<p>Let's try a crude back of the envelope calculation to get orders of magntitude:</p>

<p>The tidal force near the event horizon is of the order of <span class="math-container">$G M/r^3$</span> which is something like <span class="math-container">$10^{18} g/m$</span>. So a probe with a mass of 1 gram and diameter of 1cm would experience about <span class="math-container">$10^{12} N$</span> of force trying to "spaghettify" it by accelerating ends of it at about <span class="math-container">$10^{16} g$</span> relative to the centre. If it experienced that force for a time <span class="math-container">$t$</span> the ends would likely move about <span class="math-container">$10^{17} t^2 m$</span> relative to the centre, assuming <span class="math-container">$t$</span> is short enough that relavity does not complicate things, so if we want to limit that to say 1mm we need <span class="math-container">$t &lt; 10^{-10}$</span>. So basically we want the probe to go from a few Schwarzchild radii down to 1 in about 100ps in its internal time frame, so that the tidal forces do not have time to tear it apart. Using the Newtonian approximation this is a few times faster than the speed of light, so what we learn is that the probe must be going at relativistic velocities, to have a chance of surviving. From its perspective, that flattens out the gravitational field around the black hole in the direction of travel, so that the tidal force seems to even briefer in duration. </p>

CC BY-SA 4.0
2020-02-13T14:11:27.220Z
Does it mean that there's no realistic chance to send a probe into the black hole without the probe being ripped apart?
user30007
CC BY-SA 4.0
2020-02-13T16:06:05.527Z
@user30007 What do you call realistic? You would somehow need to fire the probe in at quite close to light-speed, but there is no law of physics which says you can't do that. 

Also, how do you tell? Once the probe is inside the event horizon you will never hear from it again.
Steve Linton
CC BY-SA 4.0
2020-02-13T16:10:17.857Z
You know what I mean. I said "no realistic", not "no possible chance". Even the Breakthrough Starshot probe doesn't go at 0.95c or something. But how can such a small black hole tear the probe so easily apart? I thought that about 11 miles/second (about the speed of Voyager 1) would be enough for the probe to survive.
user30007
CC BY-SA 4.0
2020-02-13T16:29:54.957Z
The smaller the black hole, the more intense the tidal forces. A 12 billion solar mass black hole with a radius  of  35 billion km  would have tidal forces around $10^{-12} gm^{-1}$. The gravity is strong but applies to the whole probe uniformly. For a tiny black hole, one end of the probe is much closer to the black hole than the other
Steve Linton
CC BY-SA 4.0
2020-02-13T16:43:49.037Z
But 11 mi/sec is extremely fast. I can't understand how such a speed isn't enough to prevent being torn apart.
user30007
CC BY-SA 4.0
2020-02-13T17:11:17.387Z
@user30007 at that speed the probe would be within a couple of scarily radii of the black hole for about 10 microseconds. During that time the front is accelerating into the black hole about 100 thousand million million gravities faster than the back.
Steve Linton
CC BY-SA 4.0
2020-02-13T18:46:17.863Z
Whoa, black holes are not to be underestimated!
user30007
CC BY-SA 4.0
2020-02-13T13:58:35.010Z
2020-02-13T13:58:35.010Z
Steve Linton
<p>If there really is a primordial black hole beyond the Kuiper belt, we can send a probe to the black hole and into it. But how fast must the probe be in order to enter the black hole without being ripped apart by spaghettification? The black hole in question has an event horizon diameter of 2-3 inches and 5-15 Earth masses so it is a tiny probe (tiny enough cameras <em>do</em> exist) we would have to launch. Let's say the probe is 1.5 inches broad and has a length of 2.5 inches. How fast must it be in order to not be torn apart and successfully enter the black hole?</p>

CC BY-SA 4.0
2020-02-13T14:39:25.550Z
What's the point of sending a probe into a black hole? Even if your probe survives for a few microseconds it cannot send any data back across the event horizon.
PM 2Ring
CC BY-SA 4.0
2020-02-13T14:51:38.417Z
BTW, a black hole of that size has a mass around 4.5 Earth masses, and a test particle falls from the event horizon to the centre in about 0.2 nanoseconds. Its Hawking temperature is almost 4.6 millikelvin, with a luminosity of $4.9\times10^{-19}$ watts - not exactly easy to see. ;)
PM 2Ring
CC BY-SA 4.0
2020-02-13T14:53:07.357Z
Also, for a distant observer who is not also falling to cross the event horizon, the probe takes infinite time to reach the event horizon.
notovny
CC BY-SA 4.0
2020-02-13T15:12:09.383Z
@PM2Ring and notovny: First, we don't know what's in the center and if there is something like that at all. Second, there are uncountable reasons why we should send a probe to the black hole and also to try to send it into it. Third, we could send two probes: an orbiter and an impactor (similar to Cassini-Huygens) where the orbiter would observe from outside what the impactor looks like when falling into the black hole.
user30007
CC BY-SA 4.0
2020-02-13T15:39:44.853Z
Sure, we don't know if there's really a singularity at the centre of a BH - we need a quantum gravity theory to handle questions like that. Which is why I carefully said "centre" and not "singularity". ;) But standard GR is perfectly adequate to discuss what happens outside the event horizon, and it's also correct inside the event horizon, as long as you avoid the very centre of the BH. No light or other information (including gravitational signals) can come from inside the horizon, and a quantum gravity theory won't change that.
PM 2Ring
CC BY-SA 4.0
2020-02-13T16:04:39.647Z
@PM2Ring But the impactor probe would anyway transfer data until it would reach the event horizon. The orbiter would watch it (and could film it) from outside. The orbiter also might study any possible planets orbiting the black hole (or rule them out) and much more.
user30007
CC BY-SA 4.0
2020-02-13T16:15:23.120Z
Yeah, ok. But you're going to have a hard time navigating to your mini black hole, since it's invisible unless it's accreting stuff. Flying by gravity alone isn't easy!
PM 2Ring
CC BY-SA 4.0
2020-02-13T16:18:58.590Z
@PM2Ring Yeah, but once we discover it, we will know its precise orbit. So it's just a matter of its orbit. Just like it was predicted when and where the Voyager probes would encounter the planets and use their gravity to fly faster.
user30007
CC BY-SA 4.0
2020-02-13T16:28:35.327Z
The difference is that we can see the planets. OTOH, Neptune was discovered by its gravitational perturbation on the orbit of Uranus, so finding your black hole (if it exists) isn't impossible, just very difficult. And even with Neptune, it took careful telescope work to find its actual location, the gravity calculations just determined the general area (although admittedly they had to do all the calculations by hand back then, and they didn't know the planet masses and orbits as precisely as we do these days).
PM 2Ring
CC BY-SA 4.0
2020-02-13T16:45:47.760Z
@PM2Ring As I said, once we discover it. We first have to find it and it may not exist or may be a planet.
user30007
<black-hole><speed><space-travel>
How fast does a spacecraft have to be to enter a primordial black hole without being torn apart?
user30007
# How fast does a spacecraft have to be to enter a primordial black hole without being torn apart?

(Asked by: username_0 on 2020-02-13)

If there really is a primordial black hole beyond the Kuiper belt, we can send a probe to the black hole and into it. But how fast must the probe be in order to enter the black hole without being ripped apart by spaghettification? The black hole in question has an event horizon diameter of 2-3 inches and 5-15 Earth masses so it is a tiny probe (tiny enough cameras *do* exist) we would have to launch. Let's say the probe is 1.5 inches broad and has a length of 2.5 inches. How fast must it be in order to not be torn apart and successfully enter the black hole?

**Tags:** black-hole, speed, space-travel

> **Comments:**
> **username_1**: What's the point of sending a probe into a black hole? Even if your probe survives for a few microseconds it cannot send any data back across the event horizon.  
> **username_1**: BTW, a black hole of that size has a mass around 4.5 Earth masses, and a test particle falls from the event horizon to the centre in about 0.2 nanoseconds. Its Hawking temperature is almost 4.6 millikelvin, with a luminosity of $4.9\times10^{-19}$ watts - not exactly easy to see. ;)  
> **username_2**: Also, for a distant observer who is not also falling to cross the event horizon, the probe takes infinite time to reach the event horizon.  
> **username_0**: @PM2Ring and username_2: First, we don't know what's in the center and if there is something like that at all. Second, there are uncountable reasons why we should send a probe to the black hole and also to try to send it into it. Third, we could send two probes: an orbiter and an impactor (similar to Cassini-Huygens) where the orbiter would observe from outside what the impactor looks like when falling into the black hole.  
> **username_1**: Sure, we don't know if there's really a singularity at the centre of a BH - we need a quantum gravity theory to handle questions like that. Which is why I carefully said "centre" and not "singularity". ;) But standard GR is perfectly adequate to discuss what happens outside the event horizon, and it's also correct inside the event horizon, as long as you avoid the very centre of the BH. No light or other information (including gravitational signals) can come from inside the horizon, and a quantum gravity theory won't change that.  
> **username_0**: @PM2Ring But the impactor probe would anyway transfer data until it would reach the event horizon. The orbiter would watch it (and could film it) from outside. The orbiter also might study any possible planets orbiting the black hole (or rule them out) and much more.  
> **username_1**: Yeah, ok. But you're going to have a hard time navigating to your mini black hole, since it's invisible unless it's accreting stuff. Flying by gravity alone isn't easy!  
> **username_0**: @PM2Ring Yeah, but once we discover it, we will know its precise orbit. So it's just a matter of its orbit. Just like it was predicted when and where the Voyager probes would encounter the planets and use their gravity to fly faster.  
> **username_1**: The difference is that we can see the planets. OTOH, Neptune was discovered by its gravitational perturbation on the orbit of Uranus, so finding your black hole (if it exists) isn't impossible, just very difficult. And even with Neptune, it took careful telescope work to find its actual location, the gravity calculations just determined the general area (although admittedly they had to do all the calculations by hand back then, and they didn't know the planet masses and orbits as precisely as we do these days).  
> **username_0**: @PM2Ring As I said, once we discover it. We first have to find it and it may not exist or may be a planet.  

---

## 1 answers

### Answer by username_3 on 2020-02-13. Score: 2 | Accepted answer

Let's try a crude back of the envelope calculation to get orders of magntitude:

The tidal force near the event horizon is of the order of $G M/r^3$ which is something like $10^{18} g/m$. So a probe with a mass of 1 gram and diameter of 1cm would experience about $10^{12} N$ of force trying to "spaghettify" it by accelerating ends of it at about $10^{16} g$ relative to the centre. If it experienced that force for a time $t$ the ends would likely move about $10^{17} t^2 m$ relative to the centre, assuming $t$ is short enough that relavity does not complicate things, so if we want to limit that to say 1mm we need $t < 10^{-10}$. So basically we want the probe to go from a few Schwarzchild radii down to 1 in about 100ps in its internal time frame, so that the tidal forces do not have time to tear it apart. Using the Newtonian approximation this is a few times faster than the speed of light, so what we learn is that the probe must be going at relativistic velocities, to have a chance of surviving. From its perspective, that flattens out the gravitational field around the black hole in the direction of travel, so that the tidal force seems to even briefer in duration.

> **Comments:**
> **username_0**: Does it mean that there's no realistic chance to send a probe into the black hole without the probe being ripped apart?  
> **username_3**: @username_0 What do you call realistic? You would somehow need to fire the probe in at quite close to light-speed, but there is no law of physics which says you can't do that.   Also, how do you tell? Once the probe is inside the event horizon you will never hear from it again.  
> **username_0**: You know what I mean. I said "no realistic", not "no possible chance". Even the Breakthrough Starshot probe doesn't go at 0.95c or something. But how can such a small black hole tear the probe so easily apart? I thought that about 11 miles/second (about the speed of Voyager 1) would be enough for the probe to survive.  
> **username_3**: The smaller the black hole, the more intense the tidal forces. A 12 billion solar mass black hole with a radius  of  35 billion km  would have tidal forces around $10^{-12} gm^{-1}$. The gravity is strong but applies to the whole probe uniformly. For a tiny black hole, one end of the probe is much closer to the black hole than the other  
> **username_0**: But 11 mi/sec is extremely fast. I can't understand how such a speed isn't enough to prevent being torn apart.  
> **username_3**: @username_0 at that speed the probe would be within a couple of scarily radii of the black hole for about 10 microseconds. During that time the front is accelerating into the black hole about 100 thousand million million gravities faster than the back.  
> **username_0**: Whoa, black holes are not to be underestimated!  

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