* Bill Gray * Aug 14, 2013

Hi Pierre,

There's a standard magnitude formula, using H (absolute magnitude, the

magnitude the asteroid would have if it were one AU from the sun as seen

from the sun itself) and G (the 'slope parameter', which roughly describes

the magnitude as a function of phase angle).

The absolute magnitude H essentially combines the diameter and albedo to

say "this is how much light the object reflects". It's what you actually

observe when you point a telescope at the object: you can't tell if it's

a really big object covered in black paint, or a small object covered in

mirrors. (You can put a lower limit on the object's diameter based on the

assumption that it reflects 100% of the incoming light. It might be

twice as big if the albedo is really 25%, or five times as big if the

albedo is actually 4%. Or a truly massive alien artifact cleverly disguised

as a small asteroid, covered in black paint.)

The IAU standard magnitude formula is :

mag = H + 5 log(r * delta) - 2.5 log((1-G)phi1 + G * phi2)

phi1 = exp[ -3.33( tan( beta / 2) ^ 0.63)]

phi2 = exp[ -1.87( tan( beta / 2) ^ 1.22)]

...in which logarithms are to base 10, r = the distance between the

asteroid and the sun, delta = distance of the asteroid from the observer,

and beta = phase angle.

If an asteroid has been observed for a while over a wide range of phase

angles, then the slope parameter G can usually be determined. But for most

objects, a default value of 0.15 is assumed. I don't know what that value

corresponds to in a physical sense.

-- Bill

There's a standard magnitude formula, using H (absolute magnitude, the

magnitude the asteroid would have if it were one AU from the sun as seen

from the sun itself) and G (the 'slope parameter', which roughly describes

the magnitude as a function of phase angle).

The absolute magnitude H essentially combines the diameter and albedo to

say "this is how much light the object reflects". It's what you actually

observe when you point a telescope at the object: you can't tell if it's

a really big object covered in black paint, or a small object covered in

mirrors. (You can put a lower limit on the object's diameter based on the

assumption that it reflects 100% of the incoming light. It might be

twice as big if the albedo is really 25%, or five times as big if the

albedo is actually 4%. Or a truly massive alien artifact cleverly disguised

as a small asteroid, covered in black paint.)

The IAU standard magnitude formula is :

mag = H + 5 log(r * delta) - 2.5 log((1-G)phi1 + G * phi2)

phi1 = exp[ -3.33( tan( beta / 2) ^ 0.63)]

phi2 = exp[ -1.87( tan( beta / 2) ^ 1.22)]

...in which logarithms are to base 10, r = the distance between the

asteroid and the sun, delta = distance of the asteroid from the observer,

and beta = phase angle.

If an asteroid has been observed for a while over a wide range of phase

angles, then the slope parameter G can usually be determined. But for most

objects, a default value of 0.15 is assumed. I don't know what that value

corresponds to in a physical sense.

-- Bill