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How large a disc would it take to block a star from view for all of earth?

Posted: Thu Apr 07, 2016 12:49 am UTC
by gmoff01
Hi guys, I was flipping through random xkcd strips today and ran across this one:

https://xkcd.com/975/

And just as an intellectual excercise I started to try to determine how large a disc it would take to block out a star like this.

From any one point on the surface this is relatively simple, as you can calculate the size of the disc based on distance from the surface and desired angular size (let's say 50 mas). The point where my limited math breaks down is when I try to consider what needs to change so that the disc would block that section of sky from the ENTIRE surface instead of one point. How would one go about calculating that?

Bonus question, is it even possible to set up an orbit that would keep the disc intersecting the line between the earth and a given star?

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Thu Apr 07, 2016 1:44 am UTC
by Copper Bezel
The distance to any star is so great that there's basically no parallax between any two points on Earth's surface and all of those sight lines are effectively parallel. I think the disk would actually have to be Earth-sized.

Obviously, we get a lot more parallax due to Earth's orbit.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Thu Apr 07, 2016 1:47 am UTC
by gmalivuk
If you want to block a particular star from the entire surface of Earth, you'll need a disc at least as large as Earth itself.

If the star's center is distance D from the center of Earth and has radius R, and you want to block it from view from all of Earth with radius r, then the disc at distance d from Earth's center needs to have a radius of at least (rd + R(D-d))/D.

star.png
(Not to scale)
star.png (9.87 KiB) Viewed 6107 times


There isn't an orbit around Earth that would work, because it can't actually orbit at all. It has to stay on the same side of Earth at all times.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Mon Apr 25, 2016 10:54 pm UTC
by patzer
gmalivuk wrote:There isn't an orbit around Earth that would work, because it can't actually orbit at all. It has to stay on the same side of Earth at all times.


Well, technically, to stay on the same side of the Earth at all times it has to orbit the Earth every 365 days.

This would necessitate the object being around 2.2 million km from Earth, but the Earth's sphere of influence reaches only 0.9 km out. So I think such an orbit is impossible.

So, orbits around the Earth are out of the question, but are there any other stable positions to put a shield at? Lagrangian points wouldn't work, as from the Earth's perspective the lagrangian points move relative to the stars.

I wonder if putting the shield in some orbit of the sun that takes 365 days would work.

Like this rough diagram: (shield is brown on a grey orbit, earth is blue on a black orbit)

shield.png


Another option might be using the shield to catch photons from the sun, creating a force affecting the shield's orbit.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Mon Apr 25, 2016 11:11 pm UTC
by gmalivuk
patzer wrote:
gmalivuk wrote:There isn't an orbit around Earth that would work, because it can't actually orbit at all. It has to stay on the same side of Earth at all times.

Well, technically, to stay on the same side of the Earth at all times it has to orbit the Earth every 365 days.
Something that orbited Earth every 365 days would always be in the same position relative to the Sun, but for this we need something that remains in the same position relative to the stars.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Mon Apr 25, 2016 11:24 pm UTC
by patzer
gmalivuk wrote:
patzer wrote:
gmalivuk wrote:There isn't an orbit around Earth that would work, because it can't actually orbit at all. It has to stay on the same side of Earth at all times.

Well, technically, to stay on the same side of the Earth at all times it has to orbit the Earth every 365 days.
Something that orbited Earth every 365 days would always be in the same position relative to the Sun, but for this we need something that remains in the same position relative to the stars.

*facepalm*

You're right.

In that case, I think a shield orbiting the sun in some clever configuration is our only option.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Tue Apr 26, 2016 3:09 pm UTC
by Sandor
patzer wrote:
gmalivuk wrote:There isn't an orbit around Earth that would work, because it can't actually orbit at all. It has to stay on the same side of Earth at all times.

I wonder if putting the shield in some orbit of the sun that takes 365 days would work.

The period of an orbit is directly related to its semi-major axis. As the link says, this means that for all ellipses with a given semi-major axis, the orbital period is the same, regardless of eccentricity. So the shield's orbit's semi-major axis is going to have to match Earth's orbit. From your diagram, the shield's semi-minor axis is also going to have to match Earth's orbit, so I think your plan is not going to work - there's no suitable Solar orbit.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Tue Apr 26, 2016 6:27 pm UTC
by lorb
It would also heavily depend on which star you want to block out? Stars very close to the celestial poles could be shielded by a disc that has nearly the same orbit as earth just "above"/"below" it. And if you make the disc a little bigger than earth you have some leeway with it's orbit :)

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Tue Apr 26, 2016 7:03 pm UTC
by gmalivuk
And what do you propose to do about the fact that such an orbit intersects Earth's at two positions?

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Tue Apr 26, 2016 8:24 pm UTC
by Sandor
You will probably have to constrain the question to a given time period to get a sensible answer (e.g. the star in question only needs to be not-visible from the Earth +/- some period of time from now), and the answer will heavily depend on that period of time. For +/- 1 second - not much bigger than Earth, but for +/- 6 months - Earth's orbit plus a bit.

One example for a longer period may be a Milky Way star on the edge of inter-galactic space, with a (large*) disk at its galactic L1 Lagrange point. The disk's radius would need to be some way between the radius of the star and the radius of the Sun's orbit around the galaxy.

(*) and infeasibly light, and immune to radiation pressure.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Tue Apr 26, 2016 8:50 pm UTC
by Tub
Maybe if we put the distant star into a specific orbit around our sun, then..... nah.

Assuming that the purpose is to prevent the star from distracting humans, it's enough to block the star at night, when it isn't outshone by our sun. Depending on the location of the star, that can reduce the size of the disk during certain times of the year, so your disk does not need to sync up perfectly. I still don't see a possible orbit though, much less a way to construct a disk this size in space.

For now, I'd just pollute the upper layers of our atmosphere.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Wed Apr 27, 2016 1:25 am UTC
by lorb
gmalivuk wrote:And what do you propose to do about the fact that such an orbit intersects Earth's at two positions?


Does it absolutely have to? Could it not orbit on a plane perfectly parallel to earths but like 100000km away? (which is less than the distance the poles of jupiter have)

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Wed Apr 27, 2016 1:33 am UTC
by gmalivuk
The poles of Jupiter are kept that far from the orbital plane by the rest of Jupiter. You can't have something orbit in a plane that doesn't contain the (center of mass of) the central body it's orbiting around.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Wed Apr 27, 2016 2:36 pm UTC
by lorb
Even if it deviates by just a minuscule amount? If you put it in the right place and gave it a push in the right direction how fast would it deviate from the path we want? Or if one where to mount a rocket drive or something similar to the disc, how much energy would it take to keep it from intersecting earths orbital plane? Would that be feasible assuming that the level of resources/means to build and put in place such a disk are already present?

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Wed Apr 27, 2016 5:50 pm UTC
by gmalivuk
lorb wrote:Even if it deviates by just a minuscule amount? If you put it in the right place and gave it a push in the right direction how fast would it deviate from the path we want? Or if one where to mount a rocket drive or something similar to the disc, how much energy would it take to keep it from intersecting earths orbital plane? Would that be feasible assuming that the level of resources/means to build and put in place such a disk are already present?
Every inertial orbital path is in a plane that includes the central object. Two distinct planes that contain the same point (i.e. the sun) intersect in a line. Therefore, any orbit at the same distance from the Sun as Earth's orbit will cross Earth's orbit in two places, which means twice a year.

However, the bigger problem is keeping it hovering above Earth without falling, with or without the Sun. Earth's gravity from 100,000 km is about 0.04 m/s^2, while the Sun's total gravity from 1 AU is only 0.006 m/s^2, and the component of that force pulling back "down" toward Earth's orbit would be a tiny fraction (0.0007) of that.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Thu Apr 28, 2016 3:28 pm UTC
by solune
gmalivuk wrote:However, the bigger problem is keeping it hovering above Earth without falling, with or without the Sun.


Hovering is the keyword here. If you're technologically advanced enough to build such a disk, you can probably build a bunch of space elevators, a geostationnary railway, and mount your disk on a train going around the earth (with a weight on the other side)

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Thu Apr 28, 2016 3:39 pm UTC
by gmalivuk
solune wrote:
gmalivuk wrote:However, the bigger problem is keeping it hovering above Earth without falling, with or without the Sun.


Hovering is the keyword here. If you're technologically advanced enough to build such a disk, you can probably build a bunch of space elevators, a geostationnary railway, and mount your disk on a train going around the earth (with a weight on the other side)

How's a geosynchronous structure around the equator supposed to help with something hovering above the pole? How's a geosynchronous anything supposed to help with keeping a particular star hidden from view?

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Thu Apr 28, 2016 4:21 pm UTC
by Copper Bezel
Yeah, that doesn't actually net you any upward force to support the disc. It can't, because any unbalanced upward force that would support the disc would tear the system apart at all points it's not sitting on.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Thu Apr 28, 2016 5:17 pm UTC
by Sableagle
Ball cage, with equal mass over each pole and a lot of very strong tethers around the equator to stop the two huge discs squashing the whole structure into an oblate spheroid with the same axial length as the Earth inside it?

Wouldn't it be easier to issue everybody on the exposed hemisphere-and-a-bit of Earth with an automated parasol?

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Thu Apr 28, 2016 5:36 pm UTC
by DiEvAl
Tub wrote:Maybe if we put the distant star into a specific orbit around our sun, then..... nah.

Assuming that the purpose is to prevent the star from distracting humans, it's enough to block the star at night, when it isn't outshone by our sun. Depending on the location of the star, that can reduce the size of the disk during certain times of the year, so your disk does not need to sync up perfectly. I still don't see a possible orbit though, much less a way to construct a disk this size in space.

For now, I'd just pollute the upper layers of our atmosphere.


That's a brilliant idea! We don't need a giant disc, we can just build something that'll outshine all the stars at night!

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Thu Apr 28, 2016 5:41 pm UTC
by Sableagle
Oh, we had one of those, 20 years ago.

It was a smile.

I didn't do a very good job of making it happen more often, and 7,300 days ago today was the last time I ever saw it.

Wait. You meant literally?

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Fri Apr 29, 2016 9:41 am UTC
by solune
gmalivuk wrote:How's a geosynchronous structure around the equator supposed to help with something hovering above the pole? How's a geosynchronous anything supposed to help with keeping a particular star hidden from view?


I incorrectly assumed that the star was in the solar plane. My structure was a simplified example of the ball cage mentionned by Sableagle. (I need a large part of the structure to be moving at orbital speed to replace compression forces with tensile forces)

... It occurs to me that what I'm proposing is basically a space fountain where the base station is not on the ground, but on the opposite side of the earth, with a counterweight.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Fri Apr 29, 2016 5:45 pm UTC
by gmalivuk
In that case there's no particular need to have anything geosynchronous, and you could do the same thing over the poles.

Of course, that takes care of the center of mass of the disc, but since it's got to be bigger than Earth, the force pulling on its edges would also be substantial.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Fri Apr 29, 2016 6:08 pm UTC
by ijuin
We are reaching a point here where it would be easier to simply enshroud the entire Earth so that the entire night sky would be obscured.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Sat Apr 30, 2016 12:59 am UTC
by Soupspoon
I was long thinking along the lines of the upper-limit being a Dyson Sphere of radius >1AU, then refining that down towards a 'Dyson Ring' (same radius, less solid angle covered) covering as far from the eclptic as you'd need to perpetually cover your target star (and many others!) at all necessary points in Earth's orbit... But, yes, a sphere/ring around the Earth (possibly just a stable framework, everywhere but where the starshade element lies, to only somewhat obscure non-target starfields, with a spin and/or non-perpendicular rotation in various directions to keep the shade-track in sync with the target star upon the celestial sphere) of perhaps just marginally more than Geostationary distance1, might be marginally more practical to construct and maintain... ;)

1 So we can keep on using geostationary constellations without interuptions by our ringshade at all...

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Mon May 02, 2016 6:56 pm UTC
by Tyndmyr
ijuin wrote:We are reaching a point here where it would be easier to simply enshroud the entire Earth so that the entire night sky would be obscured.


Solution to the Fermi paradox. All sufficiently advanced systems enclose themselves in order to get some goddamned peace and quiet.

Re: How large a disc would it take to block a star from view for all of earth?

Posted: Mon May 02, 2016 7:36 pm UTC
by Whizbang
Tyndmyr wrote:
ijuin wrote:We are reaching a point here where it would be easier to simply enshroud the entire Earth so that the entire night sky would be obscured.


Solution to the Fermi paradox. All sufficiently advanced systems enclose themselves in order to get some goddamned peace and quiet.


Game of Krikkit, anyone?