We’ll assume it’s a stellar mass black hole of 5 solar masses. And it’s headed directly towards the Earth, as in, the event horizon of the black hole is aimed at the center of the planet. The Earth won’t survive.
One hundred and twenty years is a lot of time, probably enough to ensure the survival of the species, assuming the nations of the world don’t act stupidly short-sighted and monogenerational. (120 years is more than enough for a climate change apocalypse to have happened, but being such a gradual change and one that isn’t human-extinction-level, it isn’t nearly as important a topic for lawmakers apparently.) We’ll assume that the world is genuinely working towards an escape plan.
I’ve run some simulations in Universe Sandbox 2, an N-body gravitational simulator, to see what a flyby of a stellar mass black hole would do to it. Naturally, astronomers will be doing the same thing in their scenario too.
The flyby of the black hole will cause the Earth to be destroyed completely, bits of it flung every which way across the solar system. The Moon escapes, but it’s flung out at a substantial fraction of the speed of light. Mercury is largely unaffected at first, while Mars and Venus are drastically changed.
Mars is now in a lower, eccentric orbit. Before its orbit was at 1.5 au (1 au = Earth-Sun distance). Now it’s at an average of 1.3 au. Its periapsis is 0.847au, stretching to near where Venus used to orbit. Its apoapsis is at 1.75 au. This puts it in the cooler limits of the habitable zone, though it does get extra toasty in the short orbital summer before cooling down during a long orbital winter.
Venus is moved up to 1.03 au from 0.723 au. Its apoapsis is 1.38au and its periapsis is 0.723, right where it started. Venus’ greenhouse gasses haven’t gone away, so it’s still nowhere near habitable.
Jupiter’s orbit has changed as well. It has moved from its 5.2 au circular orbit to an extremely elliptical orbit. It now goes between 0.208 au, closer than Mercury, to 5.88 au. Average of 3.04 au. This will cause Jupiter’s outer moons to escape as it gets close to the Sun, but the inner four major moons will survive at first. They grow cometary tails as they approach the scorching sun and their ice melts and vaporizes. Ganymede and Callisto may grow temporary atmospheres. Once Europa’s icy crust melts completely, the oceans will boil off entirely within a decade.
Saturn, Uranus, and Neptune all escape the Solar System and fly out into deep space.
Comets disturbed both by the exit and entry of the black hole into the solar system’s oort cloud will make their way down to the inner solar system after a few hundred thousand years.
Every Jovian orbit, as the giant planet comes in from its ellipse, it flies by the inner solar system’s planets, perturbing and changing their orbits. But the chances of direct flyby are minimal, as Jupiter’s new orbit is very inclined from the plane of the other planets. Over thousands of years the system is unstable, and chaotic enough that astronomers don’t know exactly how it will play out. Mercury, Venus, and Mars are all subject to being thrown out of the solar system, captured into Jupiter orbit, or colliding with each other, Jupiter, or the Sun.
The world’s space agencies gear up to start colonizing Mars. A true, self-sustaining base that is itself capable of expanding into the rest of the new, alien solar system, but be built. No one is putting restrictions on Nuclear power anymore. The most powerful spaceship that can be built for its budget is a Nuclear Pulse Rocket. Essentially, you detonate nuclear bombs behind the ship to generate thrust. A fleet of these is built as soon as possible on a military-sized budget, and by the late 2020s the first shipments of equipment to Mars begins.
A lot of havock involving asteroids and space junk is going to occur on the Final Day and the decades following it. You can’t just build one colony to be safe. You have to build several, or you risk your colony being destroyed by killer fasteroids.
Ready-to-use bases are set up on several asteroids whose orbits are determined to be close enough to Mars’s new orbit to be of use. Having space infrastructure set up already will make the Mars colony’s exploration and exploitation of the new solar system so much easier.
Copies of the genomes of every species scientists can get their hands on, fossils, scientific records dating back centuries will be stored on Mars, and copies of them on asteroids. Backups of the entirety of the Earth’s culture and humanity’s knowledge will be stored in various formats on many of the bodies projected to be flung out of the system, on the off chance that explorers charting the rogue planets and asteroids may one day find evidence of humanity’s existence.
The Earth can’t be fully evacuated practically, not with Orion anyway. The amount of heat released into the atmosphere would cook the Earth long before you got everyone off. But 150 years and a fleet of Orion Nuclear Pulse rockets is enough time to get millions of people off of Earth and reproducing on Mars.
Those who get to leave will have to be decided based upon merit, and must take into account families and friends as well.
150 years is enough time, especially with all of the spinoffs that the huge space program budget will have generated, that people will be considering launching generational or hibernational ships to other star systems as well. They might aim towards the black hole during its approach and try to get a gravity assist to slingshot them to another star. I have no doubt that at least one company will attempt something like this. 150 years is a lot of time to develop technology, and they may have perfected embryo freezing and microtechnology, meaning you could send interstellar ships the size of houses to other stars and unfreeze the embryos, growing them in an artificial womb.
Humanity realizes all too well know that you don’t want to put all of your eggs in one basket. Venus’ surface is not habitable in any way whatsoever. But its upper atmosphere, above the cloudtops, is very Earthlike. It’s an acidic environment with CO2 air, but the temperature and pressure is very much like Earth’s. At least one colony of 150 people is set up in the upper cloudtops of Venus, using nitrogen/oxygen breathing mix for buoyancy (CO2 is denser than N2 and O2.). The colony is established fairly late, but they managed to buy one of the Orion Nuclear Pulse Rockets that was starting to get old, and modified it to have a hydrogen balloon to ensure its buoyancy in the Venusian atmosphere. Nuclear ramjets and Carbon Monoxide/Oxygen chemical rockets are built to ensure that Venus has a fleet of refuelable launch vehicles of its own. Venus colony’s growth will be stunted, but it is at least self-sustaining enough to survive as a potential base for the reemergence of humanity if something goes wrong. By the time The Event happens, the colony had grown to 400.
A few dozen space habitats (rotating cylinders and wheels with centrifugal Earthlike gravity) are also launched, many of them as nature preserves. These tend to have populations of 150–5000, but the largest, built by China, was placed onto an orbit that would get altered by the Black Hole flyby into one that was almost identical to that of the old Earth. A population of 200,000 people in a modern, green city in space.
The Event happens. The Black Hole collides with the Earth. Cameras around the world feed live data of the destruction of Earth, to the horror of anyone who would watch them. Anyone who didn’t get a ride on an escape ship—and that is a fairly large population of over 7 billion people (People still had lots of babies and the population still grew over the last 150 years, and less than a Billion people could ever hitch a ride off of the Earth)—were panicking, though some of the younger generation especially managed to keep calm. This was, as they thought, their destiny all along. At least it would be cool to look at. One of the livestream cameras caught a hiker who had managed to bring a drawing of his all the way up to the site of the camera and show it off. It was a drawing of the Earth, the Moon, humans, plants, and animals. A somewhat mediocre piece of art from a critical standpoint, but that camera would be destroyed ten minutes later during volcanic eruptions. It was the last piece of art that the Earth would ever show.
After The Event, a new calendar starts. It still uses Earth years, in memory of the original planet that once lived in the Solar System. The Event is year 0. The Martian colony officially began using the calendar 50 years before The Event. Those still on Earth started using the new calendar around 5 years before.
After the Event, Martian astronomers observe the result of the Earth’s collision with the Black Hole. It is an intensely energetic phenomenon, and the Earth shines brighter than the Sun for several hours as it expands in a cloud of plasma that is luckily moving away from Mars. A rain of highly energetic micrometeors showers down on the surface, but luckily the astronomers predicted this and the habitats were built underground, so the damage here is minimal. All surface equipment is covered beneath armored shields and Mars runs off of batteries and reactors for several days until the showers have effectively stopped.
Martian astronomers now re-evaluate the orbits of the solar system. They measure the orbits of the three other planets and the Sun to find Mars’ new orbit. Over several days and weeks the orbits of the planets are now known to a high degree of precision, and many of the largest asteroids are too. After a year, no asteroids are detected on a collision course with Mars within the next few thousand years at least.
Mars’ new orbit warms it up significantly. The ice caps, composed largely of dry ice (CO2), melt, increasing Mars’ atmospheric pressure to about 1/100th of the Earth’s atmospheric pressure, enough that water can, just barely, remain liquid when it’s cold. Saltwater lakes slowly form as Mars’ underground and polar ice caps melt, but they evaporate completely in the summer as temperatures climb to as much as 100 degrees fahrenheit. In the winter, all but the saltiest lakes freeze.
An asteroid is detected on a collision course with Venus in 78 years. It’s fairly small. A continent killer, not something that would cause a mass extinction on Earth, and since all of the colony spheres on Venus are manueverable it won’t be as much of a problem as a spectacle.
With panic mode officially over, the Nuclear Pulse Rockets are retired from lifter duty. You have to be careful with radioactive material if you ever want to terraform Mars, after all. Chemical rockets are fine for launching from Mars, although many nuclear thermal designs can be made more efficient and safer than either chemical or nuclear pulse rockets. From the eccentric, inclined orbit, it is much more difficult to reach the asteroids and Venus than it was in the past. The Orion fleet, with their ability to use direct transfers instead of using slow orbital mechanics, start operating the asteroid bases within a few months, returning bulk materials to Martian orbit. The nuclear thermal rocket freighters start bringing refined materials from asteroids, and eventually Venus-Mars passenger services start.
Humanity is now spread across a messy and uncertain solar system. But they’re closer than ever to species immortality, with habitats across the solar system and a few interstellar ships headed out to deep space. Whoever shot that black hole at the Earth utterly failed to bring about the end of humanity.