Cfrgtkky

Short: No

Long

Why? (heat)

The sun uses its gigantic mass to fuse hydrogen. If the sun was light enough to orbit the Earth it would not generate enough pressure to start the nuclear fusion.

Can't it burn normally?

No because:

1. You don't have oxygen in/on the sun


2. Burning would only work for a couple of months maybe years.

Why (light/energy)

When the sun doesn't burn/fuse it doesn't create any light and thereby won't light up the world. The moon doesn't receive any light from the sun and so it will also always be dark. Because of the lack of reactions in the small sun it will also not radiate any energy to earth.

Additional Info

Any thing with the same mass as the Sun of our universe wont work because:

1. If the "sun" would be in the proximity stated by the question it would rip the earth apart $F = Gcdot frac{m1 cdot m2}{r^2}$ m1= mass1 and m2 = mass2 G = gravitational constant, r = radius/distance of the two objects F = force.

If we plug our values in (mass of sun mass of earth distance of the moon from earth) we get: $5.367 cdot 10^{27} N$ which is "only" abit more than 100 000 times stronger than in our universe. The problem is because the sun would be more massive the moon would be lost within days. (it would be attracted more by the sun than by the earth)

Yes a white dwarf does fusion but it would be way bigger than a moon, would also rip earth apart and the fusion is not enough to provide energy for any organisms bigger than a centimeter. (if at all)

"Ripping Earth apart"

Upon research I have discovered that the Force of the "sun" may not be enough to rip the earth apart but would be stronger than the gravitational force of the earth which would cause everything not connected with the crust of the earth to fall into the "sun".

Also the hot core of the Earth would melt through the cold crust after a while and so in the end earth would still fall apart. (because of the same reason everything not directly connected with earth would fall of of it)

So, obviously the natural answer is NO.

But what everyone really wants is an answer that is YES!

Because you have a world where you are not going to let facts get in the way of a good story, right? So now we have to look at ways of making this happen. The situation you describe is the Geocentric Conundrum. How to make things work with an Earth-sized planet at the centre of the universe. At least one famous work of fantasy does this; and that work in itself is simply a spiritual descendant of the Flat Earth cosmology, in that a tiny Sun orbits a much larger Earth.

• Naturally tiny Sun: this option is out, as even Jupiter, while warm, is not large enough to begin stellar fusion, unless you posit some form of unobtainium that does what hydrogen does, but at much lower pressures


• 
  

  Artificial Sun: this is going to be your answer, in form or fashion. Essentially, you are going to have some kind of orbital station or platform that generates light and heat for the planet it orbits

  
  
  

  I'd suggest an artificial rig comprising an armillary-like platform of gantries supporting a network of substations that generate an atomic force field. The forcefield allows for hydrogen to be pumped in through inlets at the poles, but enforces a spheroid shape throughout. When the "bag" is full of hydrogen such that the automatic safety on the inlet valves is engaged (the pressure being great enough that the vast pumps can no longer support the back pressure), the forcefield generators squeeze with equal pressure all around, thus driving up the already high pressure within. Stellar fusion is initiated and hey presto! Instant orbiting star.

  
  
  

  The brightness of the light obliterates the gantry rig from view by people on the planet, so all they see is pure & wholesome sunlight!

  
  

In my answers to this question

Day/night cycle science help?1,

and this question

Could this planet exist?2

I discuss factors which could change the relative length of day and night on a planet.

There is a simple geometric reason why normal stars illuminate half of a planet's surface at any one time.

The planet Earth has a diameter of 12,742 kilometers, the Sun has a diameter of 1,391,400 kilometers, 109.19 times as great. So if the Sun and the Earth were touching, the Sun would illuminate a lot more than half of the Earth's surface at any one time. The farther away the Sun was from Earth, the smaller the proportion of Earth's surface it would illuminate at any moment, But even at infinite distance the Sun would still illuminate at least half of the Earth's surface at any one moment.

It is possible for a small white dwarf star or an extremely small red dwarf star to be slightly smaller in diameter than the planet Earth.

But in order to shine they would have to have sufficient density and mass to have many times the mass of the Earth in order to have natural nuclear fusion reactions in their interiors. So even if one could get a red dwarf or a white dwarf small enough to have only the diameter of the Moon, it would still be many times, thousands of times, as massive as the Earth, which in turn is about 81 times as massive as the Moon.

If it was possible to have a shining star that had only the diameter of the moon - and it isn't possible to have a naturally shining star with so small a diameter - it would still have probably at least a hundred thousand times the mass of the Moon and probably be at least a thousand times as massive as the Earth.

So even if a Moon-sized natural star was possible - and it isn't - it would be many times as massive as the Earth, and so the Planet would orbit around the tiny star, not the tiny star around the Planet.

Could any tiny natural star be at the same distance from planet as the Moon is from Earth and yet give that planet the same amount of light and heat as the Sun gives to Earth?

The Sun has an average distance of 149,597,870.7 kilometers from Earth, while the Moon has an average distance of 384,399 kilometers, so the Sun is about 389 times as distant as the Moon. If a star as bright as the Sun was at the distance of the Moon, it would give a planet about 15,000 times as much heat and light as Earth gets from the Sun, and the planet would be many times as hot as Venus or Mercury.

Proxima Centauri is a M5.5V red dwarf star, and is pretty dim for a star. A planet, Proxima Centauri b, has been detected orbiting Proxima Centauri in the habitable zone of Proxima Centauri, at a distance of only about 7,500,000 kilometers and with a day only 11.186 Earth days long.

And even that close orbit is 19.5 times the distance of the Moon from Earth. If a planet was only 384,399 kilometers from Proxima Centauri it would get about 380 times as much radiation as Proxima Centauri b gets and would be hotter than Mercury or Venus.

As far as I know the potentially habitable exoplanet that orbits its star the closest is a planet of TRAPPIST-1, a M8V class star much dimmer than Proxima Centauri. Planet TRAPPIST-1c orbits in the habitable zone only about 2,370,000 kilometers out. But that is still about 6.16 times as far as the Earth-Moon distance, which means that a planet only 384,399 kilometers from TRAPPIST-1 would get about 36 times as much radiation as Earth gets from the Sun.

It is possible that an even more dim natural star could be only about 384,399 kilometers from a planet and give it the same amount of radiation as Earth gets from the Sun.

But that dim natural star would still be about as wide as the Earth and would thus look about four times as large as the Sun and the Moon look from Earth. To make even the smallest possible natural star have the same apparent diameter as the Sun and the Moon, it would have to be moved out to about four times the distance of the Moon, or out to about 1,537,596 kilometers.

And it would be more likely that a natural star could be dim enough to illuminate a planet with only the same amount of radiation as Earth gets from the Sun if that star was at a distance of about 1,537,596 kilometers as it would be if the star was at a distance of 384,399 kilometers.

But that star wouldn't have the diameter or mass of the Moon, it would have about the diameter of the Earth and thousands of times the mass of the Earth. And it wouldn't be at the distance of the Moon.

So IMHO it is almost certain that even if such a dim natural star is possible, it wouldn't satisfy any of your requirements exactly. Though perhaps expert astrophysicists might know of a dim enough star, the diameter and mass requirements seem totally impossible for any kind of a natural star.

Therefore, either you change your requirements or else you need a giant artificial satellite of your planet that has power generation and countless giant lamps.

This artificial "star" or "sun" would be a vast artificial satellite orbiting the planet and containing countless vast fusion power generators that power countless lamps on the surface of the satellite pointed toward the planet and illuminating and heating the planet.

Day/night cycle science help?1

No.

At the moons size it would not be a nuclear furnace, it would just be a ball of gas. The mass of the sun is needed. So if Jupiter (also a ball of gas), had the mass of the Sun it would also be a Sun, but since it doesn't, it's just a ball of gas.

Other answers have explained that our sun's simple design would not work if scaled down to the size of the moon.

Our sun's design is: pile enough hydrogen and helium together that the pressure at the center is so hot that you fuse hydrogen to make helium. The waste heat from this nuclear reaction eventually gets to the surface, where the surface' plasma releases black-body radiation at 5,500°C.

But it is conceivable to design a moon-sized replacement for the sun, in lunar orbit. You would need to come up with a way to contain 5,500°C hydrogen-helium plasma on the surface of the lamp that faced the Earth. You would want to aim most of the output of the lamp towards the Earth, because this reduces the power output needed by a factor of 2,200,000,000. Our sun has about 64,000,000 times the volume of our moon, so there would be enough room to store enough fuel for the lamp to match our sun's lifespan.

You would need to build quite a few large fusion reactors on the "dark side" of the lamp to power the plasma devices that produce the light. Specifically, you would need the equivalent of 175 million 1 GW (GigaWatt) fusion reactors, or about 20 reactors per square kilometer of lamp. You would need to build storage systems for a large amount of hydrogen. (You might choose to use hydrogen compounds instead of molecular hydrogen. Green cheese would work.) You would need to build a substantial heat radiator to disperse waste heat. And of course, you would need a substantial structure to hold the whole thing together as it rotates once per month to keep the lamp facing the Earth.

Yes. Except.

(Note: This answer presumes that the distance to the sun remains constant between our world and your work.)

Glossing over how this would happen, the strength of the sun's gravitational field is related to its mass, not its volume. Sticking with Newtonian physics, the strength of gravity is:

F = GMm/r^2

where

G:= Gravitational constant

M:= greater mass

m:= lesser mass

r:= radius, or distance between m and M

You'll note that nowhere in there is volume. With fixed r, the Earth would still orbit the sun every 365 days. Things would continue as normal.
However, there's still the exception part.

Strictly speaking, after a star is compressed below a certain radius, it collapses into a black hole, as near-range light can no longer escape it. I did a quick calculation and determined the hypothetical Swartzchild radius of the sun to be roughly 3000 km. That's about 400 km too low. So, at this point, the sun would not emit any light whatsoever. Near-range gravitational attraction, which is normally canceled out by attraction from "higher" matter, would be so strong that light could not escape it.
This doesn't actually mean that Earth's orbit would be compromised, but the luminous output of the sun would be flat-out missing. Sounds bad, right?

Even if it didn't collapse completely, it would likely form a neutron star, which would completely scramble the light emissions. But, that's a bit off topic.

Of course, aside from that conundrum, it would be reasonable to consider how it is that that much mass could actually collapse to the size of the moon. Fusion convection does a pretty predictable job at keeping stars of a set mass at a set size. This wouldn't ever actually happen in our universe, as we know it.

I leave that to you, though.

One thing you might want to look up is black dwarf stars. None of them exist yet (the universe just hasn't been around for long enough, even distantly), but they're roughly the size of Earth and are what happens when a star burns out, but lacks the mass to form a neutron star or black hole.

Good luck!

Yes it is absolutely possible; despite that other answerers insisting that the sun wouldn't work scaled down, it does; as long as you scale up what they fuse. - What you're asking about is called a "white dwarf". Read more here:
https://en.wikipedia.org/wiki/White_dwarf

It has mass comparable to that of our sun; meaning that we'd either be spinning around it in a fraction of the time, or we'd be similar distance.

It has volume comparable to that of Earth (which isn't THAT far off the size of our moon)

It is a star near the end of its life, and is no longer fusing hydrogen or helium, but carbon and oxygen (not burning them, fusing them). The star is very hot internally during this time, but the luminosity is low because of it's small size.

This might allow the planet near it to not end up looking like Mercury or Venus.

The big issue of can it have a moon - well, that you can't have - because you already have something at similar distance. In all likelyhood, that moon will have hit the sun.

If you change the way stars work, then yes.

The sun and the moon are almost the same size as viewed from Earth. If the surface of the moon was as hot as the surface of the sun and we had no other sun, Earth would receive close enough to the same amount of radiative energy as we do currently.

If you move the moon-sun twice as far away, it would have to have a surface area fours times its previous area to occupy the same amount of sky. The inverse square law means the planet would receive the same amount of energy (four times as much energy at one quarter the strength).

$$ a = (C d)^2 $$
$$ E = {a over d^2} $$
$$ E = C^2 $$

$a$ is the area of the moon-sun, $C$ is a constant multiplier (not $c$, the speed of light), $d$ is the distance between the moon-sun and the planet, and $E$ is the amount of energy received by the planet. As you can see, the area and distance exactly cancel each other out, leaving just the amount of sky taken up and the temperature.

So, if you want to come up with some way that a very small sun (maybe with the same mass as our sun, maybe less or more) can have a surface temperature the same as our own sun for billions of years, then yes, you can do it. You just have to sell the concept to your audience so they can suspend their disbelief.

Fission moon.

Prior answers establish that you need stellar-scale masses to sustain fusion. But not fission. I put forth the idea of a fission powered radiant moon here. It could serve as a star with the size and distance of a moon.

Can a fission satellite duplicate the radiance frequencies of a star?

and there is a bunch more discussion of the concept here
http://forums.xkcd.com/viewtopic.php?t=111216

This would be a moon sized object containing a lot of fissile material - uranium, plutonium, thorium etc. The XKCD forum establishes that at star size, this would explode with an enormous energy output, so it cannot be anywhere near that big. The object needs to be the size of the moon (or smaller?) and larded with a lot of stuff that does not participate in fission - iron, perhaps. Compressed in the core to criticality, the fissile elements do their thing. Fission heats the metal moon to blackbody glowing and there is your star equivalent.

The problem is that the fission accelerates. Maybe it is perfectly balanced with the iron so it doesn't but probably the heaviest stuff migrates to the core and so the mix would stratify. The best conjecture I thought was the "sputter" moon. The fission accelerates, getting the reaction core (and the entire moon) hotter and hotter and eventually gets so hot that it explodes. The moon increases in size and as it does, the fissile elements are spread from each other. The fission peters out. The moon falls back into itself, mixing back up as it cools. But as the fissile elements get close to each other, the fission starts back up.

This would produce a lunar cycle of smaller and brighter then larger and cooler.

It really all depends on which laws of physics you want to obey and which ones you want to ignore. If you are willing to accept special laws of physics working in the interior of the sun to produce the heat, but you want basic optics and thermodynamics to work correctly, then I think the answer is yes. The radiant heat you get from something basically depends on its temperature and the spherical angle it takes up from wherever you are. This is why forest fires can burn people even when they are standing pretty far away from them.

Since the Moon takes up the same area of sky as the Sun, if the Moon were radiating with the exact same energy spectrum as the Sun, it would heat the Earth in pretty much the same way. Someone else mentioned that, because the Moon is closer, it wouldn't be visible from as much of the Earth at once, but that is a small effect.

If you really want some plausible explanation of how there could be a Moon-sized body radiating like the Sun, that's a lot harder. But sometimes you are willing to postulate one crazy thing and you want to get the rest correct, and I think a Sun-hot Moon would heat the Earth just fine.

The first thing I thought of was a White Dwarf; they could actually be cool enough not to cook the Earth, while holding onto their heat for long enough for live to evolve.

Sadly, ut they max out at 1.44 solar masses (and get smaller the heavier they are). A typical white dwarf is the radius of the Earth, 4 times too big.

Neutron Stars are much smaller than White Dwarves, but they are too small for your needs. They also weigh multiple solar masses. They radiate energy, but usually in really a really harsh spectrum.

You'd think that "less white dwarf" would work, but white dwarves with less mass don't get smaller, they get larger as the gravitational attraction pulling them together gets weaker.

There isn't anything really stable between a white dwarf and a neutron star; white dwarfs, when you add matter, just nova (not supernova), and if you pass the limit at construction time they supernova into a neutron star. And even if there was, a solar+ mass object that close to the Earth would tear it apart; the Roche limit of something solar mass is 700,000 km, twice the distance to Earth's moon.

Now, the moon has a volume of 22 billion km^3. If made out of a heavy element (like uranium), that gives it a mass of 10^23 kg. Such an object wouldn't tear the Earth apart.

You'd have to extremely carefully pick the blend of isotopes, but you might be able to build a fission nuclear reactor that would run for a few billion years.

The reactor would glow with thermal heat; odds are most of the radiation would be in its core. It gets really tricky trying to ensure that it has enough heat to glow white-hot and maintain it for the duration we are talking about, while relying on fission, and never blowing itself apart as concentrations of various isotopes and elements vary.

Such a structure could never occur naturally, and it would be a megaproject for even a T2-3 civilization.