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Predicting Sunset and Sunrise Predicting Sunset and Sunrise

Predicting Sunset and Sunrise - PowerPoint Presentation

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Uploaded On 2016-07-23

Predicting Sunset and Sunrise - PPT Presentation

Katie Sullivan Emily Olsen amp Haily Yelle Trigonometry and analytical geometry can be used to predict times that the sun will rise and set This involves use of the sine function and celestial mechanics branch of astronomy dealing w celestial orbits ID: 416041

sun sunset sunrise minutes sunset sun minutes sunrise earth

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Slide1

Predicting Sunset and Sunrise

Katie Sullivan, Emily Olsen& Haily YelleSlide2

Trigonometry and analytical geometry can be used to predict times that the sun will rise and set.

This involves use of the sine function and celestial mechanics (branch of astronomy dealing w/ celestial orbits)Determined when the sun lies in the center of earth’s tangent plane

Calculus and the SunSlide3

On the first day of spring a coordinate system is set up so that the positive x-axis passes through Earth’s center.

Ecliptic plane charts Earth’s orbitEarth rotates in 2pi radians in 1440 minutes

R stands for radius of Earth (6378 km)

L is the person’s latitude at noon

Earth rotates at 2pi radians in

1440 minutes (24 hours)ϴ=0 on the 80th day of the year

BackgroundSlide4

W

hat time will the sun rise and set on June 10th at a latitude of 40 degrees?-June 10th is 161 day of the year, d=161-ϴ=(2π/365.25)(d-80) ϴ=1.3934

-L=40 degrees

-t₀ = (1440/2π)[cos−1( R − z

sinL)/(rp cosL)] (zs = 5.8560 × 10⁷ and rp = 1.3766 × 10⁸)-Therefore, t₀ =444 minutes (t₀ value gives the number of minutes after noon that sunset occurs)-t^= 449

(Experience suggests replacing t₀ by t ˆ = t₀ + 5 minutes)-In conclusion, on June 10th at a latitude of 40 degrees, sunrise occurs at 4:31 am and sunset at 7:29 pm

Sample ProblemSlide5

Predictions for sunrises and sunsets are used everyday:

It can be used to determine when it will begin to get dark, or when it will be light enough to get up

Also, it can be used to schedule long walks at the beach at sunset

Life ApplicationSlide6

Math can be used to predict sunrise and sunset times by calculating the point at which the sun is at the center of earth’s tangent plane, to create a set of coordinates

.ConclusionSlide7

Teets, D. A. (2003). Predicting sunrise and sunset times.

The College Mathematics Journal, 34, 317-321. References