UNIT 4.

Altitude Corrections: 7 hrs

Visible, sensible and rational horizons; horizontal parallax;

Sextant altitude and corrections; Observed altitude, apparent
altitude and true altitude; Dip, refraction, semi-diameter and
parallax; Index error; Altitude correction tables; True zenith
distance; Calculation based on above.
 ALTITUDE CORRECTIONS
VISIBLE HORIZON: Visible horizon is a small circle on the
Earth’s Surface that binds the observer’s view. It is the boundary
of the Sea Horizon as seen by the observer
RATIONAL HORIZON: Rational Horizon is a great circle on the
celestial sphere, the pole of which is the Observer’s zenith or the
great circle every point on which is 90° from the observer’s zenith.
SENSIBLE HORIZON: Sensible Horizon is a small circle on the
celestial sphere whose plane is parallel to the Plane of rational
horizon and passes through the eye of the observer.
ALTITUDE CORRECTIONS
Outer Circle is the Celestial Sphere,
Inner circle is Earth,
SS = Sensible Horizon,
VV = Visible Horizon,
RH= Rational Horizon,
O = Observer,
Z = Zenith,
C = Centre of Earth/Celestial Sphere,
OE = HE(Height of Observer’s Eye
above sea surface),
X = Celestial Body(CB)
SEXTANT ALTITUDE: Sextant altitude is the altitude of a body, above the
visible horizon, as read off from the sextant.
OBSERVED ALTITUDE: Altitude of the body above the visible horizon is
called observed altitude. It is sextant Altitude corrected for Index Error(IE).
Note: If IE is ON the arc you SUBTRACT IE from Sextant Altitude to obtain
Observed Altitude. If IE is OFF the arc, then ADD IE to Sextant Altitude to
obtain Observed Altitude.
APPARENT ALTITUDE: It is the altitude of the body above the sensible
horizon and is obtained by applying dip correction to the observed altitude.
Note: Dip is always subtracted from Observed Altitude to obtain Apparent
altitude. Dip varies with HE & its value is given in Nautical Almanac &
Norris Tables.
TRUE ALTITUDE: True altitude of the body is arc of vertical circle passing
through the body contained between the observer’s rational horizon and the
body or it is the angle at the centre of the earth between the observer’s
rational horizon and the centre of the body.
DTP: Dip is the angle at the observer between plane of the observer’s
sensible horizon and direction to his visible horizon.
Note: Dip is always subtracted from Observed Altitude to obtain
Apparent altitude. Dip varies with HE & its value is given in Nautical
Almanac & Nories Table.
Higher the HE, the greater the value of DIP & Vice Versa
REFRACTION: Refraction is the deviation of light rays passing
from one medium to another. When passing from a rarer medium
into a denser medium, the ray bends towards the normal to the
surface of separation between the two media. The atmosphere of
the Earth is most dense at the Earth’s surface and becomes rarer
as the height above the surface increases. Refraction is max when
altitude is 0° (when CB is on SS) as the light rays pass obliquely
through the atmosphere. It is nil when the altitude is 90° (CB is
overhead at Zenith) as light rays pass through layers of the
atmosphere with angle of incidence = 0°.
⸫Refraction corrn. Varies as the cos of App Alt.
REFRACTION
SEMI-DIAMETER: Tabulated semi-diameter is the angle
subtended by the radius of the Sun or the Moon at the centre of
the Earth. Half the visible diameter of the Sun (or Moon),
expressed in minutes of arc, is called Semi- Diameter (SD). What
we require in Cel Nav is the altitude of the centre of the Sun (or
Moon). However, only the Upper end (called the Upper Limb or
UL) orlower end (called the Lower Limb or LL) is visible to us.
Hence we measure the Altitude up to the LL or UL & then apply a
correction called SD corn. & obtain the altitude of the centre of
the Sun(or Moon).
App Alt of Sun’s centre = App Alt of UL - SD of Sun
App Alt of Sun’s centre = App Alt of LL + SD of Sun
∠XEV = Obs. Alt
∠ZSEV = Dip
∠ZXES = App Alt
App. Alt = Obs. Alt – Dip
X is the CB
∠EXC = Parallax in altitude
∠XES = Apparent Alt
∠CH = True Alt
In triangle JEX, ∠SJX = ∠JEX + ∠EXJ
Exterior ∠ = Sum of Interior opposite angle
Or, ∠SJX = App Alt + parallax
But ∠SJX = ∠ XCH (corresponding angles)
Hence = True Alt
Hence True Alt = App Alt + Parallax in Alt
Parallax is max when App alt is 0°
(CB is on SS Horizon)
The value of parallax is then termed as
Horizontal Parallax(HP)
Parallax is Zero when
CB is overhead at Zenith.
⸫Parallax in Alt = HP x Cos App Altd
PARALLAX: Parallax is the angle at the centre of the body
between a line drawn to the observer & another to the center of
the Earth.
Horizontal Parallax (HP): is the angle subtended at the centre of
the body by the radius of the Earth, when the body is at sensible
horizon.
True Altitude = Apparent Altitude + Parallax
Hence Parallax is always added.
PARALLAX IN ALTITUDE: Horizontal parallax is the parallax
when the body is on the observer’s sensible horizon. Parallax in
altitude is the angle at the centre of the body between the centre of
the earth and the observer at the surface. The parallax like the
refraction is maximum when the altitude is zero and nil when, the
altitude is 90°.
Parallax in Altitude = Horizontal Parallax X Cos Apparent Altitude
a) DCXO is called as the Parallax in altitude.
b) Parallax increases with the nearness of the body to the earth.
In fig above the True altitude RCX = U STX (alternate angles)
But STX = SOX + TXO (ext angle of triangle XOT)
⸫ True altitude = altitude above the sensible horizon + Parallax in altitude.
This means that the parallax in altitude is always additive
 Corrections to Sextant Altitude of

Stars Planets Sun Moon

1. IE 1. IE 1. IE 1. IE

2. Dip NA 2. Dip NA 2. Dip NA 2. Dip NA

3. Refraction NT 3. Refraction NT 3. Refraction NT 3. Refraction NT

4. Corrn. For 4. SD NA 4. SD + Augmented

Parallax & Phase SD NA+NT
(Venus & Mars
Only) NT
5. Parallax In Alt. 5. Parallax In Alt.
NT NT
On 14th Oct 2008, Sextant altitude of Sun’s UL was observed to be
35°19.1’, I.E. = Nil; Height of Eye = 12.8 m. Calculate the true
altitude of Sun without using the ‘Total Correction Values’?
Sextant Altitude 35° 19.1’
I.E. NILL
Observed Altitude 35° 19.1’
Dip (H.E = 12.8m) - 6.3’
Apparent Altitude 35° 12.8’
Refraction - 1.4’
35° 11.4’
Semi-Dia. (U/L) - 16.1’
34° 55.3’
Parallax + 0.1’
True Altitude 34° 55.4’ (Ans)
On 16th March 2008,the sextant altitude of the sun lower limb was
56° 11.4’. If the index error of sextant was 2.8' off the arc and
the height of eye was 12m, find the true altitude.

Sextant Altitude = 56° 11.4’

Index error (off the arc) = + 2.8’
Observed altitude = 56° 14.2’
Dip (HE = 12m) = - 6.1’
Apparent altitude = 56° 8.1’
Total Corrections = + 15.6’
True altitudes = 56° 23.7’
On 14th SEP 2008, the sextant altitude of the sun upper limb was
70° 29.8’. If the IE was 3.2’ off the arc and HE was 14m, find true
altitude.

Sextant Altitude = 70° 29.8’

Index error (off the arc) = + 3.2’
Observed altitude = 70° 33.0’
Dip (HE = 14m) = - 6.6’
Apparent altitude = 70° 26.4’
Total Corrections = - 16.2’
True altitudes = 70° 10.2’
On 1st Dec 2008, the sextant meridian altitude of the star
PROCYON was 39°28.8’. If IE was 1.5’ off the arc and HE was
25m, find true altitude.

Sextant Altitude = 39° 28.8’

Index error (off the arc) = + 1.5’
Observed altitude = 39° 30.3’
Dip (HE = 14m) = - 8.8’
Apparent altitude = 39° 21.5’
Total Corrections = - 1.2’
True altitudes = 39° 20.3’
On 15th Dec 2008, the sextant altitude of VENUS was 19° 48.6’. If
IE was 2.1’ on the arc and HE was 19m, find true altitude.

Sextant Altitude = 19° 48.6’

Index error (on the arc) = - 2.1’
Observed altitude = 19° 46.5’
Dip (HE = 19m) = - 7.7’
Apparent altitude = 19° 38.8’
Total Corrections = - 2.7’
True altitudes = 19° 36.3’
On 29th NOV 2008, the sextant altitude of Moon LL was 68° 53.7’
at 29d 09h 23m 25s GMT. If HE was 14m and IE was 0.2’ off the
arc, find true altitude.

Sextant Altitude = 68° 53.7’

Index error (off the arc) = + 0.2’
Observed altitude = 68° 53.9’
Dip (HE = 14m) = - 6.6’
Apparent altitude = 68° 47.3’
1st Correction = + 31.2’
(HP = 53.9, SD = 14.7) = 69° 18.5’
2nd Correction = + 2.6’
True altitudes = 69° 21.1’
On 29th NOV 2008, the sextant altitude of Moon LL was 68° 53.7’
at 29d 09h 23m 25s GMT. If HE was 14m and IE was 0.2’ off the
arc, find true altitude.

Sextant Altitude = 52° 26.8’

Index error (off the arc) = + 0.6’
Observed altitude = 52° 27.4’
Dip (HE = 149) = - 7.7’
Apparent altitude = 52° 19.7’
1st Correction = + 45.2’
(HP = 54.7, SD = 15.0)
2nd Correction = + 2.6’
True altitudes = 53° 07.5’ + 30’
= 52° 37.5’
LTITUDE CORRECTIONS
Greenwich
INDEX ERROR
The Marine Sextant, even after adjustment, can contain small residual
errors. These errors are termed "on the arc" or "off the arc" and must be
applied to the "sextant altitude" to correct it to "observed altitude".
Index Error "on the arc" is subtracted from the sextant altitude to obtain
observed altitude.
Index Error "off the arc" is added to the sextant altitude to obtain observed
altitude.
Sextant Altitude + Index Error = Observed Altitude.
DIP (HEIGHT OF EYE)
The height of an observer above sea level will affect the observed altitude.
"Dip" is the angle between the Visible Horizon and the Sensible Horizon.
Dip is always negative.
Observed Altitude – Dip = Apparent Altitude.
LTITUDE CORRECTIONS
Greenwich

TOTAL CORRECTIONS
The Total Correction allows for: Refraction, Parallax and Semi-
Diameter, where applicable. SUN, Entered with: Date, Limb and
Apparent Altitude. PLANETS, Entered with Apparent Altitude.
N.B. Additional corrections for Venus and Mars. STARS, Entered
with Apparent Altitude.
Apparent Altitude - Total Correction = True Altitude.
TRUE ZENITH DISTANCE
90° - True Altitude = True Zenith Distance