I was watching a Nova episode with the physicist Janna Levin describing the mass of the supermassive black hole at the center of the Andromeda galaxy. She mentioned that its mass is estimated at 100 million solar masses.
She mentioned that if it were placed at the center of our solar system (in place of the sun), it would be large enough to fit within the orbits of Earth or Mars. She also said that it would quickly swallow up Jupiter and Saturn, but that the outer planets might remain intact.
Considering that the sun’s gravity affects objects all the way out into the Kuiper Belt and Oort Cloud, how would something 100 million times the Sun’s mass not swallow up all massive objects much further out?
It’s really not clear what’s meant by “if it were put in the Solar System”. It sounds like she’s just saying what its size is relative to the size of the orbits of the planets. But of course, the orbits of anything would be vastly different if the central object were a hundred million times more massive.
What would the orbits actually do? Well, to answer that, we’d have to first explain precisely how we’re putting the black hole there. “Poof, it just suddenly exists” isn’t an acceptable answer, because objects don’t just spontaneously come into existence.
On the face of it, the statement you mention about the outer planets remaining intact in their orbits is clearly wrong, unless you’re omitting some crucial detail. No matter how far away an orbiting object is, with vastly increased gravity at the center of its orbit, its orbital speed would have to correspondingly increase or it would spiral into the black hole.
Is the mental image something like a big vacuum cleaner sucking things up? That’s not quite how orbits work or we’d have been swallowed up by the sun long ago.
You can have something at the distance of Saturn, or the Oort Cloud, or whatever, orbiting a supermassive black hole. But it would be a very different orbit (in particular, moving much faster).
Start with a simple case: replace our Sun with a 1-solar mass black hole. The orbit of the planets will not change. Gravity does not care what the physical size of a mass is, only the amount of mass.
The solar radius is 6.96e8 m. The radius of a black hole with 1 solar mass is 2.95e3 m (4.24e-6 solar radiuses). The Andromeda galaxy is 1.71e8 solar masses, and since the radius of a black hole scales linearly with the mass, a black hole with the mass of that galaxy will have radius of 725e0 solar radiuses.
Converting to orbital units, the radius of an Andromeda-massed black hole is 3.3 astronomical units (AU). Earth orbits at 1 AU, Mars at 1.5, asteroids around 3, and Jupiter at 5.2. There are no stable orbits within in the Schwarzschild radius.
Of course, swapping out a 1-solar mass black hole with one 8 orders magnitude larger will have a dramatic impact on the current orbits of planets, even ignoring the radius. Planets would need 8 orders of magnitude more kinetic energy to stay in the same orbit. So the question becomes more of how many things are we going to magically change. On a large scale, of course putting a second galactic core in the Milky Way galaxy is going to have a large impact on the galaxy, how could it not be otherwise?
I was thinking “what’s the orbital radius of an orbit around a supermassive black hole where the orbital velocity is the speed of light?”, and then I realized I already knew the answer: it’s the Schwarzschild radius. Within the radius, even an orbital velocity of c is insufficient to prevent infalling.
Actually, the innermost stable circular orbit is somewhat larger than the Schwarzschild radius. 1.5 times it, IIRC, for a non-rotating hole. For a rotating hole, it depends on the relative directions of the rotation and the orbit.
Agree, that was my first thought as well. I even “rewound” it, and she really doesn’t give any context. Oftentimes, these science shows tive well-known examples known by many physicists, so I thought perhaps someone here would recognize the point. I’ll try to find a clip to post here.
An Andromeda central mass BH has a Schwartzchild radius near our asteroid belt.
The 3x fact given just above says 9AU is about the closest a planet could stably orbit.
Which suggests Saturn would be the innermost survivor. If it was also magically accelerated to a wacky orbital velocity.
She is most certainly talking about the Roche limit, not orbital mechanics. The Roche limit in this hypothetical scenario sits a bit beyond Saturn for the solar-system objects in question. Objects closer in would be tidally shredded.
Why not? When dealing with a hypothetical situation, there is no need to explain how such a situation could happen, because it very likely couldn’t happen. My local science museum has an exhibit showing how each planet would appear in our sky if they replaced the moon in its orbit. It is understood by most users that the planets couldn’t possibly replace the moon, but it is still an impressive exhibit.
The volume around a supermassive black hole is dangerous for another reason. Supermassive black holes are either surrounded by a big gap full of practically nothing, because everything nearby has been dragged in by collisions or ejected into interstellar space, or it is surrounded by an accretion disc where the remnants of planets, stars and gas clouds are currently being torn apart. Saturn would be tidally shredded, and form a rapidly orbiting disk of material that would impact Uranus and Neptune, probably dragging them in too. When practically everything in the Solar System was either absorbed or dissipated, this hypothetical black hole would calm down to become inactive.
If you say that something happens by magic, then you can’t use science to say what happens as a result of that. You’d need to know the laws of magic to answer that.
Meh, science has a tradition of gedanken experiments. When someone says “replace” the Sun with a black hole, they don’t mean that literally. They mean imagine a solar system just like ours, but with one difference. It’s a way to build understanding of how the world works.
Yes I think it would be quite limiting if thought experiments were not allowed without a full accounting of how that state of affairs came about from the current state.
One difference is impossible. You’ll always have multiple differences, which means you need to choose which difference you want.
For instance, does “our solar system, but with a more massive central object, but everything else the same” mean that the orbital paths of the planets are the same, or the orbital speeds? You can’t have both.
I agree w your philosophical point about magic poisoning the physics. As I’ve said a bunch of times over the years.
But sometimes you can overcome the magic objection and continue to compute. It’s not quite the same idea as the hoary old comment about “Understand quantum mechanics? Bah; just shut up and compute.”, but there are similarities if you squint enough.
You can imagine a world where one thing changes instantly in a single (handwave) quantum of time, then we observe how the now-different system evolves under changed circumstances from what had been a (mostly) stable state.
In the instant example, yes, absolutely if you drop a big BH in place of the Sun, the planets will not continue to orbit serenely along as they have for millions of years.
But with their current orbital positions and current orbital velocities, what happens next given a suddenly much more massive primary?
Broadly speaking they’re now in highly elliptical orbits where each of their immediately post-magic positions is the aphelion (apoBH?) of a new and radically different orbit. One that they may not complete even one revolution of before diving through the event horizon never to return.
But we can, at least in principle, compute e.g. Neptune’s suddenly revised orbit and future path using the same physics and algorithms we use for the non-magic world.