# Black Hole Math Question **URL:** \ **Category:** Factual Questions\ **Created:** [October 26, 2020, 9:54pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977 "2020-10-26T21:54:56Z")\ **Posts on this page:** 15\ **Page:** 2
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [October 28, 2020, 2:25pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/21 "2020-10-28T14:25:16Z")
> [@eburacum\_45](#): > > I can’t imagine how you’d keep an atmosphere on an object from escaping using a magnetic field. You’d have to ionise the outermost layer somehow, as neutral molecular oxygen and nitrogen would not be affected by the flux So – on Earth, gravity is sufficient to keep our air down for the most part; without our magnetic fields, photons would over time strip away our atmosphere because when a molecule of atmosphere is at the very top of its natural trajectory, it can get hit by a photon gaining enough energy to escape. But on a much smaller world, the problem wouldn’t be photons from the sun that can be kept away with magnets - the problem would be that there just isn’t enough gravity to keep the air molecules from escaping under their own power as they bounce off each other like molecules in a gas do. Is that about right? ---
**Author:** ![eburacum\_45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eburacum_45/32/3385_2.png) [@eburacum\_45](https://boards.straightdope.com/u/eburacum_45)\ **Post date:** [October 28, 2020, 2:52pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/22 "2020-10-28T14:52:51Z")
Not really; our magnetic field protects us against protons from the Sun, not photons. A magnetic field around an artificial world would do the same, but this would be a tiny effect compared to the rapid loss from a tiny artificial suprahole. ---
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [October 28, 2020, 4:21pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/23 "2020-10-28T16:21:33Z")
> [@eburacum\_45](#): > > Not really; our magnetic field protects us against protons from the Sun, not photons. 🤦‍♂️ doh. I USUALLY know what Solar Wind is made of. > [@eburacum\_45](#): > > A magnetic field around an artificial world would do the same, but this would be a tiny effect compared to the rapid loss from a tiny artificial suprahole. This bit is what I meant to ask - so the solar wind atmosphere stripping pales in comparison to losses from just having too small a gravity well. ---
**Author:** ![dtilque](https://avatars.discourse-cdn.com/v4/letter/d/d6d6ee/32.png) [@dtilque](https://boards.straightdope.com/u/dtilque)\ **Post date:** [October 28, 2020, 4:51pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/24 "2020-10-28T16:51:35Z")
> [@Babale](#): > > This bit is what I meant to ask - so the solar wind atmosphere stripping pales in comparison to losses from just having too small a gravity well. Definitely. The atmosphere loss from the solar wind that a planet experiences is a very long term thing, not something that’s going to happen immediately. Think about it. The solar wind is very diffuse, basically a vacuum in terms of density. So its short term effects are very slight. It’s only when you add up those small effects over a long time (as in tens or hundreds of millions of years) does it make a significant effect. The loss from a weak gravitational field is going to be lots faster than that. ---
**Author:** ![DesertDog](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/desertdog/32/11503_2.png) [@DesertDog](https://boards.straightdope.com/u/DesertDog)\ **Post date:** [October 28, 2020, 5:11pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/25 "2020-10-28T17:11:38Z")
> [@Chronos](#): > > Yeah, the thing with black holes is, they’re weird, but they’re not really all that weird. Their gravity follows the same rules as everything else’s. True. If the sun were to be replaced by a solar-mass black hole. the Earth would continue to orbit it as if nothing had happened. The freezing-solid thing would be kind of worrisome… ---
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [October 28, 2020, 5:22pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/26 "2020-10-28T17:22:20Z")
> [@dtilque](#): > > Definitely. The atmosphere loss from the solar wind that a planet experiences is a very long term thing, not something that’s going to happen immediately. Think about it. The solar wind is very diffuse, basically a vacuum in terms of density. So its short term effects are very slight. It’s only when you add up those small effects over a long time (as in tens or hundreds of millions of years) does it make a significant effect. The loss from a weak gravitational field is going to be lots faster than that. This all makes sense – however you don’t need to go quote as big as Earth is for a breathable atmosphere, right? For example Venus is smaller but has a much thicker atmosphere. The problem is that because we’re getting earthlike gravity around a smaller body by condensing it and hanging out closer to the center of mass, we have a steeper but smaller gravity well that’s easier to escape since it falls off more rapidly with altitude. So, what’s the smallest we can go while maintaining a breathable atmosphere with no domes or shells – assuming we can use magnetic fields to deal with solar wind, so gravity losses are all we need to counter? ---
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [October 28, 2020, 5:31pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/27 "2020-10-28T17:31:50Z")
Too late to edit, but: Can we go moon sized for our black hole? Our moon squashed to a black hole and with an artificial surface at a radius that gives earth gravity at the surface, according to the calculator, would be a body with a radius of 400 miles, or around 650 km - so roughly comparable to Charon, which has a surface area of 4.6X10^6 KM, or 4,600,000 KM, giving us an area between the size of India to Australia to work with. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [October 28, 2020, 9:52pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/28 "2020-10-28T21:52:56Z")
> [@Folly](#): > > I’m a little confused. How is there heat given off? Is it Hawking radiation? Would it be safe? It’s Hawking radiation. It would heat the inside surface of the planetoid, keeping it at a reasonable temperature. It’s not safe–by my math, it’s emitting gamma radiation with a peak energy of 3.7 MeV. I think that might be small enough that a few meters of lead could bring it down to safe-ish levels, but I couldn’t say for sure. Do not look directly at the black hole, in any case. ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [October 28, 2020, 10:18pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/29 "2020-10-28T22:18:41Z")
Weird to think about a “black” hole glowing red hot, or even blue… ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [October 28, 2020, 11:40pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/30 "2020-10-28T23:40:26Z")
“Blue” is a very optimistic way of thinking about high energy gamma rays. Though it’s true that the black hole would look blue until it blinded you, due to the nature of blackbody emission. ---
**Author:** ![Folly](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/folly/32/3219_2.png) [@Folly](https://boards.straightdope.com/u/Folly)\ **Post date:** [October 29, 2020, 12:14am UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/31 "2020-10-29T00:14:09Z")
I was thinking about whatever size it would have to be to actually be blue. But then, i guess it would be too small to actually see any light anyway? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [October 29, 2020, 12:42am UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/32 "2020-10-29T00:42:27Z")
You should be able to see it just fine–stars are visible despite their being virtually point sources. And it would be an extremely intense light. I’m not really sure of the exact effect, but the only way you’re not seeing it is if it blinded you immediately. That shouldn’t be an issue if you’re standing very far away. And maybe behind several meters of leaded glass to block the gamma rays. ---
**Author:** ![eburacum\_45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eburacum_45/32/3385_2.png) [@eburacum\_45](https://boards.straightdope.com/u/eburacum_45)\ **Post date:** [October 29, 2020, 10:28am UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/33 "2020-10-29T10:28:03Z")
> [@Babale](#): > > Can we go moon sized for our black hole? Our moon squashed to a black hole and with an artificial surface at a radius that gives earth gravity at the surface, according to the calculator, would be a body with a radius of 400 miles, Well, an artificial planet with a radius of 400 miles and 1 Earth gravity at the surface could have an atmosphere about 200 miles thick- but the gravity at the top of that atmosphere would be about half that at the surface. That means the atmosphere would be lost more rapidly than on Earth, but less rapidly than on Mars; you could probably get away with it for a while. Trouble is, any gas that passes the 200 mile level would wander into a region with even lower gravity, so you would lose atmosphere pretty steadily. Best to put an atmosphere roof over the surface. > **[Paraterraforming](https://terraforming.fandom.com/wiki/Paraterraforming)** > > Paraterraforming (also known as the "worldhouse" concept or domes in smaller versions) involves the construction of a habitable enclosure on a planet which eventually grows to encompass most of the planet's usable area. The enclosure would consist of... ---
**Author:** ![Quercus](https://avatars.discourse-cdn.com/v4/letter/q/7ab992/32.png) [@Quercus](https://boards.straightdope.com/u/Quercus)\ **Post date:** [October 29, 2020, 1:28pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/34 "2020-10-29T13:28:30Z")
> [@eburacum\_45](#): > > Well, an artificial planet with a radius of 400 miles and 1 Earth gravity at the surface could have an atmosphere about 200 miles thick- but the gravity at the top of that atmosphere would be about half that at the surface. What would the air pressure be at the surface with that atmosphere? With the quicker drop off in gravity, you’d need a thicker atmosphere than Earth’s to get the same pressure. And an atmosphere that only gives you the air pressure of the Everest Death Zone probably isn’t useful enough to be worth the bother. ---
**Author:** ![Babale](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/babale/32/15666_2.png) [@Babale](https://boards.straightdope.com/u/Babale)\ **Post date:** [October 29, 2020, 1:51pm UTC](https://boards.straightdope.com/t/black-hole-math-question/923977/35 "2020-10-29T13:51:04Z")
> [@Quercus](#): > > What would the air pressure be at the surface with that atmosphere? With the quicker drop off in gravity, you’d need a thicker atmosphere than Earth’s to get the same pressure. And an atmosphere that only gives you the air pressure of the Everest Death Zone probably isn’t useful enough to be worth the bother This would definitely be an issue. Would there be any way to mess with the atmospheric composition to increase pressure, maybe? Or would you end up with a choking layer of your denser gas, with everything breathable floating on top/escaping? Eta: but overall a dome is definitely the easier solution here. [Previous page](https://boards.straightdope.com/t/black-hole-math-question/923977.md?page=1)