Unequal Double Star Split Calculator - Chris Lord's (1994) algorithm for secondaries brighter than 9.0

Unequal Double Star Split Calculator - Chris Lord (1994) algorithm with Brian Tung continuous indexes modification

Calculator assumptions: Primary brighter than 9.0, the secondary is brighter than 13.0, the secondary is between 0 magnitudes and 7 magnitudes dimmer than the primary.

Table 1 - Antoniadi's 5 point seeing scale

Scale	Description	Disk diameter for 8" (203mm) to 20" (508mm) scopes per the Canadian Weather Service	Corresponding Lord's step
I	Perfect steadiness; without a quiver.	< 0.4"	I<0.25 rho
II	Slight undulating, with moments of calm lasting for several seconds.	~ 0.4-0.9"	II>0.25 rho
III	Moderate seeing, with larger air tremors.	~ 1.0-2.0"	III<0.50 rho
IV	Poor seeing, with constant troublesome undulations.	~ 3.0-4.0"	IV<1.00 rho
V	Very bad seeing, unsuitable for anything except possibly a very rough sketch.	< 4"	V> 1.50 rho

Source: Antoniadi scale wikipedia
Canadian Weather Service. http://weatheroffice.ec.gc.ca/astro/seeing_e.html
Lord, C. Jan. 2008. Personal Communication.
Notes: Lord's seeing performance characteristic ( n_e * rho) is expressed as a radius. The third column above is twice that radius - a diameter - in order to be comparable to the Canadian Weather Service table.

Math Appendix

S = 1.033 * 10 ^ [ 1/n * ( Abs(delta mag) - 0.1 ) ] * rho

where performance index n is the sum of three indices from the following table with a range between 4.0 and 12.0:

Table 2 - Performance indices for Lord's algorithm

Aperture Dmm	Aperture index	Obstruction ratio	Obstruction index	Seeing - suprious disk	Seeing index
<75	4	0	4	I<0.25p	4
75-150	3	0.1	3	II>0.25p	3
151-300	2	0.2	2	III<0.50p	2
301-450	1	0.33	1.5	IV<1.00p	1
451-600	0.5	0.4	1	V>1.50p	0.5
600	0.5-0.25	0.5	0.5

where rho is Dawes criteria or rho = 116 / D_mm.

Although not explicited stated in Lord's 1994 paper, the following computational restrictions are added to this calculator for computational convenience and to assure valid results always are returned to the user:

The secondary is at most 7.0 magnitudes dimmer than the primary; and,

The primary is brighter than or equal to 9.0 and the secondary is brighter than or equal to 13.0. This is the approximate magnitude domain from which Lord constructed his performance index model.

Tung's proposal for continuous indices, implemented in this calculator, are:

nD = (2.4 - (D_mm/150)) {Eq. 1}

nE = (2.0 - (5*obstruction_fraction)) {Eq. 2}

nS = (2.3 - (8*FWHM*(D_mm/lambda_nm))) {Eq. 3}, where FWHM is in arcseconds and D_mm and lambda_nm their unadjusted values, not reduced to common units of meters

References

Lord, Chris. Jan. 2008. Personal Communication.

Tung, Brian. 8/14/2006. Personal Communication

No copyright is asserted as to any material in this web document including embedded astronomy javascript functions.

Prepared K. Fisher fisherka@csolutions.net org. 7/2006 rev. 2/3/2008

Unequal Double Star Split Calculator - Chris Lord (1994) algorithm with Brian Tung continuous indexes modification

Chris Lord Algorithm Unequal Double Split Calculator

Math Appendix

References