The Demystified Astro Navigation Course Unit 3 Part 2


Unit 3 Part 2 – Altitude Correction tables for the Sun, Stars and Planets.

As shown in the table extract below, corrections for the Sun are divided into two parts to allow for changes in the Sun’s semi-diameter during the course of a year.  The first part is for the period October to March and is based on a semi-diameter of 16’.15.  The second part is for April to September and is based on a semi-diameter of 15’.9.

na_2009-A2-A4-A2 cropped

Example:

Date = 20 May

Apparent altitude of the Sun’s lower limb = 10o 47’.0

Correction = +11’.1 (interpolating as necessary).

Full example of altitude corrections for the Sun.  The following example shows how altitude corrections for index error, dip, semi-diameter, refraction and parallax are applied to a sextant altitude of the Sun:

On 12 Feb. a reading of the Sun’s lower limb was taken.

Sextant altitude = 14o 35’.5.  Index error = -2’.3.  Height of eye = 4.2m.

Temperature = 20oC.  Pressure = 1020 mb.

Using the extracts of tables A2 above and A4 below, the calculations for the True Altitude would be as follows:

Sext. Alt.            14o 35’.5

I.E.                            -2’.3

Observed Alt.     14o 33’.2

Dip                            -3’.6

Apparent Alt.      14o 29’.6

Sun’s correction       +12’.6  (combined correction)

True Alt.             14o 42’.2

If the upper limb had been used instead of the lower limb, the result would be:

Sext. Alt.           14o 35’.5

I.E.                            -2’.3

Observed Alt.     14o 33’.2

Dip                             -3’.6

Apparent Alt.      14o 29’.6

Sun’s correction       -19’.7

True Alt.              14o 09’.9

Corrections for the stars and planets are listed in only one column since semi-diameter corrections are not necessary.  However, a column of additional corrections for Venus and Mars is provided for use when extreme accuracy is required.

Example:

Corrections for Altitude of a Star:  Using the following data and the extracts from table A2 and table A4 on the preceding pages, calculate the true altitude of a star.

Data:  Sextant altitude = 12o 20’.4     I.E = +1’.8      Ht. of eye = 4.8m.

Temperature = -20oC.   Pressure = 1010 mb.

(Remember, the correction for a star consists of index error, dip and refraction only since parallax and semi-diameter are negligible).

Solution:

Sext. Alt.           12o 20’.4

I.E.                            +1’.8

Observed Alt.     12o 22’.2

Dip                            -3’.9

Apparent Alt.      12o 18’.3

Star’s correction      -4’.3

True Alt.             12o 14’.0

 

Altitude Correction Tables for the Planets. 

  • As in the case of the stars, because they are so far from the Earth, parallax and semi-diameter arguments for the planets are negligible and so the only corrections necessary are for dip and refraction.
  • For normal navigational practices, the navigational planets are treated as stars and the correction table for stars is used.
  • For the very rare cases that they are needed for extreme accuracy, additional corrections for phase and parallax for Venus and parallax for Mars are given in the Nautical Almanac. 

Example:  Corrections for Altitude of a Planet.

Using the following data and the extracts from table A2 table A4 on the preceding pages, calculate the true altitude of a planet.

Sextant altitude = 10o 38’.6      I.E. =  +2’.4      Ht. of eye = 13.0 ft.

Temperature = 10oC.  Pressure = 1000 mb.

Solution:

Sext. Alt.        10o 38’.6

I.E.                       +2’.4

Obs. Alt.          10o 41’.0

Dip                        -3’.5

App. Alt.          10o 37’.5

Plnt’s corr.             -5’.0

True Alt.          10o 32’.5

Additional Corrections  An additional correction for refraction may be needed if the temperature and atmospheric pressure are greatly different to the standard conditions which are assumed to be 10oC, 1010mb.  Part of Table A4 from the Nautical Almanac is shown in the extract below.  This table tabulates the additional corrections for non standard conditions:

table6c

The graph above the table is entered with the temperature and pressure to find a zone letter.   For example, entering with a temperature of 20oC. and a pressure of 1010mb. gives zone letter J.

The table is then entered with the apparent altitude and zone letter to find the additional correction for refraction.

Example.  If apparent altitude = 4o 30’, temperature = 30 oC, pressure = 1000mb, the zone letter will be L and the correction will be +0’.8.

Self Test  Using the Nautical Almanac extracts on the given above, answer these questions:

Question 1.

On 12 June, a reading of the Sun’s lower limb was taken.

Sextant altitude: 50o 45’.2.  Index error: +1’.8. Height of eye: 24 ft.

Temperature: 25oC.  Pressure: 1000mb.

What was the true altitude?

Question 2.

Sextant altitude of Sirius: 18o 08.’5.  Index error:  +2’.1;  Ht. of eye: 12m.

Temperature: -10oC.  Pressure: 980mb.

What is the true altitude?

Question 3.

Sextant altitude of Venus:  17o 43’.3.  Index error: -1’.4.  Ht. of eye: 15 ft.

Temperature: 8oC.  Pressure: 1025mb.

What is the true altitude?

Solutions

Q1.

Sext. Alt.            50o 45’.2

I.E.                             +1’.8

Observed Alt.    50o 47’.0

Dip                             -4’.8

Apparent Alt.     50o 42’.2

Sun’s Corr.                +15’.2

Add’nl. Corr.               0’.0

True Alt.             50o 57’.4

 

Q2.

Sext. Alt.            18o 08’.5

I.E.                             +2.’1

Obs. Alt.              18o 10.’6

Dip.                             -6’.1

App. Alt.             18o 04’.5

Star’s Corr.               -2’.9

Add’nl. Corr.              -0’.2

True Alt.             18o 01’.4

 

Q.3.

Sext. Alt.          17o 43’.3

I.E.                            -1’.4

Obs. Alt.             17o 41’.9

Dip                            -3’.8

App. Alt.             17o 38’.1

Plnt’s Corr.                -3’.0

Add’nl. Corr.              -0’.1

True Alt.             17o 35’.0

Altitude correction tables for the Moon will be explained in Unit 3 Part 3.

(Note. This topic is covered in greater depth in the book ‘Astro Navigation Demystified’).

Where to buy books of the Astro Navigation Demystified series:

Astro Navigation Demystified at Amazon.com

Astro Navigation Demystified at Amazon.uk

Applying Mathematics to Astro Navigation at Amazon .com

Applying Mathematics to Astro Navigation at Amazon .uk

Astronomy for Astro Navigation at Amazon.com

Astronomy for Astro Navigation at Amazon.uk

web: http://www.astronavigationdemystified.com

e: astrodemystified@outlook.com

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