Calculating Sun Angles Today you will calculate the angle of the sun

Calculating Sun Angles Today you will calculate the angle of the sun at NOON (12:00) for different locations on Earth.

Calculating Sun Angles You will be working with complementary angles. Remember, complementary angles always add up to 90o.

Calculating Sun Angles High sun angles (45o to 90o) mean more intense sunlight.

Calculating Sun Angles High sun angles (45o to 90o) mean more intense sunlight. 80o

Calculating Sun Angles High sun angles (45o to 90o) mean more intense sunlight. 80o Low sun angles (0o to 45o) mean less intense sunlight.

Calculating Sun Angles High sun angles (45o to 90o) mean more intense sunlight. 80o Low sun angles (0o to 45o) mean less intense sunlight. 30o

Latitude of 90o Sun Angle Changes Over the year, the latitude where the sun’s rays form a 90o angle, at noon, with the surface, moves slowly between the Tropic of Cancer and the Tropic of Capricorn.

Equinox On March 22 and on September 22, the sun’s rays form a 90o angle at noon at the equator. Path of incoming sun’s rays 0o latitude

Equinox On March 22 and on September 22, the sun’s rays form a 90o angle at noon at the equator. Path of incoming sun’s rays Vertical Pole standing at the equator will not cast a shadow at noon! 0o latitude

Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree.

Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree. 1o latitude

Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree. 89o 1o latitude

Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree. 89o 1o latitude 2o latitude

Equinox At an Equinox, for every degree of latitude you move away from the equator, the sun angle at noon decreases by 1 degree. 89o 1o latitude 88o 2o latitude

Solstices

Solstices June 22

Solstices June 22 – The sun forms a 90o angle at noon at 23.5o N

Solstices June 22 – The sun forms a 90o angle at noon at 23.5o N – This latitude is called the Tropic of Cancer.

Solstices June 22 – The sun forms a 90o angle at noon at 23.5o N – This latitude is called the Tropic of Cancer. – This is the summer solstice for the Northern Hemisphere.

Solstices June 22 – The sun forms a 90o angle at noon at 23.5o N – This latitude is called the Tropic of Cancer. – This is the summer solstice for the Northern Hemisphere. – This is the winter solstice for the Southern Hemisphere.

Solstices December 22

Solstices December 22 – The sun forms a 90o angle at noon at 23.5o S

Solstices December 22 – The sun forms a 90o angle at noon at 23.5o S – This latitude is called the Tropic of Capricorn

Solstices December 22 – The sun forms a 90o angle at noon at 23.5o S – This latitude is called the Tropic of Capricorn – This is winter solstice for the Northern Hemisphere.

Solstices December 22 – The sun forms a 90o angle at noon at 23.5o S – This latitude is called the Tropic of Capricorn – This is winter solstice for the Northern Hemisphere. – This is the summer solstice for the Southern Hemisphere.

Solstices On the summer solstice the sun’s rays form a 90o angle at noon at 23.5o N Path of incoming sun’s rays Vertical Pole standing at 23.5o will not cast a shadow at noon! 23.5o N

Solstices On the summer solstice, for every degree of latitude you move away from 23.5o, the sun angle at noon decreases by 1 degree. 24.5o N (23.5 1)

Solstices On the summer solstice, for every degree of latitude you move away from 23.5o, the sun angle at noon decreases by 1 degree. 89o 24.5o N (23.5 1)

Solstices On the summer solstice, for every degree of latitude you move away from 23.5o, the sun angle at noon decreases by 1 degree. 89o 24.5o N (23.5 1) 25.5o N (23.5 2)

Solstices On the summer solstice, for every degree of latitude you move away from 23.5o, the sun angle at noon decreases by 1 degree. 89o 24.5o N (23.5 1) 88o 25.5o N (23.5 2)

Noon Sun Angle Equation

Noon Sun Angle Equation You are about to find the angle of the sun at noon at different latitudes.

Noon Sun Angle Equation You are about to find the angle of the sun at noon at different latitudes. – To do this, you will use the following formula:

Noon Sun Angle Equation You are about to find the angle of the sun at noon at different latitudes. – To do this, you will use the following formula: Noon Sun Angle 90 - Zenith Angle

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle You need to subtract from 90 because the angles you are working with are complementary.

Noon Sun Angle Equation Sun Angle 90 - Zenith Angle

Noon Sun Angle Equation Sun Angle 90 - Zenith Angle The zenith angle is the distance between the subsolar point and the latitude you are “at”.

Noon Sun Angle Equation Sun Angle 90 - Zenith Angle The zenith angle is the distance between the subsolar point and the latitude you are “at”. The subsolar point is the latitude where the sun’s rays form a 90o angle at noon.

Noon Sun Angle Equation Sun Angle 90 - Zenith Angle The zenith angle is the distance between the subsolar point and the latitude you are “at”. The subsolar point is the latitude where the sun’s rays form a 90o angle at noon. In other words: Noon Sun Angle 90 - (latitude your are at latitude where sun is 90o at noon)

Noon Sun Angle Equation To calculate the zenith angle between the subsolar point and the latitude you are “at” requires a bit of thought .

Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract.

Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. – Example: Subsolar Point 0o

Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. – Example: Subsolar Point 0o You are at 45oN.

Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. – Example: Subsolar Point 0o You are at 45oN. Zenith Angle (45 - 0)

Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. – Example: Subsolar Point 0o You are at 45oN. Zenith Angle (45 - 0) 45

Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add.

Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add. – Example: Subsolar Point 23.5o S

Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add. – Example: Subsolar Point 23.5o S You are at 45oN.

Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add. – Example: Subsolar Point 23.5o S You are at 45oN. Zenith Angle (45 23.5)

Noon Sun Angle Equation If the subsolar point and your latitude are in different hemispheres, add. – Example: Subsolar Point 23.5o S You are at 45oN. Zenith Angle (45 23.5) 68.5

Noon Sun Angle Equation If the subsolar point and your latitude are in the same hemisphere, subtract. If the subsolar point and your latitude are in different hemispheres, add.

Noon Sun Angle Equation Let’s do some problems together!

Noon Sun Angle Equation It is the June 22nd solstice (summer).

Noon Sun Angle Equation It is the June 22nd solstice (summer). The subsolar point is 23.5o N

Noon Sun Angle Equation It is the June 22nd solstice (summer). The subsolar point is 23.5o N You are visiting a friend in Brussels, Belgium

Noon Sun Angle Equation It is the June 22nd solstice (summer). The subsolar point is 23.5o N You are visiting a friend in Brussels, Belgium

Noon Sun Angle Equation It is the June 22nd solstice (summer). The subsolar point is 23.5o N You are visiting a friend in Brussels, Belgium

Noon Sun Angle Equation It is the June 22nd solstice (summer). The subsolar point is 23.5o N You are visiting a friend in Brussels, Belgium Your latitude is 50o N

Noon Sun Angle Equation It is the June 22nd solstice (summer). The subsolar point is 23.5o N You are visiting a friend in Brussels, Belgium Your latitude is 50o N What is the angle of the sun at noon?

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract!

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 50 - 23.5

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 50 - 23.5 26.5

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 50 - 23.5 26.5 Noon Sun Angle 90 - 26.5

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 50 - 23.5 26.5 Noon Sun Angle 90 - 26.5 63.5o

Noon Sun Angle Equation A noon sun angle of 63.5o is considered a high angle. This answer makes sense because it is summer time where you are.

Noon Sun Angle Equation Good Job!!! Let’s try another one!

Noon Sun Angle Equation It is the March 22nd.

Noon Sun Angle Equation It is the March 22nd. It is the Spring Equinox.

Noon Sun Angle Equation It is the March 22nd. It is the Spring Equinox. The subsolar point is 0o

Noon Sun Angle Equation It is the March 22nd. It is the Spring Equinox. The subsolar point is 0o You are going to go skiing in New Zealand.

Noon Sun Angle Equation It is the March 22nd. It is the Spring Equinox. The subsolar point is 0o You are going to go skiing in New Zealand.

Noon Sun Angle Equation It is the March 22nd. It is the Spring Equinox. The subsolar point is 0o You are going to go skiing in New Zealand. Your latitude is 43o S

Noon Sun Angle Equation It is the March 22nd. It is the Spring Equinox. The subsolar point is 0o You are going to go skiing in New Zealand. Your latitude is 43o S What is the angle of the sun at noon?

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract!

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 43 - 0

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 43 - 0 43

Noon Sun Angle Equation Noon Sun Angle 90 - Zenith Angle Zenith Angle: Subsolar point & your location are in the same hemisphere, subtract! 43 - 0 43 Noon Sun Angle 90 - 43

Noon Sun Angle Equation Noon Sun Angle 90 - Arc Distance Arc Distance: Subsolar point & your location are in the same hemisphere, subtract! 43 - 0 43 Noon Sun Angle 90 - 43 47o

Noon Sun Angle Equation A noon sun angle of is 47o a moderate angle. This answer makes sense because it is spring time where you are. The snow may be melting, but you can probably still get in a few runs!

Noon Sun Angle Equation Excellent work! Let’s try one last problem together.

Noon Sun Angle Equation It is the December 22nd.

Noon Sun Angle Equation It is the December 22nd. It is the Winter Solstice.

Noon Sun Angle Equation It is the December 22nd. It is the Winter Solstice. The subsolar point is 23.5o S

Noon Sun Angle Equation It is the December 22nd. It is the Winter Solstice. The subsolar point is 23.5o S You just won a trip to Oulu, Finland

Noon Sun Angle Equation It is the December 22nd. It is the Winter Solstice. The subsolar point is 23.5o S You just won a trip to Oulu, Finland

Noon Sun Angle Equation It is the December 22nd. It is the Winter Solstice. The subsolar point is 23.5o S You just won a trip to Oulu, Finland

Noon Sun Angle Equation It is the December 22nd. It is the Winter Solstice. The subsolar point is 23.5o S You just won a trip to Oulu, Finland Your latitude is 64o N

Noon Sun Angle Equation It is the December 22nd. It is the Winter Solstice. The subsolar point is 23.5o S You just won a trip to Oulu, Finland Your latitude is 64o N What is the angle of the sun at noon?

Noon Sun Angle Equation Noon Sun Angle 90 - Arc Distance

Noon Sun Angle Equation Noon Sun Angle 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add!

Noon Sun Angle Equation Noon Sun Angle 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add! 64 23.5

Noon Sun Angle Equation Noon Sun Angle 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add! 64 23.5 87.5

Noon Sun Angle Equation Noon Sun Angle 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add! 64 23.5 87.5 Noon Sun Angle 90 - 87.5

Noon Sun Angle Equation Noon Sun Angle 90 - Arc Distance Arc Distance: Subsolar point & your location are in different hemispheres, add! 64 23.5 87.5 Noon Sun Angle 90 - 87.5 2.5o

Noon Sun Angle Equation A noon sun angle of is 2.5o a VERY low angle. This answer makes sense because it is wintertime where you are. You will need to take a lot of warm clothes for this trip!

Noon Sun Angle Equation Congratulations! You get to try some of these problems on your own. All the hints you’ve been shown are on your worksheet! Good Luck