The details of orbital slingshots can be complicated, but for the big picture, it’s enough to just know that they’re elastic collisions. The maximum gain from a slingshot (which would surely be achievable from a black hole) is to approach the object in the direction opposite its orbit, and to then leave in the same direction of its orbit. For a slingshotting object much more massive than your spacecraft (which we would have), this amounts to a gain in speed equal to twice the slingshotting object’s orbital speed.
The gain from an Oberth maneuver would be more complicated, enough that I can’t give an off-the-top-of-my-head answer, especially if the Black Moon is spinning.
I’m fairly sure that tidal forces are going to be problematic well before you get any advantage from frame dragging, but admittedly I’ve never done the math (or seen it done).
Oberth math isn’t too bad if you just consider conservation of energy (one way of looking at it is that your propellant has far more effective energy when you’re going fast deep in a gravity well), but yeah, it’s a bit too much for a top-of-my-head answer.
Hm, true. We’d be talking about a Schwarzschild radius of less than a millimeter, and most of the really interesting effects from a black hole come when you get to within a small multiple of the Schwarzschild radius.
Kinda fun to play with. I’m mildly surprised at how some of the numbers worked out. Tidal effects become annoying even at 10 km out: for a 1.8 m person, it’s nearly 2 gees from head to toe. You could get closer if you laid flat, but watch out that your spacecraft stays aligned. You could get closer yet with an unmanned craft but you’d need to make it fairly beefy. Something like Voyager would be torn to shreds.
And even at 10 km, the Oberth advantage for a 1 km/s burn is only about 8x. That’s not bad but I was expecting more when you’re taking advantage of a black hole.
The smallness is definitely posing a problem here since you just can’t get close enough to get extreme benefits. Even if you build an ultra-durable nano probe that gets within 1 m of the singularity, you’re still only getting an 80x benefit from a 1 km/s burn. Though the advantage goes up as the delta V goes down. A tiny 1 m/s burn leaves you with 2.5 km/s excess velocity.
I used AI for this but had to fix the Oberth math manually. It just couldn’t keep the reference frames right. I spot checked everything else though and I think it’s right.
What would a solar eclipse look like - there’d be some distortion of the shape of the Sun as it passed behind the black hole/Moon and maybe some lensing?
I doubt that an eclipse would even be detectable… Maybe with very precise instruments, but probably not even then. There’d certainly be lensing, but the lens being so small and distant, any effects would also cover a very small angular area on the Sun’s surface.
If the compression into a black hole had happened back in prehistory, I wonder at what stage of our technological development would we have even discovered the thing.
We’d need an explanation for the tides. Probably sometime after Newton, but not too long. That is to say, we’d know there was a massive object out there but wouldn’t be able to detect it.
Might have sped up the discovery of dark matter. Once we knew that this kind of stuff is out there, we’d be looking for it more carefully.
I wonder whether such a force capable of giving rise to the tides that cannot be explained would rather hinder the discovery of the laws of gravity. If you don’t know about the black hole moon the force of gravity seems not to be universal: it is different close to Earth compared to the level of the Solar System or the Jovian Moons. And those were all the data points Galileo and Newton had. Lacking the visible moon, would Newton have deduced the universal law of gravity?
There would have been no Apollo program, that is for sure. Rocket technology would not have improved as it has, perhaps remaining at the level of the V2 or Sputnik, perhaps a bit more: nothing beyond geostationary orbit because: what for? I don’t see how that might have sped up the discovery of dark matter.
Would you have become such a space nerd without the Apollo program?
I’m certain we’d have figured out the orbit and rough mass of the dark moon no later than 1800 based solely on the tides. Newton would have figured out gravity anyway; the biggest motivating factor was figuring out the laws of planetary motion, which wouldn’t be affected. And he or someone else would deduce that the tides must be caused by a nearby massive object, in the same way that Neptune was predicted from its gravitational effect before it was observed.
The big mystery of course is how you can have a mass without a visible object. They’d know it had to be very dense. Or maybe they’d think it was some kind of discontinuity in space that acted as mass without having substance. Regardless, as the observations got better, they’d realize it acted no different than any other massive object, just smaller. It’s possible that this realization would prime physicists for the idea that there’s a world of invisible matter out there.
And sure, we wouldn’t have the Apollo program, but we’d try to explore the object. Send probes in and see what happens.I don’t think there would be too many surprises though since General Relativity would be understood by then. Anything entering would be crushed, and orbit too close and you’d be ripped apart by tides.
Well, sure, but there are other kinds of discontinuities out there. Cosmic strings and other topological defects, say. It’s a pretty sophisticated concept but maybe they could pull from pure math. Or show that topological defects can occur in ordinary crystalline lattices and that maybe space can have similar defects that act as mass. It would take very advanced instruments (or a space program) to show that the mass is spinning and spherically symmetric, which would rule out some of the other possibilities.
I guess you will never cease to amaze me with your optimism concerning space travel. The tides? Have you checked the internet? Most of the explanations for the tides are still wrong today!
Anyway, I believe that without the moon the interest in astronomy would have been much reduced. Starting with ancient time and on to today.
How do you find an invisible, 1 mm³ big thing 385,000 km away, no matter how heavy? Send a satellite there and you are likely to miss it by 1,000s of km!
Here is your optimism again. Maybe, but perhaps not.
Incidentally, I consider Lumpy’s question four posts ago interesting.
Yes, the moon’s influence needs to be accounted for in all satellite orbits, both in LEO and GEO. I believe long before the space age, sophisticated calculations of other planets’ orbits had to account for Earth’s moon as well, but I’m not positive there.
I think we might still have some sort of month-long cycle built into our calendars, based on how the tide cycles changed relative to the day cycle.
Tides are certainly misunderstood, even by those that think they understand them, but they were basically completely figured out by Laplace in the late 1700s. The knowledge is just not evenly distributed.
That’s fine. You watch how it deflects and then you will know exactly where the mass is for the next time. Though I think we’d have better estimates for the position by the time we had a space program.