Questions 1: 12/12-12/22: Beginning Declination _° _ (N or S) Ending Dec

ID: 290456 • Letter: Q

Question

Questions 1:

12/12-12/22:

Beginning Declination _____° _____ (N or S)

Ending Declination _____° _____ (N or S)

Total Change in Degrees _____°

Same questions as above for:

1/15-1/25

03/20-03/30

Question 2:

How much does the solar altitude in your city change over the following 10-day period? 12/12-12/22: (I live in Omaha, NE)

How much does the solar altitude in your city change over the following 10-day period? 3/20-3/30: (I live in Omaha, NE)

Question 3:

It is May 5 and you are somewhere in the Northern Hemisphere. If you determine that the noon Sun is 51° above your southern horizon, what is the latitude of your location? [a] °N

Thank you!

Explanation / Answer

In order to determine the declination we need to proceed as follows:

1. Determine how many days have passed from January 1st, for example, January 1st and December 12th = 346
2. Now add 10 to the above result i.e., 346+10= 356
3. Now divide it 360 by number of days in a year, 360/365 =0.9863
4. Now multiply the results of step 2 and 3 i.e. 356 x 0.9863 = 351.1228
5. Now find the cosine of the result obtained in step 4 i.e., cosine 351.1228 = 0.9880
6. Finally multiply the result obtain in step 5 with -23.44 i.e., 0.9880 x -23.44 = -23.159 degrees
So our Suns declination is 23.159 degree S
Above mentioned steps can be applied to calculate the values for the remaining dates as shown in the table below.

Dates

Number of days passed after January 1st

Adding 10 to the number of days passed after January 1st

Multiply 0.9863 to the number of days passed after January 1st + 10

Result obtains by taking Cosine of the Previous result.

Finally, multiple values of Cosine with -23.44

Final results

Total change in degree

12/12

346

356

351.1228

0.9880

-23.159

23.159 degree S

12/22

356

366

360.9858

0.9998

?23.4353

23.4353 degree S

23.4353-23.159= 0.2763

1/15

24.6575

0.9088

?21.3022

21.3022 degrees S

1/25

34.5205

0.8239

?19.3122

19.3122 degree S

19.3122-21.3022= ?1.99

3/20

87.7807

0.0387

?0.9071

0.9071 degrees S

3/30

97.6437

?0.1330

3.1178

3.1178 degree N

3.1178-0.9071= 2.2107

2. This can be done by using the equation
A = 90 -L +/- D
Where A= Altitude
L= your Latitude value
D = Declination
Note the D will be added to L if latitude is having summer at the time of calculation whereas it will be subtracted during winters
So our calculate can be performed by plugin the values in the above equation as

Value of altitude change between 12/12 to 12/22

A= 90- 41.2565 – 0.2763= 48.4672
Value of altitude change between 3/20 to 3/30

A= 90- 41.2565 + 2.2107= 50.9542