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I was going through an article about Bennu asteroid and OSIRIS-REx mission and done a quiz. There is an interesting question:

What's a Potentially Hazardous Asteroid?

a. One at least 500 feet wide that can come within 4.65 million miles of Earth

b. One at least 1 mile wide that can come within 1 million miles of Earth

c. Any asteroid that hits us

The correct answer shown is a. I've briefly go through information of it on Wikipedia. However, I wonder how scientists determine a as the standard of a potentially hazardous object (PHO) instead of b? Isn't b sounds more suitable and dangerous than a?

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tl;dr: That answer is not exactly correct. The correct answer is 0.05 AU and absolute magnitude = +22. You only get ~500 feet if you assume an albedo, which is going to be a good guess but really an unknown.


Wikipedia sez:

...having a minimum orbital intersection distance with Earth of less than 0.05 astronomical units (19.5 lunar distances) and an absolute magnitude of 22 or brighter.

and that sentence cites https://cneos.jpl.nasa.gov/about/neo_groups.html which explains:

Potentially Hazardous Asteroids (PHAs) are currently defined based on parameters that measure the asteroid's potential to make threatening close approaches to the Earth. Specifically, all asteroids with an Earth Minimum Orbit Intersection Distance (MOID) of 0.05 au or less and an absolute magnitude (H) of 22.0 or less are considered PHAs. In other words, asteroids that can't get any closer to the Earth (i.e., MOID) than 0.05 au (roughly 7,480,000 km or 4,650,000 mi) or are smaller than about 140 m (~500 ft) in diameter (i.e., H = 22.0 with assumed albedo of 14%) are not considered PHAs.

Absolute magnitude is the magnitude it would appear if 1 AU from both you and from the Sun, and viewed (nearly) head-on. this answer links to the CNEOS Asteroid Size Estimator where you can translate absolute magnitude that to a given size for a given albedo.

CNEOS asteroid category definitions

The reason that it's done this way is because albedo is something we can measure and report, size is extremely hard to measure except for a few large asteroids (by their gravitational effect on other bodies, or by delay-dopper radar, or by flying up to them and snapping some photos).

You can see where the 140 meters in the block quote comes from in the CNEOS table, using 14% albedo and absolute magnitude +22. More about how to use absolute magnitude and use them to esitmate apparent magnitudes in this answer (see also).

CNEOS asteroid size estimator

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  • $\begingroup$ An interesting follow-up question would be how far that Earth Minimum Orbit Intersection Distance (MOID) of 0.05 au can happen; if it is just minimum distance to Earth's orbit (regardless of time or Earth's specific position) or it has to be say minimum distance to Earth itself, say within the next 1,000 years. $\endgroup$ – uhoh Dec 5 '18 at 23:46

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