How to calculate declination of Moon? Is there any way to calculate declination of Moon for any day?I'll subtract inclination of Earth on the ecliptic from the result. I'll get Moon's the shortest angular distance from Sun.
Thanks for all answers!
The complexity of the formula depends on the precision you need.
We can make a crude approximation with two sine waves: one for the Moon's travel eastward around the ecliptic over a
tropical month

$$\delta_1 = 23.4^\circ \sin {2 \pi (u - 10.75) \over 27.32158}$$

and one for the Moon's travel north or south of the ecliptic over a
draconic month

$$\delta_2 = 5.1^\circ \sin {2 \pi (u - 20.15) \over 27.21222}$$

both modified as the Moon goes faster or slower over an anomalistic month

$$u = t - 0.48 \sin {2 \pi (t - 3.45) \over 27.55455}$$

where t is the number of days since 2000-01-01 12:00 TT (J2000.0).
Then

$$\delta = \delta_1 + \delta_2$$

is within 1&deg; of the Moon's geocentric declination most of the time.
For a topocentric declination, subtract
1&deg; sin (observer's geographic latitude).

If you need higher precision, see
van Flandern and Pulkkinen 1979
or Meeus 1999
for more complicated formulas.

Note: the u and t offsets above are near a 0&deg; longitude crossing, an ascending node, and an apogee in January 2000 but are tweaked to minimize RMS differences from JPL HORIZONS lunar positions for 2000-2018.