The sun\'s noon altitude is a relative indicator of the intensity of solar radia

Question

The sun's noon altitude is a relative indicator of the intensity of solar radiation received at the earth's surface. The change in intensity (i.e., noon altitude of the sun) throughout the year is determined by the inclination of the earth's axis to the plane of the ecliptic as the earth revolves around the sun. Two formulae can be used to determine the sun's noon altitude. Use the first for an observer in the winter hemisphere; the second applies when the observer is in the summer hemisphere. On the equinoxes, both formulae work. Winter hemisphere: A = 90 - | LB_oB + LB_vB | Summer hemisphere: A = 90 - | LB_oB - LB_vB | where: A is the sun's observed noon altitude in degrees above the horizon; LB_oB is the latitude of the observer; and LB_vB is the latitude where the sun is vertically overhead at noon (the sun's declination). ("| |" means "absolute value." Use positive numbers for LB_oB and LB_vB even if they're in the Southern Hemisphere). Determine the noon altitude of the sun on the Ungava Peninsula, northern Quebec, Canada (latitude 61 degree N) for each of the following dates (show your work): the equinoxes: June solstice: December solstice: Determine the noon altitude of the sun at Jambi, on the island of Sumatra, Indonesia (latitude 2 degree S) for each of the following dates (show your work): the equinoxes: June solstice: December solstice: During the course of a year, how many days does the sun appear directly overhead (i.e., noon sun altitude 90 degree above the horizon) at these two locations? Ungava Jambi Briefly, what can you infer from the previous answers about differences in the seasonality of northern Quebec and Sumatra?

Explanation / Answer

answer 5- Noon altitude of the sun on Ungava Penin Sula (latitude 60 N)

at march equinoxe (On 20/21 march)- 90- [60-0]= 30 (solar declination is zero in eqinoxes

at September equinox ( 22/23 september)- 90-[60-0] = 30 (solar declination is 0 in september equinox)

at June solestics ( on 21/22 june)- 90- [60-23.5] = 90- 36.5 = 53.5 (solar declination is 23.5 in June )

at December solstice ( on 21/22 december)- 90- [60+23.5]= 90-83.5 = 6.5 (solar declination is 23.5 in december equinox)

noon atitude at Northern Quebec, canada (latitude is 46.82)

at march Equinox (On 20/21 march)- 90- [46.82-0] = 43.18 (solar declination is 0 on march equinox)

at september equinox (on 22/23 september)- 90-[46.82] = 43.18 (solar declination is 0 in september equinox)

at June Solstice ( On 21/22 June)- 90- [46.82-23.5] = 66.68 (solar declination is 23.5 in june solstice)

at December solstice ( 21/22 December)- 90-[46.82+23.5] = 19.68 (solar declination is 23.5 in december solstice)

answer 6- noon altitude at jambi near sumata island, Indonesia (latidue is 2 degree south means -2N)

at March Equinox (20/21 march)- 90-[-2-0]= 88 (solar declination is zero in march equinox)

at September Equinox ( 22/23 september)- 90-[2-0]=88 (solar declination is 0 is september equinox)

at June solstice (20/21 june)- 90-[-2-23.5] = 90-[-25.5]= 90-25.5= 64.5 (solar declination is 23.5 is june solstice)

at december solstice( 21/22 december)- 90-[-2+23.5]= 90-21.5= 68.5 (solar declination is about 23.5 in december solstice)

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