Apparent Birghtness And Absolute Brightness

[Plutonium88]

Question: Considering the effect of an Earth sized plaent transiting a star, and blocking its light. How big will the change in ABSOLUTE birghtness be for different stellar classs O and A, if we subtract off this blocked light.

telescopes can detect very small changes in brightness, corresponding to DetlaFlux = 10^-18 w/m^2. What is the max distance at which we could detect the planet transiting the star.

Data And Formulas:
M = m - 5log(d/10pc) where M is absolute Magnitude
L = 4PiR^2*F
m - m_x,0 = -2.5log(f/f_x,0) (where m is apparent magnitude)

For Spectral Class O: M = 3MassSun, R = 12RadiusSun , Temp = 42000K , AbsMag(M) = -6.7 , L = 36000LumSun Number Within 30 pc = 3

For Spectral Class A: M = 3 MassSun , R= 3RadiusSun , Temp = 10000K , AbsMag(M) = 0.7 , L = 40LumSun
#Within 30 Pc = 360

My Attempt:

So initially it's asking me to find, the change in Absolute magnitude. So i will find a second absolute magnitude M, which includes the blocked portion of the light. Then i will do the AbsMag - AbsmagnitudeFound..

I was thinking that i could express the flux as a difference of the Luminosity of the star, over the Area of the star, and subtract the Luminosity of the star divided by the Area of the planet.. IE:

Change In Flux = L/4PiR*^2 - L/4PiRe^2

With this i could then use the formula for apparent birghtness, m - m_x,0 = -2.5log(changeinflux/f_x,0).

THen with the apparent brightness,i could find the second absolute magnitude

M2 = m - 5log(3) (considering the distance as 30pc)

Which would then allow me to solve for the change in absolute magnitde..

However i am not sure what i should use for F_x,0 and m_x,0 in the apparent brightness equation, or if this strategy is even valid at all.For the second part of the question, i am assuming i will use m - m_x,0 = -2.5log(deltaflux/f_x,0) and then use the formula
M = m - log(d/10pc), and for each spectral class solve for the distance. Once again I'm not sure what to use for Fo. Could i just use the flux of the sun, and apparent brightness of the sun for this?

 

[Ken G]

It might help you to realize that if a certain fraction of the star's light is blocked, that will shift both its absolute, and apparent, magnitude by the same fixed amount. That fixed shift if just the fraction blocked times a conversion factor that turns changes in log base e into magnitudes, because any small shift in log base e is just the fractional change in the thing itself. Thus if something blocks 1% of the star's light, then the shift in log base e of its luminosity (apparent or absolute, same either way) is -0.01. To turn that into the crazy magnitude unit, you merely have to multiply it by the conversion 2.3/2.5 and switch its sign (since the magnitude scale is backward). So if it blocks the fraction f of the star's light, and f is much less than 1, then the magnitude increases by 2.3*f/2.5. Whether or not you can see that depends on your instrument in difficult ways, you would need a lot of work to figure that out and it would depend very much on how stable is your photometry.