Expert: Jayendra Upadhye - 3/4/2008

Question
I have recently looked at a book that shows how much / little the intensity of sunlight is on other planets in our solar system.   I know the Sun’s illuminance in lux is 130000 (if the Sun is directly overhead and the sky is perfectly clear) and it is -26.7 in stellar magnitude.   Is there an equation to convert illuminance in lux to stellar magnitude so that I can calculate the Sun’s stellar magnitude as seen from other planets in our solar system (ie. if viewing the Sun from the surface of Pluto, what magnitude star would it appear to be)?

Answer
Hi Kurt,
Sorry for the delay..was busy..
Actually do lookup my pasted reply to Rhys Moore, on a similar matter some days back. (see references below)

Especially look up ref 1 this site lists something i have'nt seen on many many sites...lists apparent magnitude of sun planetwise!!
You will love that one.

I am sure there would be a relationship mentioned somewhere on the web, and one could calculate that out too, but why not use another reationship, which all astronomers use?
It is the distance modulus to magintude relationship equation

equation:- m - M = -5 + 5 *log(d)

where m is apparent magnitude, M is absolute magnitude, and d is distance between observer and star in parsecs.
if d is 10 parsec, absolute magnitude equals apparent magnitude.

wikipedia gives (ref:- http://en.wikipedia.org/wiki/Pluto) distance from sun to pluto as varying between 7,375,927,931 km & 4,436,824,613 km. avearge 5906376272 km.

1 parsec is 3.086×10 raised to 13 km.
[ref:- http://en.wikipedia.org/wiki/Parsec].

which makes pluto-sun distance as 1.9139 * 10 raised to -4 parsec = d.

log(d) = -3.71807, 5*log(d) = -18.59037

Absolute magnitude of the sun is 4.8 = M
(ref:- http://en.wikipedia.org/wiki/Sun)

m is apparent magnitude.
m = 4.8 - 5 + 5*log(d) = 4.8-5-18.59037= -18.79037!!
[ref 1 confirms our theoretical calculations! Nice!!]

That makes the sun still a very bright star!!


independent checks:-
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1 - "However, brightness is another matter altogether. Even from the distance of Pluto, the sun would shine at a magnitude brighter than negative 18,"...

http://blogs.earthsky.org/larrysessions/space/042610/how-bright-the-sun/

2 - it would have apparent magnitude of about -20 as per this..
http://www.gsfc.nasa.gov/gsfc/educ/science/2000/02-01-01.htm

3 - http://www.astro.northwestern.edu/labs/m100/m100dist.html

4 - http://www.astro.northwestern.edu/labs/m100/mags.html

5 - http://csep10.phys.utk.edu/astr162/lect/distances/stardistance.html


conclusion:-
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What you need to do, is knowing the sun's absolute magnitude, you may find its apparent magnitude by converting the distance between say pluto and sun into Parsec(s) ..it would be a fraction of a parsec i think, use the distance modulus etc and get the apparent magnitude.

This you can then work out for each of the other planets of interest to you.


Please do rate the answer.

regards
Jayen