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I am trying to calculate the absolute magnitude of a solar system object, given its albedo, and assuming all of its luminosity comes from reflecting light from the sun. Using $L_{sun}$ = solar luminosity, $L_0$ = zero-point luminosity, $r$ = distance from sun to object, $A$ = object albedo, and $R$ = radius of object (assuming spherical), here is my logic:

  1. Solar flux reaching out to the object's distance is $F_r = \frac{L_{sun}}{4\pi r^2}$
  2. Amount of light captured by the object's surface (half a sphere) is $F_s = 2\pi R^2 F_r$
  3. Luminosity (total flux emitted) of object is $L = AF_{s}$
  4. Absolute magnitude of the object is $M = -2.5log_{10}\frac{L}{L_0}$

However, something is wrong with this. I did a sanity check using Ceres, which should have an absolute magnitude around 3.3. I'm getting that its much much dimmer than it should be. I know my estimate is very rough, but clearly I'm off in some large way.

D = 5e5 # radius of Ceres [m]
Ls = 3.83e26 # intrinsic L of sun [kg/m2/s3]
L0 = 3.01e28 # zero-point L [kg/m2/s3]
A = 0.09 # albedo of Ceres
r = 4.19e11 # distance from sun to Ceres [m]
Fr = Ls /(4*np.pi*r**2)  # Solar flux reaching distance of Ceres [W/m2]
Fs =  2*np.pi*D**2 * Fr # Light captured by Ceres surface [W]
L = A*Fs # Intrinsic L of Ceres if only from reflecting sun [W]
M =  -2.5 * np.log10(L/L0)  # Absolute M of Ceres   
print(f'Calculated M={M})

This outputs M = 37.7. Am I missing some source of brightness? Is the logic of my formulation wrong? Do I have an issue with units?

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  • $\begingroup$ Are you determining the absolute magnitude of Ceres as if it were a star, that is assuming that you are observing it from a distance of 10 parsecs $\endgroup$
    – James K
    Commented Nov 13, 2023 at 22:20
  • $\begingroup$ I am indeed using absolute magnitude here in the same sense it is used for stars. However, I am assuming no radiation is created by the object itself, so in that sense I am not treating the body as a star. I am trying to estimate how bright the object would be just from reflecting solar light. $\endgroup$
    – CuriousCosmos
    Commented Nov 13, 2023 at 23:07
  • $\begingroup$ An asteroid absolute magnitude, denoted by $H$ (H=3.33 for Ceres; not to be confused with the NIR filter) is defined (CNEOS link) as "An asteroid’s absolute magnitude is the visual magnitude an observer would record if the asteroid were placed 1 Astronomical Unit (au) away, and 1 au from the Sun and at a zero phase angle." $\endgroup$
    – astrosnapper
    Commented Nov 14, 2023 at 2:01
  • $\begingroup$ @astrosnapper So are you saying that I am simply comparing to the wrong value, because the "absolute magnitude" recorded in the literature for an asteroid such as Ceres is not the same quantity as the absolute magntiude I am farmilier with for stars? $\endgroup$
    – CuriousCosmos
    Commented Nov 14, 2023 at 2:55
  • $\begingroup$ Correct, non-stellar objects are treated differently. It is the brightness 1AU from the Sun, and 1AU from the observer, at a phase angle of $ 0^\circ $ (even though that can't actually happen geometrically). en.wikipedia.org/wiki/… $\endgroup$
    – Greg Miller
    Commented Nov 14, 2023 at 4:36

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