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Author Topic: How big would an orbiting object have to be to appear the same size as the moon?  (Read 3914 times)

Offline Airthumbs

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Does anyone know how big an object would need to be so that it appears to be the same size as the Moon when it is in near Earth orbit?
« Last Edit: 25/01/2013 17:14:39 by JP »


 

Offline CliffordK

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Re: Inflatable Moon
« Reply #1 on: 17/01/2013 03:43:39 »
I could calculate it  :)

If you think of an isosceles triangle,
3,474 km (diameter of the moon) on short side.
1,737 km (radius of the moon)

384,399 km (distance to the moon)

SOH CAH TOA

Ok, I need a "right triangle" for my trig functions, but I can use half an isosceles triangle, ant thus use the radius.

Tan(θ) = opposite/adjacent = 1,737/384,399
θ = arctan(1,737/384,399) = 0.0045 radians.
θ = 0.0090 radians

It should be about the same as using the sin function as the hypotenuse and adjacent side are similar in length.
Sin(θ) = opposite/hypotenuse = 1,737/384,399
θ = arcsin(1,737/384,399) = 0.0045 radians.
θ = 0.0090 radians

Now, work it out the opposite direction.

Say you want to calculate size at 100km (about the max for a balloon).
tan(θ) = opposite/100km.
opposite = radius of balloon = 100*tan(0.0045)

And you get about a 0.45 km radius, or about 0.9 km diameter

========================================

Oops.
I think I did this a bit complicated. 
One should be able to do the same with merely fractions.

Consider 2343ac9370b07a038ce3c062bb56376a.gif = 3300c2a7b171d4b82ea47603de486233.gif

09ea1cb8a453f03272b6df09c4630317.gif = 5e878c43c55cd01017bb0cc6a5f6b654.gif

35f16dc084a53860f5cb3962107d5378.gif = 14d893303d2d61e5965e96e2c9fe3bfa.gif x 09ea1cb8a453f03272b6df09c4630317.gif

Ok, so for 100km, one gets, f899139df5e1059396431415e770c6dd.gif x 09ea1cb8a453f03272b6df09c4630317.gif

And at 100km altitude, one gets 0.9km diameter
At 200km altitude, one gets 1.8km diameter

It is always great to do my calculations 3 different ways, and come up with the same answer :)

Your balloon would have to be quite large if you chose to put it into a geostationary orbit.
diameter = 752e36e85679fabb52f25c2557d76e60.gif x 09ea1cb8a453f03272b6df09c4630317.gif = 323 km diameter.  Fortunately, pressure is low enough that it wouldn't take much gas to fill the balloon, provided adequate elasticity of the material, and resilience to heat, cold, and micro-meteors.
« Last Edit: 17/01/2013 03:51:21 by CliffordK »
 

Offline Airthumbs

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Re: Inflatable Moon
« Reply #2 on: 19/01/2013 16:26:55 »
Thanks fantastic CliffordK.  I think that at about 1km in Diameter the balloon would have roughly 125 square kilometres of material.
 

Offline CliffordK

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Re: Inflatable Moon
« Reply #3 on: 20/01/2013 11:36:01 »
Thanks fantastic CliffordK.  I think that at about 1km in Diameter the balloon would have roughly 125 square kilometres of material.

I think you have an error in your surface area calculation.  Either that, or you need to find a new tailor.

Surface area of a sphere:    A=4πr2

If D = 1km.
r = 0.5km.
A = 4π(0.5)2 = π = 3.14 km2
 

Offline David Cooper

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Re: Inflatable Moon
« Reply #4 on: 20/01/2013 21:06:42 »
Is your idea to create more eclipses of the sun? If so, you'd really want to make something big enough to shade enough of the sky to prevent the corona being wiped out by light coming in from the rest of the sky, as well as putting it in an orbit far enough out to keep its speed across the sun lower. A twenty mile diameter might do the trick at two and a half thousand miles up. A further trick would be to put it on the end of a long rod with a counterweight so that it can be rotated in a manner that leads to it effictively stopping in the sky for a short time before accelerating forwards and decelerating to stop again repeatedly - this would create a series of favoured viewing points from which you could see an eclipse for long enough to make it worthwhile.
 

Offline CliffordK

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Re: Inflatable Moon
« Reply #5 on: 20/01/2013 23:03:31 »
If the intention would be to eclipse the sun.  Then it would have to be put on an ecliptic orbit. 

The amount of shade created by 10x per day eclipses for 1 minute would be equivalent to 1x per day for 10 minutes.

One should be able to maintain a lighter than air object in a very low orbit.  Would it truly be orbital between 50 and 100km?  However, it might tend to drift from the desired ecliptic.  One would probably have to get it up to at least the 200km altitude to be able to easily maintain the ecliptic orbit.
 

Offline CliffordK

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Re: Inflatable Moon
« Reply #6 on: 20/01/2013 23:26:20 »
If one is designing a solar shade.  It may be beneficial to put it at the L1 Lagrangian point.

The L1 is about 1.5 Million KM from the Earth, which is about 5x the distance to the moon.  The advantage is that rather than providing some shade for a few minutes a day, it would provide partial shade 100% of the time. 

I'm having troubles comparing the two. 

If the Earth's circumference is about 40,000 km, then a 1km object in LEO would fill about 1/40,000th of the sky.  Except, that doesn't really capture the partial shade given by the object.  Also, note, I think, the farther from Earth, the wider of a path, N/S, that is covered by the eclipse.

So, a 2km object 200km from Earth might provide more shade than a 1km object, 100km from Earth, for any observer that wasn't at the Ecliptic.
 

Offline CliffordK

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Re: Inflatable Moon
« Reply #7 on: 21/01/2013 01:48:02 »
Ok,
I've been thinking about this some more.

Your satellite, in a low earth ecliptic orbit will actually be somewhere between the Earth and the sun for somewhere between 1/3 and 1/2 of the time, which is pretty good.



However, for an object with a 1 km2 cross section, the area of a complete shadow will be somewhat less than 1 km2.  It may, in fact, only create a complete shadow at a single point along the ecliptic.  A partial shadow would only be created for less than a dozen miles or so in all directions.

So much for the pretty sights in England.  Assuming an ecliptic orbit, one would never see it North of the Tropic of Cancer, or South of the Tropic of Capricorn.

The Earth has a cross section of about πr2 = 3.14 x (6,378 km)2 = 128 million km2

So, your little 1 km2 satellite, while it may be, between the Earth and sun for nearly half the time, it is only blocking about 17bf255e4140e7fd2db9a5d2189b44ad.gif of the sunlight.

You'd need a bunch of them to make much of a difference.
 

Offline Airthumbs

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Re: Inflatable Moon
« Reply #8 on: 24/01/2013 04:15:36 »
Actually CliffordK I had rather a cunning plan and wondered if it was possible.  It would be the ultimate theological coup! World peace would be simple, You call it Nibiru, then you tell the world the Aliens will save us but only if we completely disarm as a species and allow peace.  Then you send the giant pin up to pop it and save the World from destruction just as the Aliens said.

Getting a bit desperate I know but desperate times call for desperate measures!

I was actually trying to calculate the weight of the material required to create a false moon and was thinking it is actually possible.  :)  However I have serious doubts as to my other plan above!
 

Offline CliffordK

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Re: Inflatable Moon
« Reply #9 on: 24/01/2013 08:07:47 »
Ok,
Interesting, a fake asteroid entering low Earth Orbit. 

Astronomers would be quick to determine the size and distance, unless you had their cooperation to say it was bigger than it really was.

I suppose making it look big would be for the WOW effect. 

In Low Earth Orbit, It would probably only be visible for a few hundred miles each direction of its orbital path.  Put it up a few thousand miles, and it would be visible by many more people.  But, to make it appear as large as the moon, say at 1000km, it would have to be much larger.

Of course, you could just shoot it out on a solar orbit that would collide with Earth in a year or so in the future.  And, since there would be little mass, it would burn up in the upper atmosphere with little or no damage at the surface.
 

Offline Airthumbs

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Re: Inflatable Moon
« Reply #10 on: 25/01/2013 17:08:26 »
I'm up for any suggestions that might get this project off the ground :)

 

Offline yor_on

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Re: Inflatable Moon
« Reply #11 on: 25/01/2013 17:15:19 »
I would say it need a he* of a lot of 'lighter air' :)
At least initially. Then you have a problem..

And as Clifford points out, a lot of astronomers, mathematicians and physicists benevolent silence.
 

Offline Airthumbs

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I would say it need a he* of a lot of 'lighter air' :)
At least initially. Then you have a problem..

And as Clifford points out, a lot of astronomers, mathematicians and physicists benevolent silence.

I understand, yor_on, how about just doing it for fun...... people fly kites for fun, maybe scientists should fly artificial moons :)  Space is so serious!
 

Offline Airthumbs

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I would just like to say that an inflatable moon might give some protection to areas of the Earth from Gamma ray bursts?
 

Offline Pmb

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I'm up for any suggestions that might get this project off the ground :)
Im curious as to how you're going to avoid it getting hit by all the space junk in orbit?
 

Offline Airthumbs

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Im curious as to how you're going to avoid it getting hit by all the space junk in orbit?

What a fantastic idea PMB, if you could fill it with some kind or aero gel you could mop up space debris with it. 
 

Offline Bill S

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And if we keep this thread going long enough there will be plenty of hot air about to lift the thing off the ground. :)
 

Offline Airthumbs

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And if we keep this thread going long enough there will be plenty of hot air about to lift the thing off the ground. :)

From what I understand hot air will only get it so far, Helium would be better but that still won't reach orbit.  However if it's hot air that's needed and possibly quite a lot of methane too then it's a start, at least it's off the ground :)
 

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