How to adjust our Goldilocks Zone if Nemesis turns out to be real?

I'm drafting a story where a solar system is a binary star system, except that one of its stars turns out to be a black hole with 1.5 solar mass. However, I have realized that adding a black hole might disrupt the orbit of all the planets. So I would like to shift their orbits a little. Any advice so that I can have a stable orbit and yet maintain my Goldilocks zone?

• Outside of the Swartzchild radius, physics of gravity does not change depending on what is in the center. Assuming that none of your planets were touching the star you are replacing, none of the gravitational physics would change by replacing the star with a blackhole. – Aron Apr 8 '16 at 9:27
• @user6760: What is the orbit of this BH? What eccentricity, what period? Are you describing a possible future or an alternative world? (In the first case, you probably want to know where Nemesis can be hiding without going into contradiction with that what we know about the Solar System, in the second — where to put all the Solar System bodies for the Earth to stay similar enough.) – BartekChom Apr 8 '16 at 12:18
• @user6760 , Aron isn't mistaken. Gravitationally speaking & at a distance, black holes are no different than any other mass. Granted replacing the Sun with an equal mass black hole has other implications (e.g. no sunlight), gravitationally the Earth just continues in its orbit with no change. So you just need to find a spot in our solar system to place a $1.5 M_{\odot}$ blackhole without disturbing what we see - it'll probably be very far out. – Jim2B Apr 8 '16 at 14:16
• @Jim2B: picture a winter melon resting on a trampoline now I add a watermelon, do you think the profile of the sheet of the trampoline changes? This is just an analogy to demo gravity also try to imagine that the two melons are moving in circles at high speed... how far out will the profile of the sheet to become gentle? We don't wanna slingshot Earth do we? also I need there to be liquid water that's problematic. – user6760 Apr 9 '16 at 1:31
• @user6760, binary star systems come in all shapes and sizes. There's no particular reason the black hole needs to be within the habitable planet's orbit. Heck, it's possible that the system is binary and the inhabitants of the planet aren't even aware of it. It's conceivable that is true of our Solar System (but the mass values of the second star are probably pretty low due to luminosity and Solar motion observations). – Jim2B Apr 9 '16 at 2:30

Adding a black hole would cause the total mass that the earth is orbiting around to be 2.5 solar masses, so the orbit would need to speed up to remain at the same distance. If the black hole doesn't emit any radiation* then the goldilocks zone (GLZ) would stay the same. To keep the earth at the current orbit, it would need to speed up when moving around the star. This would shorten the year by a factor of $\sqrt{2.5} = 1.58$, which means that each year is $231.17$ days (and the day is the same length).

*There is the problem that the black hole could suck in some matter from the sun which would lead to radiation, which could sterilize the earth in any habitable zone. This calculation is determined by how close the black hole is to the star.

I assumed that the black hole was fairly close to the star, so it essentially isn't a 3-body problem. However the radiation could make that assumption unreasonable. If it is reasonable though (or you just want to ignore it for your story) then simply reducing the years of all of the planets would do the trick of keeping them at the same orbits.

Also note that this black hole is super small. The radius of the sun is $696,342 \ km$, and the radius of this black hole is just over $4\ km$. It'll be hard to see.

How do you have to adjust the habitable zone? Well, the answer is that you don’t.

The classical Nemesis hypothesis puts some unseen object at around 100,000 astronomical units from the Sun (and yes, for those curious, it’s generally regarded as being nonexistent). It’s generally thought to be a brown dwarf or red dwarf, either or which would account for its apparently extremely low luminosity. Your choice of a black hole makes the observations even more difficult, because the Hawking radiation put out by this black hole will be negligible. An accretion disk could light things up a bit (literally, though the generation of a magnetic field near the center of the disk), but that would still likely be nowhere near Earth, or any of the other plants, for that matter. 100,000 AU is far.

For those wanting exact numbers, Wikipedia puts the power output from a 1 M$_\odot$ black hole at about 9$\times$10^-29 watts, roughly 55 orders of magnitude lower than the luminosity of the Sun, and at 100,000 times the distance. Actually, given that the power is inversely proportional to the mass of the black hole squared, this figure will be even lower. There will be virtually no contribution to the radiation received by the Earth.

But because I’m a bit nerdier, I ran some quick simulations using My Solar System. I started with a body of 0.0006 units of mass orbiting another body of 200 units of mass at a distance of 38 units of distance with an orbital eccentricity of ~0 (I have no idea what their units are, for the record). This ratio is approximately that of the masses of the Earth and Sun; I chose these figures so the simulation would run reasonably well. The period of the planet is 1 unit of time, which I’m equating to 1 year.

I then added another body of 300 units of mass, or 1.5 solar masses, orbiting at a distance of 380 units of distance, or the equivalent of 10 AU. Here’s the initial setup:

Here’s the configuration after one period (28.4 years) of the two main bodies orbiting each other:

The planet is not at all perturbed by the newer body. It remains at a distance of about 38 units of distance through the entire time. Now (in your head) make the second body orbit at 100,000 AU - 10,000 times as far away - and see the complete lack of non-negligible perturbations on the planet.

This simulation isn’t fantastic, but I hope it showed that at distances greater than about ten times the orbit of the planet, the black hole will have virtually no effect on how the planet orbits its parent star - which is the real issue. If it perturbed the planet such that it moved out of the habitable zone, that would be a problem. However, that’s clearly not the case here.

• Good answer. However a) Hawking radiation is of course neglegible. The real question is how visible and dengerous the radiation caused by the infalling mater (acreation disc and maybe something else) is. b) The neglibility of perturbations is not so obvious. We need stability over miliards of years. It is a lot of time. – BartekChom Apr 9 '16 at 7:47