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###Summary version: So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow (but sturdy) unobtanium sphere with a radius about 1 AU. The sphere has an intermediate sized singularity at the core providing gravity of $1~g$ at sphere surface.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light both equatorial and in my polar regions. How do I get it, without further liberal use of unobtanium?

###Full Description

So I've been toying with the idea of a large Niven-like world. I don't like rings however. So instead, in an act of cosmic vandalism, I've handwaved in a hollow unobtanium sphere, using its frankly unbelievable compressive strength to effortlessly resist collapsing under $1~g$ of acceleration from a bikini-clad singularity at the center of the sphere, massing a moderate $1665~M_{☉}$ (solar masses). To make it more fun, my land, seas, tectonic simulators, dinosaur bone planters and other such-stuff is on the outside of the sphere.

This spares them from withering under the gaze of the bikini-singularity (for it is written that none shall see a near-naked singularity and live).

However, it does bring up the rather annoying question of providing adequate lighting for my inhabitants. First, however, a bit about the sizes we're talking about.

Let there be: $$g=G\frac{M}{r^{2}}$$

where
$g$ - local ("surface") gravitational field
$G$ - gravitational constant
$M$ - mass of another body
$r$ - distance from another body

$G=6.67428 \cdot 10^{-11}~\text{N}\left(\frac{\text{m}}{\text{kg}}\right)^{2}$
$M = 1,665~M_{☉}=3.33 \cdot 10^{33}~\text{kg}$ - our constructors like the number 3.

Solving for $g = 9.8~\frac{\text{m}}{\text{s}^{2}}$

We get $r=1.50 \cdot 10^{11}~\text{m}$, which suspiciously conveniently is right about 1 astronomical unit (i.e Sun-Earth distance).

So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow unobtanium sphere with a radius about 1 AU.

Now, I'm ok with the polar regions being a bit dark, but I don't want them in eternal darkness either, as it tends to do nasty things to my sphere's vapor circulation (think 60 mile glaciers). To provide lighting, I'll have a series of planets (I'm thinking somewhere in the range of Jupiter to Brown dwarf in size), which contain sufficient artificial fusion burners to provide day-like illumination.

I was thinking about having them in a nice Klemperer rosette (circling about sharing an orbit, with my burners causing occasional flaring to maintain orbits) like thus (not to scale, obviously):

But assuming they're on the black-hole equatorial plane, this leaves my polar regions depressingly dark.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light in my polar regions. How do I get it, without further liberal use of unobtanium?

Summary version:

So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow (but sturdy) unobtanium sphere with a radius about 1 AU. The sphere has an intermediate sized singularity at the core providing gravity of $1~g$ at sphere surface.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light both equatorial and in my polar regions. How do I get it, without further liberal use of unobtanium?

Full Description

So I've been toying with the idea of a large Niven-like world. I don't like rings however. So instead, in an act of cosmic vandalism, I've handwaved in a hollow unobtanium sphere, using its frankly unbelievable compressive strength to effortlessly resist collapsing under $1~g$ of acceleration from a bikini-clad singularity at the center of the sphere, massing a moderate $1665~M_{☉}$ (solar masses). To make it more fun, my land, seas, tectonic simulators, dinosaur bone planters and other such-stuff is on the outside of the sphere.

This spares them from withering under the gaze of the bikini-singularity (for it is written that none shall see a near-naked singularity and live).

However, it does bring up the rather annoying question of providing adequate lighting for my inhabitants. First, however, a bit about the sizes we're talking about.

Let there be: $$g=G\frac{M}{r^{2}}$$

where
$g$ - local ("surface") gravitational field
$G$ - gravitational constant
$M$ - mass of another body
$r$ - distance from another body

$G=6.67428 \cdot 10^{-11}~\text{N}\left(\frac{\text{m}}{\text{kg}}\right)^{2}$
$M = 1,665~M_{☉}=3.33 \cdot 10^{33}~\text{kg}$ - our constructors like the number 3.

Solving for $g = 9.8~\frac{\text{m}}{\text{s}^{2}}$

We get $r=1.50 \cdot 10^{11}~\text{m}$, which suspiciously conveniently is right about 1 astronomical unit (i.e Sun-Earth distance).

So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow unobtanium sphere with a radius about 1 AU.

Now, I'm ok with the polar regions being a bit dark, but I don't want them in eternal darkness either, as it tends to do nasty things to my sphere's vapor circulation (think 60 mile glaciers). To provide lighting, I'll have a series of planets (I'm thinking somewhere in the range of Jupiter to Brown dwarf in size), which contain sufficient artificial fusion burners to provide day-like illumination.

I was thinking about having them in a nice Klemperer rosette (circling about sharing an orbit, with my burners causing occasional flaring to maintain orbits) like thus (not to scale, obviously):

But assuming they're on the black-hole equatorial plane, this leaves my polar regions depressingly dark.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light in my polar regions. How do I get it, without further liberal use of unobtanium?

###Summary version: So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow (but sturdy) unobtanium sphere with a radius about 1 AU. The sphere has an intermediate sized singularity at the core providing gravity of $1~g$ at sphere surface.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light both equatorial and in my polar regions. How do I get it, without further liberal use of unobtanium?

###Full Description

So I've been toying with the idea of a large Niven-like world. I don't like rings however. So instead, in an act of cosmic vandalism, I've handwaved in a hollow unobtanium sphere, using its frankly unbelievable compressive strength to effortlessly resist collapsing under $1~g$ of acceleration from a bikini-clad singularity at the center of the sphere, massing a moderate $1665~M_{☉}$ (solar masses). To make it more fun, my land, seas, tectonic simulators, dinosaur bone planters and other such-stuff is on the outside of the sphere.

This spares them from withering under the gaze of the bikini-singularity (for it is written that none shall see a near-naked singularity and live).

However, it does bring up the rather annoying question of providing adequate lighting for my inhabitants. First, however, a bit about the sizes we're talking about.

Let there be: $$g=G\frac{M}{r^{2}}$$

where
$g$ - local ("surface") gravitational field
$G$ - gravitational constant
$M$ - mass of another body
$r$ - distance from another body

$G=6.67428 \cdot 10^{-11}~\text{N}\left(\frac{\text{m}}{\text{kg}}\right)^{2}$
$M = 1,665~M_{☉}=3.33 \cdot 10^{33}~\text{kg}$ - our constructors like the number 3.

Solving for $g = 9.8~\frac{\text{m}}{\text{s}^{2}}$

We get $r=1.50 \cdot 10^{11}~\text{m}$, which suspiciously conveniently is right about 1 astronomical unit (i.e Sun-Earth distance).

So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow unobtanium sphere with a radius about 1 AU.

Now, I'm ok with the polar regions being a bit dark, but I don't want them in eternal darkness either, as it tends to do nasty things to my sphere's vapor circulation (think 60 mile glaciers). To provide lighting, I'll have a series of planets (I'm thinking somewhere in the range of Jupiter to Brown dwarf in size), which contain sufficient artificial fusion burners to provide day-like illumination.

I was thinking about having them in a nice Klemperer rosette (circling about sharing an orbit, with my burners causing occasional flaring to maintain orbits) like thus (not to scale, obviously):

But assuming they're on the black-hole equatorial plane, this leaves my polar regions depressingly dark.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light in my polar regions. How do I get it, without further liberal use of unobtanium?

###Summary version: So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow (but sturdy) unobtanium sphere with a radius about 1 AU. The sphere has an intermediate sized singularity at the core providing gravity of $1~g$ at sphere surface.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light both equatorial and in my polar regions. How do I get it, without further liberal use of unobtanium?

###Full Description

So I've been toying with the idea of a large Niven-like world. I don't like rings however. So instead, in an act of cosmic vandalism, I've handwaved in a hollow unobtanium sphere, using its frankly unbelievable compressive strength to effortlessly resist collapsing under $1~g$ of acceleration from a bikini-clad singularity at the center of the sphere, massing a moderate $1665~M_{☉}$ (solar masses). To make it more fun, my land, seas, tectonic simulators, dinosaur bone planters and other such-stuff is on the outside of the sphere.

This spares them from withering under the gaze of the bikini-singularity (for it is written that none shall see a near-naked singularity and live).

However, it does bring up the rather annoying question of providing adequate lighting for my inhabitants. First, however, a bit about the sizes we're talking about.

Let there be: $$g=G\frac{M}{r^{2}}$$

where
$g$ - local ("surface") gravitational field
$G$ - gravitational constant
$M$ - mass of another body
$r$ - distance from another body

$G=6.67428 \cdot 10^{-11}~\text{N}\left(\frac{\text{m}}{\text{kg}}\right)^{2}$
$M = 1,665~M_{☉}=3.33 \cdot 10^{33}~\text{kg}$ - our constructors like the number 3.

Solving for $g = 9.8~\frac{\text{m}}{\text{s}^{2}}$

We get $r=1.50 \cdot 10^{11}~\text{m}$, which suspiciously conveniently is right about 1 astronomical unit (i.e Sun-Earth distance).

So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow unobtanium sphere with a radius about 1 AU.

Now, I'm ok with the polar regions being a bit dark, but I don't want them in eternal darkness either, as it tends to do nasty things to my sphere's vapor circulation (think 60 mile glaciers). To provide lighting, I'll have a series of planets (I'm thinking somewhere in the range of Jupiter to Brown dwarf in size), which contain sufficient artificial fusion burners to provide day-like illumination.

I was thinking about having them in a nice Klemperer rosette (circling about sharing an orbit, with my burners causing occasional flaring to maintain orbits) like thus (not to scale, obviously):

But assuming they're on the black-hole equatorial plane, this leaves my polar regions depressingly dark.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light in my polar regions. How do I get it, without further liberal use of unobtanium?

###Summary version: So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow (but sturdy) unobtanium sphere with a radius about 1 AU. The sphere has an intermediate sized singularity at the core providing gravity of 1g at sphere surface.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light both equatorial and in my polar regions. How do I get it, without further liberal use of unobtanium?

###Full Description

So I've been toying with the idea of a large Niven-like world. I don't like rings however. So instead, in an act of cosmic vandalism, I've handwaved in a hollow unobtanium sphere, using its frankly unbelievable compressive strength to effortlessly resist collapsing under 1g of acceleration from a bikini-clad singularity at the center of the sphere, massing a moderate 1665 M☉ (solar masses). To make it more fun, my land, seas, tectonic simulators, dinosaur bone planters and other such-stuff is on the outside of the sphere.

This spares them from withering under the gaze of the bikini-singularity (for it is written that none shall see a near-naked singularity and live).

However, it does bring up the rather annoying question of providing adequate lighting for my inhabitants. First, however, a bit about the sizes we're talking about.

Let there be: $$g=G(M/r²)$$

where
g - local ("surface") gravitational field
G - gravitational constant
M☉- mass of Earth's Sun
r - distance from Sun

$G=6.67428×10^{-11} N(m/kg)²$
$M_{1,665☉}=3.33e33 kg$ Our constructors like the number 3.

Solving for $g=9.8 m/s²$

We get $r=1.50×10^{11}m$, which suspiciously conveniently is right about 1 astronomical unit (i.e Sun-Earth distance).

So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow unobtanium sphere with a radius about 1 AU.

Now, I'm ok with the polar regions being a bit dark, but I don't want them in eternal darkness either, as it tends to do nasty things to my sphere's vapor circulation (think 60 mile glaciers)  . To provide lighting, I'll have a series of planets (I'm thinking somewhere in the range of Jupiter to Brown dwarf in size), which contain sufficient artificial fusion burners to provide day-like illumination.

I was thinking about having them in a nice Klemperer rosette (circling about sharing an orbit, with my burners causing occasional flaring to maintain orbits) like thus (not to scale, obviously):

But assuming they're on the black-hole equatorial plane, this leaves my polar regions depressingly dark.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light in my polar regions. How do I get it, without further liberal use of unobtanium?

###Summary version: So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow (but sturdy) unobtanium sphere with a radius about 1 AU. The sphere has an intermediate sized singularity at the core providing gravity of $1~g$ at sphere surface.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light both equatorial and in my polar regions. How do I get it, without further liberal use of unobtanium?

###Full Description

So I've been toying with the idea of a large Niven-like world. I don't like rings however. So instead, in an act of cosmic vandalism, I've handwaved in a hollow unobtanium sphere, using its frankly unbelievable compressive strength to effortlessly resist collapsing under $1~g$ of acceleration from a bikini-clad singularity at the center of the sphere, massing a moderate $1665~M_{☉}$ (solar masses). To make it more fun, my land, seas, tectonic simulators, dinosaur bone planters and other such-stuff is on the outside of the sphere.

This spares them from withering under the gaze of the bikini-singularity (for it is written that none shall see a near-naked singularity and live).

However, it does bring up the rather annoying question of providing adequate lighting for my inhabitants. First, however, a bit about the sizes we're talking about.

Let there be: $$g=G\frac{M}{r^{2}}$$

where
$g$ - local ("surface") gravitational field
$G$ - gravitational constant
$M$ - mass of another body
$r$ - distance from another body

$G=6.67428 \cdot 10^{-11}~\text{N}\left(\frac{\text{m}}{\text{kg}}\right)^{2}$
$M = 1,665~M_{☉}=3.33 \cdot 10^{33}~\text{kg}$ - our constructors like the number 3.

Solving for $g = 9.8~\frac{\text{m}}{\text{s}^{2}}$

We get $r=1.50 \cdot 10^{11}~\text{m}$, which suspiciously conveniently is right about 1 astronomical unit (i.e Sun-Earth distance).

So we're talking people living on top of 30 miles of topsoil, fake dino fossils and water on the outer surface on a hollow unobtanium sphere with a radius about 1 AU.

Now, I'm ok with the polar regions being a bit dark, but I don't want them in eternal darkness either, as it tends to do nasty things to my sphere's vapor circulation (think 60 mile glaciers). To provide lighting, I'll have a series of planets (I'm thinking somewhere in the range of Jupiter to Brown dwarf in size), which contain sufficient artificial fusion burners to provide day-like illumination.

I was thinking about having them in a nice Klemperer rosette (circling about sharing an orbit, with my burners causing occasional flaring to maintain orbits) like thus (not to scale, obviously):

But assuming they're on the black-hole equatorial plane, this leaves my polar regions depressingly dark.

How can I provide sufficient lighting? I am not fussy about things like day length, I just want some light in my polar regions. How do I get it, without further liberal use of unobtanium?