How can I derive an mass/size estimate of an asteroid from JPL parameters?

Question

I'm looking for a list of objects with a semi-major axis between 0.95 AU and 1.05 AU that are probably larger than 1 km in diameter. For this, the JPL Small-Body Database Search Engine seems to be the best option.

Here is an example search query:

• a >= 0.95 (AU) (Semi-major axis)
• a <= 1.05 (AU)

This gives 403 objects. Estimated diameter is only given for 6. Largest is 2.48 km. 3753 Cruithne has a diameter of about 5 km and orbits at a=0.998 AU. It's even in those search results, but it just doesn't have a diameter listed.

As far as I know, diameter estimates are made roughly from magnitude information. Obviously albedo factors into this, but let's say I'm happy with the uncertainty of using a standard albedo and standard density. I have absolute magnitude, H, as a parameter for all objects, but the problem is I don't know how far away it was when the measurement was taken. It seems obvious to me that you couldn't get orbital parameters without at least having a distance estimate at the time of when you recorded magnitude. In other words, there absolutely must be enough information taken to estimate the object's diameter, but it's not obvious how to do it.

There is another database tool for Near Earth Objects that NASA has online for candidates for an asteroid mission. However, the objects in this database are already restricted by some criteria that excludes larger objects I'm trying to tabulate.

Using the output fields available from the JPL database, how can I calculate an estimate of object diameter?

Answer 1

As Wikipedia mentions, Absolute Magnitude is a standard measurement of how bright an object would be, if measured from $1\ ㍳$ (Earth Mean distance from sun), away. Furthermore, it uses the same logarithmic scale to measure relative brightness, such that a $1.0$ magnitude change relates to a $10^{0.4}=2.512$ scale. Put all of the pieces together, and you should be able to estimate how big an object is, with some assumed albedo.

Answer 2

The prior answer cleared up the issue I was having. It is true that with only the absolute magnitude (H) and albedo (p) you can estimate the size. The formula is the following:

$$D(km) = \frac{1329}{\sqrt{p}}10^{-0.2H}$$

For objects in my search range, here are some examples:

(object name) (JPL diameter estimate) (formula result)

• Aten 1.1 km 1.14 km
• Khufu 0.7 km 0.634
• Amun 2.48 km 2.48 km
• Cruithne none 2.84 km
• Xanthus 1.3 km 1.3 km

As you can see, this is probably the exact method JPL uses for the diameter calculation. Also, most objects that do not have a listed diameter also have no listed albedo, which explains why they didn't provide an estimate. For my calculations I assumed an albedo of 0.2 where I did not have one. This is likely the reason that Wikipedia gave 5 km for Cruithne while I found about half that - it could be a fairly dark object.