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A blog about a system to determine terrestrial albedo by earthshine observations. Feasible thanks to sheer determination.

What did Allen mean?

Relevant papersPosted by Peter Thejll Sep 13, 2013 07:47PM
In researching material for our first paper we come across the data in Allen for the colour index of Earth: "0.2". There is no evident source of that piece of information so in order to interpret it and use it in the paper we have to do some detective work. Here it is:

References given by Allen (various editions)
in the table that gives B-V of Earth as '0.2'.

The references are both in the caption of the table, and in the B-V/U-B
column of that table. The table is on page 299 of the fourth edition
by Cox.

reference numbering as in Allen 4th ed.

1. Astronomical Almanac, 1998, USNO

In the 1997 edition there is on p. E88 a table with a dash '-' for
Earth's B-V. For the Moon there is 0.92 without a reference.

2. Allen 1973 - the two colour columns of the table on page 144 of this
3rd edition - gives references to Irvine and Harris (see below).

In Allen 1955 there is on p. 159 a table with 'C' for planets and
Earth has 0.2. In the notes it is explained that C is the 'colour
index' and that it is offset from the larger published value by 0.1
to 0.2 ... What was 'C' as published and where and what is C compared
to B-V? The references on p.160 of the 1955 edition are not specific
for each piece of information, but we find as number [4] a reference to
Danjon. There are two references, it seems - 1936 and 'Danjon, Comptes
Rendus, 227, 652, (1948)'. The 1936 is an observatory publication on
earthshine observations I am trying to find. The CR reference is about
Mercury and Venus. Using information from Wildey's paper on Mariner 2 data
for Earth where the mean Danjon C.I. of earthshine/light, BS Moon and Sun
are given, we can estimate the linear transformation from the C.I. system
to B-V. We get, using Wildey's data for Moon and Sun C.I. but not his
B-V data for same (using instead Holmberg et al for Sun) that

B-V = .112+.671*.(C.I.)

With 0.2 for C.I. we get B-V=0.25.

We can test the effect of using B-V for Moon = 0.92 (an often cited
value), this gives
B-V= -0.0665+.8968*(C.I.)
and C.I. = 0.2,0.3,0.4 gives B-V=0.11, 0.20, 0.29, respectively.

3. Irvine et al 1968, AJ 73, 251, 807
Paper is on B-V for the planets - not Earth.

4. Harris, in Vol III, (eds) Kuiper and Middlehurst, p. 272.

The Harris chapter in the book briefly discusses the photometry of Earth
- mainly in the form of a citation to Danjon's chapter in Book II of the
series by Kuiper and Middlehurst. The Danjon phase law is given for earth,
but no comment on colours.

Summary: The source of the '0.2' for Earth in Allen is thus not source 1,
nor 3 - but 2 and 4 point at Danjon. The 1933 An. d'Obs. Strasbourg Vol
3 reference is in fact available online (now) at ADS. It is in French, and
it is long - but towards the end things hot up because a summary of color
index data for the Earthshine (Lumiere cendree) and Earthlight (Earth
itself) are discussed, although in the Rougiere system. The effective
wavelengths of this system are given in chapter 4 on p 171 and are

Rouge 606 nm
Vert 545 nm
Bleu 467 nm

so Rouge is between Johnson V and R, Vert is between Johnson B and
V, closer to V, and Bleu is between Johnson B and V, closer to B.

Of interest is a description of the areas on the Moon used - it seems
Crisium and Fecunditatis are used but only after 1928 is this fixed.

Also of interest are mean values (mean over several years) for the colour indexes,
given on
p 174 earthlight C.I. = 0.33 from -0.01 to 0.6
p 175 earthshine C.I. = 0.62
The variability is large and is said to be mainly seasonal. Note the
addendum at the very end (p. 179) where everything important seems to be
updated in a breathless paragraph! An updated value for C.I. for the Moon
by Rougiere is given as 1.10 (cited by Wildey in the Mariner 2 paper),
and the EarthSHINE C.I. is therefore updated to 0.64. There is a note
that there isn't space to also update the earthLIGHT number but I assume
it is upped by 0.02 also. So, if Allen is referring to Danjon's C.I.
as 0.2 and states that it is 0.1 to 0.2 lower than the published value,
we can see that Allen is talking, indeed, about the C.I. for Earth itself
- earthLIGHT - and not earthSHINE.

So, using the linear equation developed above
B-V = .112+.671*.(C.I.)
and now inserting C.I.=0.35 (with limits at +0.01 to 0.62)
we have for the earthLIGHT B-V = .35 (with limits from 0.12 to 0.53).
For an earthSHINE colour of C.I. =0.64 +/- 0.3 we get a B-V range of 0.54 +/- 0.2
Conclusion: This spans our observation as well as Franklin's, but with large uncertainties. Note the numerically identical B-V and C.I. values - so Allen is right in as much as replacing the 'C' from the 1955 edition with the 'B-V' of the 1973 (and on) editions.

Data to plot

Year (B-V)ds-(B-V)bs
1926-1935 0.54(pm0.2) - 0.85 = -0.31 to -0.11
1967 -0.17 pm 0.05
2012 -0.16 pm 0.02

Plotting this we have:

The Danjon data are an average of measurements from 1926 to 1935 and upper and lowe rend of the bars indicate the extent of seasonal variability, surmized by Danjon. The Franklin bars represent +/- 1 standard deviation based on the 12 determinates from 2 nights in his paper, and our error bars represent +/- 1 standard deviation based on scatter due to photon statistics in our measurement from a single night in two images.

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