Submitted 1st double star measurement

[lunator]

Guys

Just submitted my 1st DS measurement to Bob Argyle (President of the Webb Society).

If you want to be reminded of your school days I'll let you know how I measured it (It is a bit like being back in maths again).

Cheers

Ian

[The Warthog]

Let's go back a page. What did you measure, and how did you measure it?

[daz]

Great news Ian!

Let's have the details then!!!

[lunator]

I measured the star STF 196 CD.

It is an optical double in Aries.

The measurement was was taken using a stop watch with a lap timer facility.

By measuring the time it takes to cross the field of view and knowing the size of the FOV you can measure the relative positions of the stars using trigonometry.

The stars were last measured in 1983.

The Positions angle was 5 dergees and the seperation 219.5

This is the rough sketch I drew before measuring them.

These were the timings I made on the transit of the stars.

STF196 CD Timing 1 Timing 2 Timing 3 Timing 4 Timing 5 Timing 6 Timing 7 Timing 8 Timing 9 Timing 10 Timing 11 Timing 12 Average 1 Mean

C 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0 0.0 0.0

D 7.39 8.33 8.03 8.49 9.18 8.30 8.37 8.78 9.31 10.02 11.24 10.02 9.0 8.8 8.9

D 30.73 30.21 28.86 29.80 28.84 28.52 29.62 32.58 29.15 29.99 28.71 29.17 29.7 30.4 30.1

C 35.11 36.27 35.36 35.52 35.30 35.39 35.43 35.50 36.09 35.96 36.24 36.27 35.7 36.0 35.8

STF196 CD Timing 1 Timing 2 Timing 3 Timing 4 Timing 5 Timing 6 Timing 7 Timing 8 Timing 9 Timing 10 Timing 11 Timing 12 Average 2

C 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.0

D 7.77 7.46 7.95 8.65 9.52 10.70 8.77 7.70 7.92 9.15 8.55 11.52 8.8

D 32.17 31.83 30.74 30.34 29.46 28.48 30.39 31.05 32.17 29.99 30.86 27.71 30.4

C 35.45 35.64 35.55 36.71 36.65 35.62 35.83 36.55 35.77 35.83 36.08 35.77 36.0

Field Radius 252.5"

Using Mean figures

PA 5.90

Sep 220.5"

Average 1

PA 5.20

Sep 225.9"

Average 2

Gave errors on the calculation

I calculated the PA was 5.9 and the Seperation was 220.5".

Cheers

Ian

[daz]

Excellent stuff Ian

I am about to start Variable Star estimations, but this is also very interesting! Real science - wow!!

[lunator]

Excellent stuff Ian

I am about to start Variable Star estimations, but this is also very interesting! Real science - wow!!

Daz

The real beauty of it is I have an undriven EQ5 & and £6 stopwatch to gain this information.

[daz]

Ian

Do you have a reticule EP that you use to measure the transits, or do you measure from one side of the EP to the other?

What do the timings show (e.g. laptimes between two points) ?

Hope you don't mind the q's!!

[The Warthog]

I measured the star STF 196 CD.

I

Using Mean figures

PA 5.90

Sep 220.5"

Average 1

PA 5.20

Sep 225.9"

Average 2

Gave errors on the calculation

I calculated the PA was 5.9 and the Seperation was 220.5".

Cheers

Ian

I can see what you did, but, but, but, Ian - that looks like actual work! Glad you had a productive night, and get to do a lot more of these. ;D

[lunator]

I measured the star STF 196 CD.

I

Using Mean figures

PA 5.90

Sep 220.5"

Average 1

PA 5.20

Sep 225.9"

Average 2

Gave errors on the calculation

I calculated the PA was 5.9 and the Seperation was 220.5".

Cheers

Ian

I can see what you did, but, but, but, Ian - that looks like actual work! Glad you had a productive night, and get to do a lot more of these. ;D

Cheers WH

Believe me when I say from my light polluted back garden this is less like work than looking for faint fuzzies.

Cheers

Ian

[lunator]

Ian

Do you have a reticule EP that you use to measure the transits, or do you measure from one side of the EP to the other?

What do the timings show (e.g. laptimes between two points) ?

Hope you don't mind the q's!!

Daz

No i don't have a reticle eyepiece. (£150 for the eyepiece beyond permissable expenditure at present) and I would need to motorise the mount for it to work.

The theory goes something like this.

A star of a given declination will transit a given fOV in a fixed amount of time. If I know the primary stars declination and the size of the FOV in arc seconds I can work out the position angle and seperation of the secondary star.

You use the lap timer to take the 4 measurements.

the 1st is always 0.00 as this is when the primary enters the field of view. The second time is taken when the secondary enters the FOV. The third timing is when the either the primary (or secondary) leaves the FOV and the fourth is when the secondary (or primary) leaves the FOV.

Using these 4 number you can calculate the position of the secondary from the primary by working out how far from the centre of the FOV they are during the transit. This give you the basic difference in declination and RA.

Using Pythagoras (X sq times Y Sq = Z sq) allows you to work out the PA and seperation.

Cheers

Ian

[GazOC]

Ian,

Does the primary have to go through the middle of the FOV?

Gaz

[GazOC]

Damien,

Either I'm not understanding properly or Ian isn't using triangulation (could be either one really!!) You can't triangulate from one point, surely?

Gaz

[daz]

Gaz sort of asks the next one....

HJow do you measure the distance from the centre of the FOV?

[lunator]

Gaz

No the primary can go through any part of the FOV.

I think the easiest way is to take the STF 196 CD as an example. This should explain it better than I ever could.

The mean timings for the stars crossing the FOV are

Primary 0.00/ 35.8 seconds

Secondary 8.9/30.1 seconds

To work out the difference in right Ascension (RA) is delta PA = b1+b3/2 - A1+A2/2 so 30.1+8.9/2 - 0+35.8/2 = 19.5 - 17.9 = 1.6

To work out the difference in declination we need to work out the angles as the star enters & leaves the FOV this is given by equation

7.5205cos Primary dec (a2-a1)/fov(Radius)

SinYa is given 7.5205cos20.5954(35.8-0)/252.5= 0.998 so Ya = 86.5

Sin Yb 7.5205cos21.0331(30.1-8.9)/252.5 = 0.59 Yb = 36.1

To work out how far the stars were from the centre of FOV you use the equation

FOV (radius) CosYa (or Yb)

252.5cos86.5 = 15.4

252.5cos36.1 = 204

Because on star passes north of the centre line & one South you add these together so 219.4 arc seconds.

To turn the RA figure into arc seconds by taking the following equation

1.6x 15.0411 xcos 20.0143 (this is the mean declination of the 2 stars) = 22.47 arc seconds. (this is why neither star has to go throught the centre of the field)

The equations to give the PA and seperation are

PA theta Tan-1 (22.47/219.4) = 5.9 degrees

Seperation = square root of 22.47sqd+219.4sqd = 220.5 arc seconds.

I hope this is a bit clearer.

Cheers

Ian

[GazOC]

Ian,

I havn't had a proper look yet but I can see what I thought might have been estimation of the centre of the FOV is taken care of by Cos/Sin which figures....

Whats the reason that you use the mean declination instead of one for each component? Is it "good enough" or wouldn't it make any difference?

Gaz

[GazOC]

I wouldn't say they were the same thing, triangulation is an application of trigonometry and don't think it's being used here? I'm sure Ian will enlighten us....

[daz]

Blimey!!

Can you clarify

7.5205cos Primary dec (a2-a1)/fov

for me, as I can't see where the 7.5205 comes from, or how the expression should be evaluated (probably me being a bit thick!)

This is great!!!!

[GazOC]

I think we'd be better of getting into variable star stuff Daz...

As 7.5205 is mentioned in both expressions it may be a constant rather than a computed value?

[daz]

This should be easy for you Gaz

I agree it is a constant - just wondered what and where it came from....

Sad as it seems, I LOVE this sort of stuff!!!

[GazOC]

Easy? I learnt the bare minimum of maths to pass my degree (and bought a programmable calculator!!)

[daz]

Easy? I learnt the bare minimum of maths to pass my degree (and bought a programmable calculator!!)

:lol:

I used to have a decent Ti one that I wrote a Decimal to Binary converter on... :?

[lunator]

This should be easy for you Gaz

I agree it is a constant - just wondered what and where it came from....

Sad as it seems, I LOVE this sort of stuff!!!

Daz, Gaz

The figure is a contant.

You convert time seconds into arc seconds by multipling by 15.0411. (and the cos of the declination)

The 7.5205 is half this figure. I guess you use this figure as the calculations are based on the field radius and not the field diameter.

[daz]

Thanks Ian

Next bit then :- Have figured out how to calculated those two expressions, apart from the Sin bits! I can't get from 0.998 to 86.1 - what have I missed / not going??

The rest, I think, makes sense (you'll be glad to hear!!), oh apart from the statement that you add the two values to give you a total of arc seconds, because one star was above the centre line and one was below. Could you just clarify this a bit more.... I mean do you plot the stars on the chart (as per your sketch) for this bit.......

Thanks mate

[Astroman]

T4U: You are talking about "Paralax" measurements. Both Ian's double star measurement and paralax uses trigonometry to solve for the desired answer, but Ian's uses the diameter of his FOV in arcseconds while paralax uses the diameter of the orbit of Earth as the "base measurement". Ian's is using the time it takes a star to cross his FOV and extracting the difference in RA/Dec to get the observed distance from each other. Paralax measures the position of a "nearby" star against the background stars at one time of the year and compares it to the position exactly 6 months later. It's the same as holding your finger at arm's length and observing it with first one eye, then the other. The finger will appear to have shifted against the background. You can measure these two distances and using trig calculate how far away they are. This method is good to about 50 LY.

I hope this helps.

[lunator]

T4U: You are talking about "Paralax" measurements. Both Ian's double star measurement and paralax uses trigonometry to solve for the desired answer, but Ian's uses the diameter of his FOV in arcseconds while paralax uses the diameter of the orbit of Earth as the "base measurement". Ian's is using the time it takes a star to cross his FOV and extracting the difference in RA/Dec to get the observed distance from each other. Paralax measures the position of a "nearby" star against the background stars at one time of the year and compares it to the position exactly 6 months later. It's the same as holding your finger at arm's length and observing it with first one eye, then the other. The finger will appear to have shifted against the background. You can measure these two distances and using trig calculate how far away they are. This method is good to about 50 LY.

I hope this helps.

I couldn't have put it better myself.

Thanks Astoman 8)