"To date we have covered 624 square degrees of sky near to and interior to the orbit of Venus" meaning wrt Asteroid survey Interior to Earth and Venus

Question

CNN's October 31, 2022 ‘Planet killer’ asteroid spotted hiding in the sun’s glare links to Sheppard et al. (2022) A Deep and Wide Twilight Survey for Asteroids Interior to Earth and Venus. The abstract is long, and includes sentences like

We are conducting a survey using twilight time on the Dark Energy Camera with the Blanco 4 m telescope in Chile to look for objects interior to Earth’s and Venus’ orbits.

Our new discovery 2021 PH27 has the smallest semimajor axis known for an asteroid, 0.4617 au, and the largest general relativistic effects (53 arcsec/century) known for any body in the solar system. The survey has detected ∼15% of all known Atira NEOs. We put strong constraints on any stable population of Venus co-orbital resonance objects existing, as well as the Atira and Vatira asteroid classes.

Atria asteroids never go out as far as Earth's orbit; Vatria and Vulcanoids never as far as Venus' and Mercury's, respectively.

However, it's hard for me to understand how much we can get from the following sentence in the abstract.

To date we have covered 624 square degrees of sky near to and interior to the orbit of Venus.

Since both the Earth and the asteroids are rotating around the Sun and at substantially different rates, somehow citing the amount of sky covered seems a bit misleading. Couldn't all those square degrees that have been covered be full of undiscovered objects a year or two later? They're not marked "finished, done, no need to revisit later" are they?

Question: What exactly is the meaning of "To date we have covered 624 square degrees of sky near to and interior to the orbit of Venus"?

Isn't there a higher dimensional space that takes into account period vs radius (as well as the problem with the Sun's glare" that is a more honest metric of how far along they've progressed?

Answer 1

Couldn't all those square degrees that have been covered be full of undiscovered objects a year or two later?

Yes, absolutely. Luckily orbital periods are rather short for this kind of objects - Venus needs 7 months for one full orbit. That means, objects could come into the field of view rather quickly, if the phasing with Earths' position is right.

What exactly is the meaning of "To date we have covered 624 square degrees of sky ["?]

Essentially, this can be understood straight forwardly: They took pictures of the sky, and covered this amount of area. The total area of the sky inside Venus' orbit, including all possible inclinations can be found easily by using the largest angle Sun-Earth-Venus that can be observed, about 45°. This gives a solid angle of about 6000 square degrees. Obviously, there's a large part that can never be observed close to the Sun. In addition, the Earth-bound observer is moving so that the actual position of this part of the sky changes throughout the year.

Indeed there's

a higher dimensional space that takes into account period vs radius.

Population of all the possible orbits is far from homogeneous (e.g. polar orbits are very rare). Hence it's rather complicated to arithmetically calculate how many possible objects could have been seen.

Instead the authors of the paper did a Monte Carlo simulation to determine how many objects they would have missed. In the "Discussion" chapter (pages 12/13) are several tables showing the expected coverage. Obviously, the probability of detection depends on three main parameters:

• The type of orbit - they added 5 tables with different orbital parameters
• The size of the object - each table has three columns for sizes of 0.5, 1 and 1.5 km.
• The albedo of the object - grouped in six categories labeled with capital letters.

The detection efficiency of this one survey for objects sized 1 km or above varies greatly between 25% and 5% depending on how unfavorable the orbital geometry is. Dark objects with less than 1 km diameter are likely to have been missed completely due to the sensitivity of the instruments.

Answer 2

624 square degrees of sky is a circle around the sun 17 degrees in radius. But venus moves 45 deg away from the sun, so yes, there's lots of sky between Venus and the sun NOT in this survey.

Yes, the survey would have concentrated those square degrees along the ecliptic. But that's still 45 deg vs. 17.