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The question Can we see asteroid 1998 OR2 with unaided eye? got me thinking. Space.com's Vesta: Facts About the Brightest Asteroid says:

Vesta is the second most massive body in the asteroid belt, surpassed only by Ceres, which is classified as a dwarf planet. The brightest asteroid in the sky, Vesta is occasionally visible from Earth with the naked eye. It is the first of the four largest asteroids (Ceres, Vesta, Pallas and Hygiea) to be visited by a spacecraft. The Dawn mission orbited Vesta in 2011, providing new insights into this rocky world.

The brightness of an object seen from Earth is proportional to (among other things) $1/r^2$ so an object which occasionally passes very close to Earth will occasionally be far brighter than normal; an object normally of order 200 million km away that comes to within 200 thousand km will be a million times brighter, and at 2.5 magnitudes per power of ten that means that for a brief time it could be 15 magnitudes brighter than average.

Questions:

  1. Has a near earth object in heliocentric orbit ever been bright enough to be visible to the unaided eye?
  2. Are there any predictions of events in the foreseeable future when this will happen?

Please exclude comets which are themselves invisible and it's the giant clouds of dust and gas they produce that we see and planets (and dwarf planets) who's heliocentric orbits make them regularly visible.

The following may provide some helpful definitions:

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The Near-Earth close approches website shows close approaches to the Earth by near-Earth objects (NEOs). The table showing all close encounters indicates the absolute magnitude.

The data can be exported to a CSV file to estimate the apparent magnitude for each object, using the following equation.

$$ m = H + 5 \log_{10} \bigg( \frac{d_{BS}d_{BO}}{d_0^2} \bigg) - q(\alpha) $$ where $H$ is the absolute magnitude, $m$ is the apparent magnitude, d_{*} are the distances between the objects and $a(\alpha)$ is the reflected light. $q(\alpha)$ is a number between 0 and 1.

I only want to know what happens when the object is closest to the Earth, so I use the approximation that the distance from the Sun to the NEO is 1AU.

$q(\alpha)$ is complicated to compute, so I just compute $m$ using $q=0$ and $q=1$. This leads to

min value $ = H + 5 \log (d_{BO}) - 1 < m < H + 5 \log (d_{BO}) = $ max value

with $d_{BO}$ the distance between the Earth and the NEO expressed in astronomical units (AU).

The server is unhappy when I try to get the entire database, so I limited my export to the objects that come reasonably close to Earth (d<0.05 AU), with no time limit.

Among these 24588 objects, 4 have a maximal magnitude less than 6, and 16 have a minimal magnitude less than 6. So between 1900 and 2200, no more than 16 NEOs are visible by the naked eye.

In particular, 99942 Apophis (2004 MN4) has an apparent magnitude between 1.7 and 2.7 based on these estimates. Its close approach date is April 13 2029.

enter image description here

But this doesn't say anything on NEOs from before 1900 or after 2200.

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  • $\begingroup$ This seems pretty definitive, can always accept a new answer once one does. Thanks! $\endgroup$ – uhoh May 7 at 9:39
  • $\begingroup$ The magnitude on the table is the solar-system-body absolute magnitude, not the visual magnitude at closest approach. Absolute Magnitude 10.4 (433 Eros) at 1 AU fully-illuminated reference distance, is about 6.3 visual if you shrink the ideal reference distance to 0.15 AU (distance of the 1975 approach.) $\endgroup$ – notovny May 7 at 11:14
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    $\begingroup$ @notovny Thank you for that explanation. I fixed my answer accordingly :) $\endgroup$ – usernumber May 7 at 15:17
  • $\begingroup$ ha! This still seems pretty definitive, but more appealing now :-) Okay in the 2027 to 2030 timeframe there are about four objects to "keep an eye out" for. This is great news! $\endgroup$ – uhoh May 7 at 16:27

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