Celestial Nav?

[Mike1956]

I understand the light from stars is considered to strike the Earth at the same angle irrespective of our location on Earth. I have no problem with this whatsoever but have become curious to discover how far from Earth we need to venture before there is a difference of say 1 minute. Obviously it depends on the star but take for example SIRIUS.

I reckon the calculation would look something like this but I am no mathematician.......

5878625373183.6 x 8.611 x 22 divide by 7 divide by 360 divide by 60

This should give the distance from Earth to give a 1 minute difference

An additional calculation would determine what difference exists from various parts of the Earth.

Perhaps a mm or 2

I attempted the calculation on my calculator from the £1 shop and is started to smoke

Mike

[Lodesman]

Originally Posted by Mike1956

I understand the light from stars is considered to strike the Earth at the same angle irrespective of our location on Earth.

If that was the case, then celestial nav would have been a non-starter from the get-go.

[Mike1956]

Good point!

I will make another attempt at explaining myself.

I should have said rays of light from stars are considered to arrive at the Earth parallel.

Additionally I realised I had missed out a crucial part of my calculation in my original formula when I was attempting the calculation by mental arithmetic in the middle of the night. The answer I came up with was around a billion miles.

The bit I missed out was to multiply the first 2 figures by 2 to determine the diameter of the circle.

The first figure is about 6 trillion being 1 lyr 8.611 lyrs being the approx distance to Sirius giving radius of about 50 trillion x2 to give diameter 100 trillion x 3 and a bit to give circumference 300 trillion divide by 360 to give distance of 1 degree of arc divide by 60 to give 1 minute of arc.

Anyone got a good calculator?

Before someone points it out of course I know James Cook would have done this calculation with no trouble with a quill & parchment

Mike

[44'cruisingcat]

Originally Posted by Mike1956

I understand the light from stars is considered to strike the Earth at the same angle irrespective of our location on Earth.

So, the Earth really is flat after all...

[El Pinguino]

I assume you are talking parallax.

The sun is only 8 minutes away by phast foton and the parallax for it never exceeds .15 of a minute of arc.

Nearest star is XX light years away and parallax is as good as non existant.

Parallax.... https://astronavigationdemystifieddo...6/parallax.jpg

[StuM]

Just to put it into perspective, a Parsec (parallax second) is the distance subtended by one SECOND of arc across the Earth's mean ORBIT.

That is 3.26 light years, or considerably less than the distance to the nearest star (Alpha Centauri at 4.3 light years).

Now consider that that is only 1/60th of your "minute" and the Earth's diameter of 8000 miles is only about 1/23thousandth of its mean orbit.

IOW, the light from the nearest star is parallel to all intents and purposes, unless you can measure accurately less than to 0.00001 of a minute of angle.

[charliehows]

Considering a; the best result you can expect from celestial nav is a matter of miles in inaccuracy and b; gps calculations are so accurate that calculations of time differentials between satellites have to take into account the light bending effects of gravitational waves - - - what exactly is the point you are trying to make? In the best tradition of naïve scientists you start with the entirely self evident statement that “I am no mathematician but...”

[charliehows]

nearest star - alpha centauri - is 4 light years away...

[Mike1956]

Fully accept and fully aware of all points raised.

Thing is I simply do not have a calculator to handle the figures I am dealing with. Thought someone on the forum might have.

However pointless my question seems to you I happen to be interested to determine what I asked. How far away from Earth would I need to go to make a difference of 1 minute of arc in the rays of light from Sirius?

I am sure this sort of calculation is bread and butter to many people on here with a decent calculator.

Mike

[gjordan]

Mike, no dis-respect, but you are asking the wrong crowd. We are sailors, and most of this crowd has never even held a sexton or done calcs. What you are asking has no bearing on anything we do. I would think you would have far better luck finding a yahoo group about astronomy where people would (maybe) have some knowledge about what you are asking. Good Luck with it. ____Grant

[wiekeith]

Originally Posted by Mike1956

I am sure this sort of calculation is bread and butter to many people on here with a decent calculator.

Mike

Here you go, you could try this online one? - Scientific Calculator

Good luck with it

[Scott Berg]

Originally Posted by gjordan

Mike, no dis-respect, but you are asking the wrong crowd. We are sailors, and most of this crowd has never even held a sexton or done calcs. What you are asking has no bearing on anything we do. I would think you would have far better luck finding a yahoo group about astronomy where people would (maybe) have some knowledge about what you are asking. Good Luck with it. ____Grant

I'd disagree with the generalization concerning Nav skills. And I'd hope that most (used to be all) who voyage off soundings are capable of navigating without the black boxes. I will spend some time with your question when Ive got a few minutes... it's a good discussion

[44'cruisingcat]

Originally Posted by gjordan

Mike, no dis-respect, but you are asking the wrong crowd. We are sailors, and most of this crowd has never even held a sexton ......

Probably true. But what does a church caretaker have to do with navigation?

[jackdale]

For the purposes of celestial navigation we use a Ptolemaic universe.

https://astronavigationdemystified.c...-the-universe/

[Kelkara]

Originally Posted by Mike1956

However pointless my question seems to you I happen to be interested to determine what I asked. How far away from Earth would I need to go to make a difference of 1 minute of arc in the rays of light from Sirius?

As far as celestial nav ... your question is indeed pointless.

But you asked nicely, so you deserve an answer:

it's a simple trig calculation y=x.tan(A)

x=distance to target (Sirius)= 8.6 ltyr * 9.5e+12 km/ltyr
A=angle of parallax (1 minute) = 2.9e-4 radians
tan(A)~=A for small A = 2.9e-4 (no calculator needed)

y=distance needed to move to create parallax =
(8.6*9.5*2.9) *10^(0+12-4)
~=9*9*3 *10^8 = 243*10^8 = 2.43e+10km (quill and parchment optional)


or to put into perspective that is about three times as far away as the orbit of Pluto. If you were interested in 1 second of arc you would still need to go most of the way to Jupiter.