Are two stones of the same brightness necessarily the same size?
White stones are more reflective, and black stones may need to be larger to appear equally bright.
Planets and Small Solar System Objects
Astronomers sometimes know an asteroid's brightness before estimating its size. But without knowing the surface's ability to reflect light, brightness cannot uniquely determine diameter. Drag the albedo to see how big the model needs to be to be equally bright.
Guess first
What area would typically be required for a darker surface to be equally bright?
Show answer and explanation
bigger — In order to reflect the same amount of light, a larger effective reflection area is required.
Then connect experience and science
diameter estimate
Diameter unit is km.
d=10^(3.12−H/5)/√A
albedo
A is the reflection ratio between 0 and 1.
Fixed H: d√A is constant
apparent diameter
Small angle approximation, Δ in AU.
θ=0.0013788d/Δ
model boundaries
Irregular asteroids only have equivalent dimensions.
Not a geometric outline model
First estimate the diameter d (kilometer) from the absolute magnitude H and albedo A, and then estimate the angular diameter θ (arc seconds) using the geocentric distance Δ (AU). H is not the current apparent magnitude; albedo uncertainty propagates directly to magnitude.
give it a try
Keep H still and adjust the albedo from 0.04 to 0.4. Compare the two estimated diameters.
No need to memorize symbols
- H
- absolute magnitude
- A
- albedo
- d
- Estimated diameter km
Algorithm, accuracy and scope of application
Covers the diameter and apparent diameter of asteroids at the end of Chapter 55. The coefficients are according to the original book and do not claim to be equivalent to modern thermal infrared size measurements.
my understanding check
Can this formula automatically measure unknown albedo?
cannot — Albedo is the input or a priori hypothesis.
Can the absolute magnitude be directly replaced by the apparent magnitude at any time?
Can't — The distance and lighting definitions between the two are different.
Do asteroid irregularities affect diameter interpretation?
meeting — Here is the equivalent scale estimate.
Brightness is not a ruler. Reflectivity, distance and geometric conditions must all be clearly explained.
Jean Meeus · Astronomical Algorithms, 2nd ed. · No. 55 chapter
Planets and Small Solar System Objects · All interactive courses