# The Naked Scientists Forum

### Author Topic: At what radius to the earth would the Sun ''vanish''?  (Read 4240 times)

#### Thebox

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##### At what radius to the earth would the Sun ''vanish''?
« on: 23/10/2015 11:12:40 »
Hello all, as title. if the sun moved away from the earth at what radius would the sun ''vanish'' from observation?

present distance = 149.6 million km

present suns diameter = r*2= 696,000*2=1392000km

so if earth to sun = r1*2=299.2 million km

does the suns diameter r2*2/2?

« Last Edit: 23/10/2015 11:28:08 by Thebox »

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #1 on: 27/10/2015 09:22:38 »

#### chiralSPO

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #2 on: 27/10/2015 13:36:40 »
If the question is, "how far would we have to be from the sun such that we could not see it with our eyes, even though we are looking directly at it?"

I think the best way to try to calculate this is looking at the amount of light reaching the Earth now (about 1000 W/m2). We can easily see a 2W light bulb (my bike headlight) from 100 m away at night, which works out to 0.0001 W/m2 (if it's a 45° cone). Since the Sun is currently shining at 10 million (107) times stronger than that, and light spreads out 1/r2, we would have to be 103.5 times further than we are now, which would be about 4.7x1011 meters, or almost exactly 5 light years. This is a lower limit on how far away one would have to be to not see the sun, but I think it would be visible quite a bit further (I just don't know how bright our sun's neighborhood will be, which also depends on where the observation is taking place). Remember how many stars we can see by the naked eye, and many of them are quite a bit farther away than 5 ly.

#### alancalverd

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #3 on: 27/10/2015 14:55:31 »
It can't! In principle, if we can detect one photon and ascribe it to a given source, we have "seen" the source object.

Since the sun is a massive object, it cannot recede from us quicker than its photons are travelling towards us. The intensity of photon radiation decreases with the inverse square of distance, but that just means you have to wait a bit longer for another photon to come along within a given receptor area.

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #4 on: 27/10/2015 16:58:22 »
That seems a bit obtuse to the actual question,  when things move away from they scale down in size by increased distance, regardless whether it produces light or not at distance x the object will vanish from sight, this can be observed with a flash light walking backwards away from the observer.

Alan says ''It can't! In principle'', that would go against the physics of distance and scaling.

Chiral says ''I think the best way to try to calculate this is looking at the amount of light reaching the Earth now (about 1000 W/m2).''

How is that the best way? once something has scaled down by increased distance it vanishes, looking at light is not quite the same.

I do not see how this answers my question?

present suns diameter = r*2= 696,000*2=1392000km

so if earth to sun = r1*2=299.2 million km

does the suns diameter r2*2/2?

If it is twice as far , does it look twice as small?

To extend why I asked the question is because if we was to observe from a star that was far way looking in at our galaxy and the sun was to small to see, it had past position x, the observer would see a black hole?
« Last Edit: 27/10/2015 17:03:52 by Thebox »

#### alancalverd

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #5 on: 27/10/2015 17:12:59 »
"Vanish" means you can't see it. We see things because the emit light. Received photon = visible, no received photon = vanished.

Just because your eye, or even a telescope, can't measure the diameter of something, doesn't mean it has vanished.

http://www.astronomynotes.com/starprop/s11.htm

Quote
All but a few stars appear as mere pinpoints in even the largest telescopes. They are much too far away to derive their diameters from measuring their angular diameters and distances.

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #6 on: 27/10/2015 18:14:08 »
"Vanish" means you can't see it. We see things because the emit light. Received photon = visible, no received photon = vanished.

Just because your eye, or even a telescope, can't measure the diameter of something, doesn't mean it has vanished.

http://www.astronomynotes.com/starprop/s11.htm

Quote
All but a few stars appear as mere pinpoints in even the largest telescopes. They are much too far away to derive their diameters from measuring their angular diameters and distances.

It as vanished relative to sight or observation by a telescope, yes of cause it is still there, it is just gone beyond point x, so what is the radius from the earth if the sun was to  move away, would point x be?

Is twice the distance of radius of a mass from an observer , diameter of the mass divided by 2?  Is that the scale?

#### Colin2B

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #7 on: 27/10/2015 18:15:34 »
To extend why I asked the question is because if we was to observe from a star that was far way looking in at our galaxy and the sun was to small to see, it had past position x, the observer would see a black hole?
If a distant sun is too small to see then we would certainly not see it as a black hole. If it had sufficient width to be seen as a hole, then we would also see its light.

does the suns diameter r2*2/2?
Because r2*2/2=2r=d you are asking is the sun's diameter its diameter. This sort of question puts people off answering.

#### Colin2B

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #8 on: 27/10/2015 18:19:39 »

Is twice the distance of radius of a mass from an observer , diameter of the mass divided by 2?  Is that the scale?
What do you mean by this? What scale?
Why have you just introduced mass into a question about visibility.

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #9 on: 27/10/2015 18:22:07 »

Because r2*2/2=2r=d you are asking is the sun's diameter its diameter. This sort of question puts people off answering.

I wasn't saying that, r1 and r2 was like m1 and m2,

r1 being the distance between the sun and earth and r2 being the radius of the sun,

r2*2 = diameter of the sun then divided by 2.

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #10 on: 27/10/2015 18:23:36 »

Is twice the distance of radius of a mass from an observer , diameter of the mass divided by 2?  Is that the scale?
What do you mean by this? What scale?
Why have you just introduced mass into a question about visibility.

an object when moving away from you scales down in size relative to sight relative to distance away, an 100ft tree looks a dot on a horizon. I was just referring to the object as mass , sorry for confusing.

What is the scaling ratio?

You can see the first line is different

present suns diameter = r*2= 696,000*2=1392000km

so if earth to sun = r1*2=299.2 million km

does the suns diameter r2*2/2?

« Last Edit: 27/10/2015 18:38:47 by Thebox »

#### chiralSPO

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #11 on: 27/10/2015 18:52:06 »
This sounds more like a question of trigonometry...

The apparent size of the sun (A, measured as an angle) will be A = 2*sin–1(rsun/robs)

where A = apparent size
sin–1 is the inverse sine or arcsine function
rsun = radius of the sun in km
robs = distance of observer to the sun

when A = 0, the sun has vanished (the only problem is there is no value of robs for which the A is 0 (as long as rsun is nonzero; A will only approach 0 as robs approaches infinity)
« Last Edit: 27/10/2015 18:54:18 by chiralSPO »

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #12 on: 27/10/2015 19:23:20 »
This sounds more like a question of trigonometry...

The apparent size of the sun (A, measured as an angle) will be A = 2*sin–1(rsun/robs)

where A = apparent size
sin–1 is the inverse sine or arcsine function
rsun = radius of the sun in km
robs = distance of observer to the sun

when A = 0, the sun has vanished (the only problem is there is no value of robs for which the A is 0 (as long as rsun is nonzero; A will only approach 0 as robs approaches infinity)

That can't be true,

robs=y & rsun=x then +dy=-dx?

dy²=dx/^2?
« Last Edit: 27/10/2015 19:46:12 by Thebox »

#### chiralSPO

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #13 on: 27/10/2015 19:48:54 »
This sounds more like a question of trigonometry...

The apparent size of the sun (A, measured as an angle) will be A = 2*sin–1(rsun/robs)

where A = apparent size
sin–1 is the inverse sine or arcsine function
rsun = radius of the sun in km
robs = distance of observer to the sun

when A = 0, the sun has vanished (the only problem is there is no value of robs for which the A is 0 (as long as rsun is nonzero; A will only approach 0 as robs approaches infinity)

That can't be true,

robs=y & rsun=x then +dy=-dx?

No. As I defined it, rsun is a constant (the actual radius of the sun), so your dx =d(rsun) = 0.

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #14 on: 27/10/2015 19:56:26 »

No. As I defined it, rsun is a constant (the actual radius of the sun), so your dx =d(rsun) = 0.

Obviously the sun does not change size, I am talking visual observation, an object relative shrinks the more distant away from it, so relatively the radius of the sun shrinks relative to distance to an observer.

At a point Z point X viewed along a Y-axis will ''vanish'' to observation, so distance must have a scaling system, that is why we have magnification is it not?

Your avoiding the actual question and coming back with something not the same as the question, my answer requires a distance of robs  that rsun ''vanishes''.  At what distance from the earth does 1392000km of diameter of the sun ''vanish'' if the sun was moving away?
« Last Edit: 27/10/2015 19:57:59 by Thebox »

#### chiralSPO

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #15 on: 27/10/2015 20:18:39 »

No. As I defined it, rsun is a constant (the actual radius of the sun), so your dx =d(rsun) = 0.

Obviously the sun does not change size, I am talking visual observation, an object relative shrinks the more distant away from it, so relatively the radius of the sun shrinks relative to distance to an observer.

At a point Z point X viewed along a Y-axis will ''vanish'' to observation, so distance must have a scaling system, that is why we have magnification is it not?

Your avoiding the actual question and coming back with something not the same as the question, my answer requires a distance of robs  that rsun ''vanishes''.  At what distance from the earth does 1392000km of diameter of the sun ''vanish'' if the sun was moving away?

The apparent diameter of the sun will never be zero (as shown by the equation I gave earlier)

The distance at which the sun is no longer visible will depend on the observer and the environment more than the distance from the sun (this is why we cannot see most stars during the day, even if we can see them at night from 100s of light years away.)

As alan pointed out, the light of the sun will still be visible for distances so great that the sun appears to have no diameter (just a point of light).

#### evan_au

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #16 on: 27/10/2015 20:26:11 »

Quote from: Wikipedia
Naked Eye Angular resolution: about 1 arcminute, approximately 0.02° or 0.0003 milliradians,[1] which corresponds to 0.3 m at a 1 km distance.
On an astronomical eye-chart, the "Sun Line" would become unreadable around the orbit of Uranus.

But the Sun is not a black letter on a white eye-chart, or even a white letter against the black backdrop of space.

Astronomers measure the visibility of a star as "Apparent Magnitude". Magnitude 7 is the faintest anyone can see with the naked eye, under excellent conditions.

Astronomers compare the brightness of different stars by "Absolute Magnitude", which is the Apparent Magnitude at a distance of 10 parsecs, or 32 light-years. The Absolute Magnitude of the Sun is 5, which is still very visible.

To reduce the Sun to magnitude 7 (ie invisible to the naked eye), you would need to be at a distance of about 80 light-years. (If I've done the calculations correctly!)

See:
https://en.wikipedia.org/wiki/Naked_eye
https://en.wikipedia.org/wiki/Absolute_magnitude
https://en.wikipedia.org/wiki/Apparent_magnitude

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#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #17 on: 27/10/2015 21:03:38 »

Quote from: Wikipedia
Naked Eye Angular resolution: about 1 arcminute, approximately 0.02° or 0.0003 milliradians,[1] which corresponds to 0.3 m at a 1 km distance.
On an astronomical eye-chart, the "Sun Line" would become unreadable around the orbit of Uranus.

But the Sun is not a black letter on a white eye-chart, or even a white letter against the black backdrop of space.

Astronomers measure the visibility of a star as "Apparent Magnitude". Magnitude 7 is the faintest anyone can see with the naked eye, under excellent conditions.

Astronomers compare the brightness of different stars by "Absolute Magnitude", which is the Apparent Magnitude at a distance of 10 parsecs, or 32 light-years. The Absolute Magnitude of the Sun is 5, which is still very visible.

To reduce the Sun to magnitude 7 (ie invisible to the naked eye), you would need to be at a distance of about 80 light-years. (If I've done the calculations correctly!)

See:
https://en.wikipedia.org/wiki/Naked_eye
https://en.wikipedia.org/wiki/Absolute_magnitude
https://en.wikipedia.org/wiki/Apparent_magnitude

Thank you, so in reverse if we was 81 light years away from the Sun, we would observe nothing of the sun?

#### chiralSPO

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #18 on: 27/10/2015 21:12:32 »

Thank you, so in reverse if we was 81 light years away from the Sun, we would observe nothing of the sun?

Evan means we could not see the sun by naked eye if it was 81 ly away. With a telescope, we could easily observe the sun from this distance...

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #19 on: 27/10/2015 23:12:55 »

Thank you, so in reverse if we was 81 light years away from the Sun, we would observe nothing of the sun?

Evan means we could not see the sun by naked eye if it was 81 ly away. With a telescope, we could easily observe the sun from this distance...

Thank you for the answers, so I am presuming now that all the stars we see in the night sky by eye are much further away than 80ly, so I am presuming these stars are much bigger than our sun, would this be correct?

#### Colin2B

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #20 on: 28/10/2015 00:15:54 »
....I am presuming now that all the stars we see in the night sky by eye are much further away than 80ly.....
Why would you assume something that is incorrect when it is easy to check on the net?

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #21 on: 28/10/2015 07:04:47 »
....I am presuming now that all the stars we see in the night sky by eye are much further away than 80ly.....
Why would you assume something that is incorrect when it is easy to check on the net?

I like to consider things myself before I know what google says, I also prefer interaction and discussion, google does not answer back or tell me why I am wrong, so If my assumption is incorrect, then why please?

#### Colin2B

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #22 on: 28/10/2015 08:46:03 »
[so If my assumption is incorrect, then why please?
By the rules of logic. What you have created what is known as an excluding premise.
By assuming that the Stars we see are further away than 80ly you have automatically excluded stars which are closer but might be the same size as our sun. The rest of your sentence then becomes a circular argument based on an incorrect premise.
Logic is only as good as the assumptions it is based on, so it is always worth checking any assumptions first. Otherwise you can end up with frustrating discussions where people feel they are wasting their time and stop responding.

If you really value discussion there is a lot you can do to encourage it, for example
Your avoiding the actual question and coming back with something not the same as the question,
When people are trying hard to decider your question, or when there are a number of different angles to a question, accusations like this are not helpful and do not encourage others to join in, also people already answering can feel frustrated and give up.
If you really do value discussion there is a lot you could do to encourage it. Use plain English (which you are very capable of doing) and avoid confusing maths.

#### evan_au

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #23 on: 28/10/2015 08:59:43 »
Quote from: Thebox
I am presuming now that all the stars we see in the night sky by eye are much further away than 80ly
There are many stars within 80 ly.  The nearest is Alpha Centauri, at 4.4 light-years.

Quote from: Thebox
I am presuming these stars are much bigger than our sun, would this be correct?
What do you mean by "bigger"?

There are many stars which are brighter in Absolute Magnitude than the Sun.

In general, stars that are more massive will burn their fuel more rapidly, and thus be brighter during their lifetime.
However, stars tend to shrink after they burn all their fuel, and this makes them less bright, even though they still have much of their original mass.

Quote
if the sun was too small to see, ...the observer would see a black hole?
A black hole is an extreme example of an old star - it has considerable mass, but it is extremely small, and no light can escape.

According to current theories, the Sun does not have enough mass to form a black hole. This is true regardless of the distance from which you try to view it.
« Last Edit: 28/10/2015 09:01:47 by evan_au »

#### Thebox

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##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #24 on: 28/10/2015 11:34:24 »

What do you mean by "bigger"?

I am a  bit confused you have to ask what I mean by bigger, if you are 20 stone and I am 10 stone, you are bigger than me, if you are 6ft and I am 4ft you are bigger than me.

I will try to rephrase my question,   if star had a smaller radius than our suns radius and was beyond lets say 70 ly away, we would not see it by eye, if the star was bigger and further away we would still see it?

#### The Naked Scientists Forum

##### Re: At what radius to the earth would the Sun ''vanish''?
« Reply #24 on: 28/10/2015 11:34:24 »