Can you See Neighboring Asteroids from an asteroid?

[Albertgauss]

TL;DR

asteroids neighbors view sight

It is well known that the asteroid belt is relatively sparse, with the asteroids spread out pretty far away from each other. From what I have read, asteroids are generally separated from other asteroids by about 500,000 to 1,000,000 km on average from their nearest neighbors. If I stood on an asteroid, how hard would it be to see the neighboring asteroids around me?

On the one hand, I know that the moon is about 400,000 km away from the earth. Of course, the moon is certainly a much larger object than an asteroid (typical size approximately 1 km or so). If a neighboring asteroid reflects light, would it look like a star in that case, or would it still be too hard to see on account of its being super small? If you can't see any of your neighboring asteroids, how powerful would your telescope have to be to see your neighbors, and would that be easy or hard?

 

[anorlunda]

The answer is simple and obvious. Sometimes.

 

[Albertgauss]

I think you're right. I thought the same, too, just wasn't sure if I missed something. Consider this post answered.

 

[russ_watters]

From what I have read, asteroids are generally separated from other asteroids by about 500,000 to 1,000,000 km on average from their nearest neighbors. If I stood on an asteroid, how hard would it be to see the neighboring asteroids around me?

On the one hand, I know that the moon is about 400,000 km away from the earth. Of course, the moon is certainly a much larger object than an asteroid (typical size approximately 1 km or so). If a neighboring asteroid reflects light, would it look like a star in that case, or would it still be too hard to see on account of its being super small?

If you can't see any of your neighboring asteroids, how powerful would your telescope have to be to see your neighbors, and would that be easy or hard?

Well, to get more specific, one can calculate apparent magnitude based on distance. The brightest asteroid visible from Earth is Vesta, and it is marginally naked-eye visible at its closest approach of about 150,000,000 km and magnitude of 5.1. So at 1 million km it would be magnitude -8, which is brighter than Venus ever gets to us. Repeat for other asteroids...

 

[Vanadium 50]

On average, asteroids are farther from each other than they are from earth. So sometimes.

 

[russ_watters]

On average, asteroids are farther from each other than they are from earth.

At first read that sounded very surprising given that the asteroid belt starts at about 2 AU so the Earth is never closer to 1 AU from any asteroid in the belt. But if "on average" means the average distance of one asteroid from all the rest, then sure; more than half of the asteroids are more than 2 AU from any given asteroid. But that doesn't seem like a salient point to me. It doesn't tell us how many or how frequently from one asteroid you could see any of the rest.

 

[Vanadium 50]

It tells you that on average asteroids are dimmer when observed from other asteroids than from earth. Since exactly one asteroid is naked-eye visible from Earth, and even so is only so about 10% of the time, the answer is pretty clearly "sometimes".

 

[anorlunda]

The asteroid belt is not a rigid structure. Neither is it a gas or a liquid, not quite. But the distances between asteroids is not fixed and there must be collisions sometimes (albeit rarely). That is why I said "obvious" in post #2. Before a collision, the other asteroid must become visible.

In other words, the average distance is not relevant. The minimum distance is what is relevant to this question.

 

[DrStupid]

It tells you that on average asteroids are dimmer when observed from other asteroids than from earth.

But the question is about neighboring asteroids.

 

[Vanadium 50]

And the answer is still "sometimes".
How long is a piece of string?

 

[DrStupid]

And the answer is still "sometimes".

I'm not sure what "sometimes" actually means. Can you translate that into a number?

 

[Vanadium 50]

Of course not. How long is a piece of string? Can you translate that into a number?

 

[anorlunda]

I'm not sure what "sometimes" actually means. Can you translate that into a number?

You have to do much better at forming the question before you can get a numerical answer.

 

[DrStupid]

Of course not.

That sounds like it is not possible. But shouldn't it be possible to estimate the probability from the spatial distribution and size distribution of asteroids in the belt? Do I miss something?

 

[russ_watters]

That sounds like it is not possible. But shouldn't it be possible to estimate the probability from the spatial distribution and size distribution of asteroids in the belt? Do I miss something?

Yes, it should be, but it can also be done deterministically. There's a real and exact answer to a properly framed question.

How many solar system objects are naked eye visible from Earth at under mag 6 right now? Answer: 8 (currently includes Uranus). You could ask the exact same question from standing on any asteroid.

There are many such lists and software for visibility of objects from Earth, some updated in real time. The same certainly could be done for asteroids if someone chose to.

I use Starry Night, which allows you to select a couple dozen locations off-earth, including Ceres. I'm not sure if it is capable of generating lists, though. Panning around, it doesn't appear that any other asteroids are currently visible from Ceres. Due to the small number of large asteroids, I suspect that is usually true. But you could also flip over the question and ask: from how many (or what fraction) of 1km+ asteroids can you currently see Ceres?

 

[Robin Davies]

Visible: > mag 6.

All calculations back of the envelope, using the relative magnitude of Ceres at closest approach (mag 6.9, 1.56AU from earth) as a reference point.

Ceres is visible from about 1/3 to 1/4 of all asteroids at any given time. Simplest argument: an asteroid 1.56AU from Ceres (the same distance that Earth is from Ceres at closest approach) will see Ceres with apparent magnitude of 6.9. The difference between mag 6.9 and mag 6 means that Ceres will in fact be visible on asteroids as far as ~3 AU away. So Ceres will be definitely be visible from an asteroid that is within +/- 1/6 of an orbit of wherever Ceres is. Which is 1/3 of all asteroids in the main belt at any given time with a generous fudge factor provided for outer belt asteroids.

Since asteroids have different orbital periods, and since Ceres sits on the outer side of the main belt, Ceres will be visible from all but the few asteroids in locked orbits with Ceres *eventually*. I think, most asteroids in locked orbits with Ceres will be able to see Ceres all the time, but not enough asteroids to chase after seriously.

As to the question of what percentage of asteroids (of any size, it doesn't matter) among the remainder can see another asteroid (of diameter greater than 1km for the sake of specificity since that does matter), at any particular time, my back of the envelope calculation says that it may be most of them in the inner belt. The top ten largest asteroids don't cover the entire orbit of the asteroid belt. However, by rough calculation: a 100km asteroid is visible for about 100th of an orbit. And conveniently, there are about 110 asteroids that are 100km or larger. Again, not enough to provide complete coverage of all asteroids. And most of these will not be visible from both belts. A 10km asteroid is visible for about 1/10,000 of an orbit; and by happy coincidence, there are about 10,000 asteroids that are 10km or larger. Again, not enough to provide total coverage of the entire orbit. The contribution of <10km asteroids is ... too complicated for a back of the envelope calculation. All in all, not nearly enough to definitively cover the full width of the asteroid belt all the way around the orbit, but enough, I think that a majority of asteroids at any given time will be able to see a large asteroid, if only because they may be able to see one of the top 10 largest asteroids. >100km asteroids provide additional coverage, but less coverage than the top 10 do; > 10km asteroids provide additional coverage but less, in turn, that the >100km asteroids provide.

Clearly not all asteroids will be able to see another asteroid. The outer belt is pretty clumpy; and there are asteroids roaming around between the main belts that are going to be pretty lonely, as well as asteroids with eccentric orbits which are going to be very lonely indeed.

I also haven't allowed for albedo in my back of the envelope calculation. Most asteroids have significantly lower albedo than Ceres. Factoring in varying albedo is complicated.

Working out exact coverage is a formidable number-crunching problem that is left as an exercise for someone who actually cares enough to put in the effort. But you're definitely going to get an answer somewhere between 1/4 (top 5 unfortunate worst case), 1/2 (top 5 typical case) and most (but not all) of them. If this was a Google interview, I'd go with "It varies. Between 65% and 80% of all asteroids can see another asteroid at any given specific time, depending on which specific time you pick. But all of them will be able to see Ceres eventually."..