Solar declination angle
It is angle between the equator and a line drawn from the center of the earth to the center of the sun. The plane of the equator and a line drawn from the center of the sun to the sun of the earth is called as declination angle, δ. The declination angle varies seasonally due to tilt of earth on its axis of rotation and rotation of earth around the sun. If the earth axis is not tilted, the declination angle is zero.
The
declination is zero at the equinox (21st/22nd March and 21st/22nd September).
It is positive during summer in the northern hemisphere and negative during
winter in the southern hemisphere. The declination angle reaches 23.45 degree
on June 21/22 and minimum on December 21/22 in the northern hemisphere.
Formula for solar declination angle
The
declination angle is given by formula
δ
= 23.45 Sin (360 (n – 81) / 365)
Where
n = Number of days, starting from 1st January
|
Date |
Day Number (n) |
Date |
Day Number (n) |
|
1st January |
1 |
31st July |
212 |
|
31st January |
31 |
31st August |
243 |
|
28th February |
59 |
30th September |
273 |
|
31st March |
90 |
31st October |
304 |
|
30th April |
120 |
30th November |
334 |
|
31st May |
151 |
1st December |
335 |
|
30th June |
181 |
31st December |
365 |
Calculation
of Declination angle for New Delhi, India as on 1.9.2023
|
Day |
No. of day |
Declination
Formula |
Declination
Angle |
|
31st January |
1 |
δ = 23.45 Sin (360 (1 – 81) / 365) |
– 23.01 |
|
31st January |
31 |
δ = 23.45 Sin (360 (31 – 81) / 365) |
– 17.8 |
|
28th February |
59 |
δ = 23.45 Sin (360 (59 – 81) / 365) |
– 8.67 |
|
31st March |
90 |
δ = 23.45 Sin (360 (90 – 81) / 365) |
+ 3.61 |
|
30th April |
120 |
δ = 23.45 Sin (360 (120 – 81) / 365) |
+ 15.20 |
|
31st May |
151 |
δ = 23.45 Sin (360 (151 – 81) / 365) |
+ 21.9 |
|
30th June |
181 |
δ = 23.45 Sin (360 (181 – 81) / 365) |
+ 23.18 |
|
31st July |
212 |
δ = 23.45 Sin (360 (212 – 81) / 365) |
+ 18.17 |
|
31st August |
243 |
δ = 23.45 Sin (360 (243 – 81) / 365) |
+ 8.10 |
|
30th September |
273 |
δ = 23.45 Sin (360 (273 – 81) / 365) |
– 3.81 |
|
31st October |
304 |
δ = 23.45 Sin (360 (304 – 81) / 365) |
– 15.05 |
|
30th November |
334 |
δ = 23.45 Sin (360 (334 – 81) / 365) |
– 21.96 |
|
31st December |
365 |
δ = 23.45 Sin (360 (365 – 81) / 365) |
– 23.08 |
The declination angle changes between + 23.45 degree to 0 degree and again 0 degree to – 23.45 degree in a year.
Declination angle of Sun New Delhi 1.9.2023 (Data
source: PVsyst)
Calculate
declination angle as on 31st January, 2023 for Mumbai.
Solution
The
declination angle is calculated by formula
δ
= 23.45 Sin (360 (n – 81) / 365)
Where
n = Number of days, starting from 1st January
n = 31
declination
angle δ = 23.45 Sin (360 (31 – 81) / 365)
= – 17.8o
FAQs on solar declination angle
What is solar declination angle?
It is angle between the equator and a line drawn from
the center of the earth to the center of the sun.
What is minimum value of solar declination angle?
- 23.45
What is maximum value of solar declination angle?
+ 23.45
What is yearly change in solar declination angle?
- 23.45 to +23.45
What is formula to find out solar declination angle?
δ
= 23.45 Sin (360 (n – 81) / 365)
Where n = Day number, starting from January 1st
On which date, solar declination angle becomes zero?
The declination is zero at the equinox (21st/22nd
March and 21st/22nd September).
Why solar declination angle varies through year?
Because earth axis is tilted at 23.45 degree on its
own vertical axis
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