SME
Physical Geography · Problem type
The Sun’s declination on a date
Use this for “Where is the Sun overhead at noon on 21 June, day 172 of the year?”
Chart
δ(172) ≈ 23.44°
This is an example. Type your own values to start a new problem.
n
Day of the year
example
δ
Declination
calculated · °
Formulas
δ
=
23.44
×
sin((360
×
284 +
n
365
)°)
23.4398
=
23.44
×
sin((360
×
284 + 172
365
)°)
Assumptions
•
Day 1 is 1 January; the sine curve is a fit good to about a degree.
•
δ peaks at 23.44° (Earth’s tilt) near day 172, the June solstice, and is near 0° at the equinoxes.
•
A positive δ is north of the equator: the Sun is overhead in the Northern Hemisphere.
Step-by-step
WE KNOW
n = 172
FIND
declination (δ)
Step 1 · Find declination (δ)
Use δ = 23.44 × sin((360 × (284 + n) ÷ 365)°)
The tilt swings the overhead Sun between the tropics once a year: one full turn of 360° in 365 days.
δ
=
23.44
×
sin((360
×
284 + 172
365
)°)
360
×
284 + 172
365
=
449.8°
sin(449.8°) = 1
δ
=
23.4398°
Check
Put the numbers back in. Both sides should match.
23.4398
=
23.44
×
sin((360
×
284 + 172
365
)°)
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.