1.When the body is on Observer’s Rational Horizon ,side $ZX = 90^ \circ$. 2.At Meridian Passage of Sun LAT is always 1200h. 3.Earth’s radius is 6350km. 4.When the body is at Observer’s Prime Vertical $\angle Z = 90^\circ$ 5.Amplitude takes name from from Declination. A body will rise from North of Oberver’s Prime vertical only if her declination is north and vice versa. 6.

$$Sin (Amp) = \frac{Sin(Decl)}{Cos(Lat)}$$

7.For a body to cross Prime vertical L and D are of same name and D < L. 8.Sidereal day is the duration of time between two successive crossing of a distant star over same meridian = 24 hrs. 9.Solar day is the duration between two successive transits of the centre of the sun over same meridian = 23 hrs 56 mins 4.1 secs. 10.Lunar day is the duration between two successive transits of the center of the moon over the same meridian = 24 hrs 50 mins approx. 11.Synodic period is the duration between two successive conjunctions of a distant fixed star and the body in Question which can be sun, moon or planets. 12.Sidereal period of moon is the time taken by the Moon to go around the Earth once = 27 d 43 m 11.5 s. 13.Lunation is the time between two successive conjunctions between Sun ,Moon and the Earth. 14.

$$\frac{1}{S_y}= \frac{1}{S_D}=\frac{1}{Y_E}$$

where $Y_E$ is the sidereal period of revolution of earth. 15.Rate of change of meridian by Sun is $15^\circ / hour$ 16.Rate of change of meridian of Aries is $15 \degree 2.46'$ 17.‘v’ correction of Moon = Actual hourly rate of change of hour angle of moon - $14 \degree 19'$. 18.‘v’ of planet = Actual hourly rate of change of meridian - $15\degree$ 19.Ephemeris of heavenly bodies given in the Nautical almanac is given in the Equinoctial System of Co-Ordinates. 20.

$$Solar Time = \frac { Solar Hour Angle}{15\degree} \pm 12 hours$$

Related to Sun - True Sun ,Mean Sun GMT,LMT,GAT and LAT. 21.Sidereal time = Star Time

$$Local Sidereal time =\frac{ \text(Local Hour angle)}{15 \degree}$$

22.

$$LAT = \frac{LHA True Sun}{15\degree} \pm 12 hours$$

23.

$$LMT = \frac{LHA Mean Sun}{15 \degree} \pm 12 hours$$

24.Equation of Time is the angle contained between meridians of True Sun and Mean Sun at the celestial pole. 25.

$$EOT = SHAMA - SHATS$$$$EOT = GHAMA -GHATS$$$$EOT = LHAMS - LHATS$$

$$EOT = GMT - GAT$$$$EOT = LMT-LAT$$$$EOT = RATS -RAMS$$

26.

$$e = \frac { \text(center to focus)}{\text(half major axis)}$$

where e is eccenticity. 27.

$$e^2 = 1-\frac{ b^2}{a^2}$$

28.perigee and apogee calculations $SA = a(1-e)$,$SA'= a(1+e)$. 29.Rate of change of Altitude :

$$dh = dz \times Sec (Lat) \times Cosec(Azimuth)$$

. 30.Rate of change of Azimuth:

$$dA = dh \times Cos(Declination) \times Sec (Altitude) \times Cos(\angle PXZ)$$

. $\angle PXZ = parallectic angle$ 31.At Meridian Passage - at Upper Meridian Passage $MZD = (L \sin D)$ - at Lower Meridian Passage $MZD = 180-(L+D)$ -

$$dA = 15' \times \frac {Cos(Declination)}{Sin (L \sin D)}$$

per minute of time. 32.Equation of Equal Altitude-

$$dh = dp (tan (L)\times Cosec (h) - Tan (D) \times Cot (h) )$$

where dh = change in hour angle between two observations, dp = change in declination during the difference in time between the two observations. 33.If stars are concerned then delination is constant therefore time of merpass =

$$t = \frac {(T_1+T_2)}{2}$$

34.We can find the exact time of merpass by the fact that $LHA = 0 \degree or 180 \degree$ during merpass. 35.Chron Time of Merpass $T_CR = \frac{T_1 +T_2}{2} \pm e (seconds)$. +e if declination is decreasing -e if declination is increasing. 36.

$$e_{seconds}= \frac{dp}{15}( Tan (L) \times Cosec (h) - Tan (d)\times Cot (h) )$$

37.The Maximum Altitude of a heavenly body =

$$\frac{Tan(L) \pm Tan(D)}{ 900 \mp x}= \frac {Tan(L) \pm Tan (D) }{900( 1\mp \frac {x}{900})}$$

where x is change of Longitude of Observer ship (in minutes of arc per hour) in minutes. 38.4 Parts Formula Cot (outer side) Sine (Inner side) = Cot (outer angle) Sine (inner angle) + Cos (inner side) \times Cos( Inner Angle). 39.In ABC Tables :

$$A = \frac { tan (Lat)}{tan(HA)}$$

,

$$B = \frac{sin( Declination)}{ tan (HA)}$$

,

$$C = A\pm B$$$$tan(Azi) = \frac {1}{C \times Cos(Lat)}$$

40.

$$\delta d'long = \frac{d'lat}{Tan(Azi) \times Cos (Lat)}$$

41.Length of Earth’s Shadow is 860 miles in space. 42.Ecliptic limits are variable due to variation in the parallax and SD of Sun and moon caused due to their varying distances from earth from time to time. 43.The inclination of moon’s orbit also varies between max of $5\degree$ 18’ to min of $4 \degree$ 59’. 44.Greatest and least value of the limits for each kind of eclipse are called the major and minor eclipse limits. 45.45.For an eclipse the moon the major and minor eclipse limits are about $11 \degree$ 38’ and $9 \degree$39’ respectively. 46.For eclipse of sun the major limit is $17 \degree$25’ and minor limit is $15 \degree$ 23’. 47.