# How Long Until the black hole causes noticeable differences? [closed]

A black hole causes immense gravitational distortion, to such a point that it is commonly recognized that not even light can not escape it. It is also a common plot line in Scify that a black hole enters our solar system and threatens earth. My questions are:

What is the maximum distance that this black hole will effect the Earth?

What would these effects be? (I am thinking the gravity would either pull us out of orbit or cause tremendous earthquakes that will impoverish us before our destruction).

EDIT

he black hole is about the size of the earth with whatever respective event horizon this would give it. It is moving at 75,500 miles per hour, slightly faster than the orbit of the earth.

Also assume that we have sufficient anti-asteroid technology as to not have to worry about asteroids hitting us every week or month.

The black hole has 2.85 Solar Mass

## closed as unclear what you're asking by Scott Downey, Samuel, ArtOfCode, Brythan, James♦Mar 12 '15 at 18:15

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• A travelling black hole? hmmn... Do you mean in or out of the event horizon? how big of a black hole? Technically, the entire solar system is caught in the gravitic pull of the super massive black holes at the center of the milkyway galaxy... – Isaac Kotlicky Mar 12 '15 at 16:32
• This will depend on the black hole's mass, velocity, and direction - there's a ton of variability here. – Dan Smolinske Mar 12 '15 at 16:33
• The black hole is about the size of the earth with whatever event horizon that would give it according to the laws of Physics. – JDSweetBeat Mar 12 '15 at 16:33
• Edited the question to help :) – JDSweetBeat Mar 12 '15 at 16:37
• @DustinJackson You can't have a black hole the mass of Earth and, as a singularity, being the size of Earth doesn't make sense either. – Samuel Mar 12 '15 at 16:42

# The Gravity of the Situation

Odds are there will be different groups of people who will notice this black hole at different times, and for very different reasons. Some may be very emotionally affected by it before they are physically affected by it. Odds are, there will be more emotions running around this impending doom well before we feel the gravitational effects of it.

Let's look at some of the things which can affect people on Earth. I'll restrict myself to the physical effects of the black hole on earth. You said the black hole is 2.85 Solar Masses. This places it in the realm of "micro" black holes, which have an even horizon up to ~1mm. That will be important.

Black holes actually do evaporate, because they give off Hawking radiation. As they give off this radiation, the energy of that radiation comes from the mass in the black hole. The black hole decreases in size, until it simply vanishes and is no longer a black hole. Using some fancy math tricks that the wiki article for Hawking radiation steps through, we have a handy formula to calculate how long this black hole would last. Here it is:

$$t_{ev} = \frac{5120\pi G^{2}M_0^3}{\hbar c^4}$$

where $M_0$ is the mass of the black hole in question. The other variables are the gravitational constant (G), plank's constant ($\hbar$), and the speed of light (c). Your 2.85 solar mass black hole will evaporate in about $1.53220513 * 10^{76}$ seconds. That's a long time from now, about $4.85 * 10^{68}$years. So it isn't going anywhere for a long while.

You black hole would have a temperature of $2.16 * 10^{-8}$ K, which would contrast with the about 3 K background radiation of the universe. It's so small, though, that I doubt we could see it coming. We wouldn't even recognize most of the light being bent around it, since it's so small. We can hardly account for space debris lower than 1cm in diameter.

# Gravity

This is how we're going to detect it. 1 Solar mass is enough to dominate the whole solar system, which is big. Neptune, being the furthest major planet, is a whole 30 AU away! How the black hole approaches us, however, would alter how soon we know about it.

If the black hole was malicious enough to come in directly perpendicular to the plane of the ecliptic, we would see the planets get drawn in and above the sun. We would learn about this as soon as it disturbs celestial objects we're looking at. This could be things like comets, but also planets and moons.

If the black hole came in at different angle, we would notice the solar system getting "sucked" down into it. Did I also mention that, as it sucked stuff in, it would get more massive? It will, and that just speeds the process up. The sun itself is not only the most massive, but much more massive than the rest of the matter we generally consider to be in the solar system.

Gravity is a weak force$^{citation}$$^{needed}$, but works well on large scales. We'll experience a force equal to our sun's gravitational force when the black hole is ~1.688 AU away. It cancels out earth's gravity at ~0.041 AU from the earth. The effect of this black hole's gravity will be noticed far before either of those instances happen.

How quickly the black hole is traveling is important as well. If you want to see how this would work, I suggest finding a planetary body simulator and throwing your massive black hole into it.

• Do you have any specific preference as to which simulator? – JDSweetBeat Mar 13 '15 at 17:57
• @DustinJackson I feel most comfortable making one of my own in Mathematica, and I'm having difficulty finding a 3-D one for free on the internet. There are plenty of 2-d ones, though. Preferably one that you can place you own masses into at varying distances. Such as: labs.minutelabs.io/Chaotic-Planets – PipperChip Mar 13 '15 at 18:27

Based upon a mean earth radius of 3,959 miles, a black hole with an event horizon the size of earth would require a mass of 1080 suns.

If we were REALLY lucky, we might have noticed the gravitic lensing of the stars in night sky, but the odds of that with such a small black hole are very low.

This would be equivalent to a star 1080 times the mass of the sun mucking about with the gravity while interacting with our solar system. Let's assume it affects our orbit once the gravitic pull on us is stronger than that of the sun. The gravity equation (f=G*m1*m2/d^2) tells us that if we multiply m1 by 1080 then d must increase by root(1080)=33 AU to keep f constant. That's just outside the orbit of Neptune. So if it hits us from the side, we might witness the loss of Pluto as a planet for the second time in our lives... :)

I'm going to assume that the black hole isn't moving at an extreme speed relative to our own solar system, and that it comes at us perpendicular to our orbital plane.

While the sun wouldn't suddenly wink out - the event horizon is too small for that - its gasses would be rapidly siphoned off to its new stellar neighbor. The sun is the largest object in our solar system by far, so the force of gravity between it and the black hole is strongest. This is probably the first clear evidence we would have of anything being amiss - sudden warping and offgassing of the Sun.

As these gasses are accelerated toward the event horizon, they would heat up and combust, just like they do on the sun itself. Now we would see major surge in high energy particles like xrays and gamma rays coming from within our neighborhood. Look up pulsars for more info.

Assuming the radiation doesn't strip us of the ionosphere and fry the earth completely, we would be pulled out of orbit by the much heavier black hole. Even if we managed to miss falling into the black hole itself - very likely considering it's relatively small size - we'd probably grab enough momentum to say sayanora to our annual orbit. We'd either follow Haley's comet and start taking trips out to the kuiper belt, or we'd be slingshotted entirely out of the solar system. Either way, say goodbye to the sun!

We'd more than likely die from starvation and darkness rather than earthquakes and event horizons.

• +1 for the loss of pluto for the second time. It's just a dwarf planet now, with new friends like Ceres and Eris. – PipperChip Mar 12 '15 at 18:19