZ93obS5Ovo70rbGLJIPOreprQkZDCH1BbXJqTpVsrMFVZ+EEBCTOLkhNXUYwCyPqaa897GJgGJ93sIIIYsrhWKy/qr7gMSZ0Bm1npEn15v/c699U/NLFp0kGCT1feaXnnWxi3SLACbDcgBcpOAxAPRUydqyD2cWsdsy2VA4qm7vsltV8hMyGY76OrYZA60gU9SuXd0b18Tv28MUkbCszYH4drsh9U2FcwcYPsAwuMjW7/QZkDiaNvHpNa0y/Lnk6W1K0idbwl6U9CUMxyL1l/l98YBFIKt8QTbBRqY8xxG+1mQNmP5fpHM3cla30/Tf51AIqAcAgi32jfR7WfeiX2yKZC5vyHINxy+aD4zIFEQaYhJU/YYsJrdHOTR9992rZMGI+5CZN8DgBLAuZmB2uVJ97VXYm9quV1vuRz4Pgptf2e0U7M2m2LVujs3FB9REBpL7aIg3zavOtCxR4M4SqCLzXec2eFaRYB2EVmWVZVt/R8EkilujW+dHjMFfZXQHgN1QLsCj8QNpfhIG3K1wd2DVj+N+R/RkYPY07Afqy08XCRrM8Zzl5VW4H1D2hBACHA2KePnc9FnaYyVIVnxkiA/3Cd+azH1TOnYXCzyfBFZ1hyPAlprkYwxgA77KjRmssl07TtvgSB9Kgi0ntzpRbi2h7Iy5VGGuWwemiOQ+Irbpv0dZIZkRPtNNmmPxRQdEW/6VnKXexdRZUMBVs4arXtPFu2js7Ke5J6NnnVqgcTNtkwAWoFWGRr/S1Ab1RdD+85b0F57tHy003sAh6mvACKPBbHxru9o/NS6trmcFggEni3i7bz7gjPl0F7f9vI58nAMJKV88OaKoKkb6jymsp+W41QeAlp4Au4NyGgYDTUMxUiy491+bFwnOzkTwf3MHVFQygUFhhHAaU+TyszNfGp9depV8R7BWAI/oOb7ggjQEnPxsxjU9csgfT8DZip49Ob4G7PyF0GXBxHY/WkQu3OZQG15viv+BqG5r3a/HH+3ggG4vpcGur5908qgcPT3FUEEJ7Fy9B2PTVqFu+Gd/pkCIuL30GcEJKRj7rG3PZe/ZUm1Jr9nuRYBA3+vb9F1+UUeHwgCwJE/AEtyhh5eHPStIGKQ0j3ez2QZfbwxiEA64Id83hKENa5QAzqOrqnOXUZGBiTu3yqugSL/OIhA0KeDsD50BJzJzawXZXY82EQ9BJf8IzcSDoK8UPslKQQXX1IrH1YOisnRdD996TEY+Zm6x0Q9GPSjILksCio7cMmCauM5AGIbNKNtDpPBE+36lZJ5XEB1MqEfCSJ9+u0gJq5tR7yY4y9z990gBHeq/y4FYTwecNTq23dido7j9z551lIH8fwjTkei8FRLZMoJYtr7QZCUnC/OoQ+SH3kK8PN4EAs1Okr5FpgyWc7kVt4J4wC03h10axB6v8vK7NuQhrKx6oNodI4LRaRT8p9kQQAiWTzBd7+yGnNdFoTitWDhnfaP3GjVkmLKrHTmqB23emAsyspBKp0gPRV/e90wtM1M6R4gpUt9cwtCLhBjcVDUhHpZAeTfo6wsmrkGlW3YO38yJvaMkOL/fdDxoMyVyd7lHvznGAUrJTyAZ7iOyBNzN5c4VF//++4DhswnWTz4wriwYl1HptQpPUIWswVWoOsyj/zAQx0U1OIv8ELOs/hGJsv0MVtA2zo/FuWwaJjLXVbTlEN7U5iRlZH55zEPBodroUN+ek+ddnPQVy3iFTCBiUIYGZQEUOX8XQAI1wWBl9L6JGWApFWmta7UNx+HAC47aIZgCEg85qT+qe1NMOkRMBYBVjfcP09h7lUu6r3/c8DdxCy4KllR0PbZePVEEBa5rGBqExj5SWnJqFvcmSwrxdu62lmdurfLbVsVkHhAygfie0pcoLL4iIAIhftrkOIa7WooK0AoifJ+J4gVtA9BM1Mus2x8khRwaifXlUt1eBAaE9SPmWfAV8p1+Djg7lFfgkFggPwA6OgAny5oLTnFIt2l9viGFl3pmQdP+xZQuf5u6Usnd8UxVwUkUpahTW0opJSwjY+4smbmnoudAwmMxC/ElyMbJJPNGef7YNq4yvnxTrt5qHWBWkvJ+wKjMXWVDlX7PsHZSnH41Ohwj9i/ZdJnmSqu5wHTjGvuTsvV6bN6M3c+W0AzF0h1pkmCVQGJkG8o7YubwuYuFJsADmVROAJJ2nqdpQ49ZSzGwiDFcogsK/8upHbAkCIL5M6N8piMfDdCwT+YBhBpkphs9rvQ148GYWW0Y8vMxmzi2kj4uvcKHG4VPvjRK75GsN0tVe8ZcveZTv643wblkU9kFktD1nUWFkCfKIdbSiYHvXRZRsb1RTpiWNTL86FQA9bTD7u2d6zxVQGJzKIsBQaT7gu6OwjXQ51m0ESGyWowGNXhgVayBmyzb1PHikS3fqZMMcwzmIm1QkoSIKANAmQElYlynwwCHLhk0fgkvSvu8zEnLoDPVxJF7KlffXMQUpBXSE87/w7iM4IFJB1TD8mPL2SZtS1ZQpY/EYQcadEChFhoSfUqTiir190NLeTKFGqBRu7RSckyQMACKtdJ8pjV6XtKvhLvEDrYCZTvN5B4ihC5IGUKYBBhZvBvCMJU49LA5aOhmH5Yz007ysPM+3sUD9DJglVMwvGuTawNrBWlrrFISGXDILkrMPSYtaG+tfcVsX8qygJs7GNRcLcb3mk/9miQ+5gyaSnTt5FL79fv9nHAN50hU2xH8IvDcXzfx4OrbDHQN3+QYbJd2h/VFyiV7Mn6ADAyWfb0PNkY1ZtlLwVO9GHXAb79BpLtm/oaUXGgODDKgQKSURZVgeJAcWCMAwUkYxyq58WB4sAoBwpIRllUBYoDxYExDhSQjHGonhcHigOjHCggGWVRFSgOFAfGOFBAMsahel4cKA6McuB5H/p0WLf+RAgAAAAASUVORK5CYII=" 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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Problem 56323. Air Mass to Star for an Observer at Mean Sea Level

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