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Mathematical Possibility


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I pose a question to all those who have learned their numbers, lol. Is it possible to calculate the distance of an object by timing how long it takes said object to move from field stop to field stop? with a particular scope/eyepiece combination. Having said that, would a planet cover the distance faster than a much more distant object? I am aware that the movement is due to earths rotation but, technically a much more distant object should move slower across the field of view, no?. Nothing save for an event horizon itself is beyond mathematical explanation, just in my case, beyond my mathematical ability. There must be a way, I think.

Considering it is now 2:30am across the pond, whomever responds to this, I’m sorry for interrupting your observing session 🤣

Edited by Sunshine
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Before I go to bed I'd say probably not because, as you say the movement you see is from the earths rotation.   To check the difference between a planets movement and a stars, I used Stellarium.  I selected Mars and told Stellarium to keep the selected object in the centre of the screen.  Fast forward the time and days whizz by with not a lot of movement between Mars and nearby stars.   A fun way to spend two minutes!

You could use your idea to calculate how fast the earth rotates - my guess is once per day 😂😂

Michael

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As @Synchronicity says the motion is due to the earths rotation so to a very good approximation is constant for most astronomical objects. Objects close to the Earth with high relative motion (satellites, moon) would show measurable difference but, it is not a simple distance relationship.

Regards Andrew 

PS changes in the earths rotation rate is measured against the positions of distant quasars. 

Edited by andrew s
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  • 3 weeks later...

Well, it should be possible if you calculate a bit more then just the movement on one night.    Over a longer period, and with some very very delicate equipment, you have to be able to make a sort of estimation.   But you’ll need some comparable objects incl their data.  Its also late here, and english is not my main language, so sorry if it all sounds a bit off

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The movement across your field of view is due to the earth's rotation, well, 99-point-a-lot-of-nines percent is. You're also assuming that the distant object is not moving and nor are you (i.e. the earth is only spinning on a fixed spot), neither of which is true in astronomical settings. Not to mention the fact that to remove the earthly-rotation component you'd need to know that to a very high level of precision in addition to measuring your transit time to very high precision. Unfortunately, it's all gone way beyond the possible. A needle in a haystack would be trivial, in comparison. That's my take, anyway!

Edited by wulfrun
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On 27/09/2020 at 03:25, Sunshine said:

Is it possible to calculate the distance of an object by timing how long it takes said object to move from field stop to field stop?

No, this is similar to perspective. What you'll be measuring is angle and objects of a different size will subtend same angle if they are at different distance. For this reason there is no way of knowing the distance if you have only angle.

There are things in astronomy that can be calculated by using similar principle - like transits of bodies - using first, second, third and fourth contact you can calculate things. You can also estimate the distance to the galaxy if you know the type and angular size in the sky.

On 27/09/2020 at 03:25, Sunshine said:

Having said that, would a planet cover the distance faster than a much more distant object?

Due to rotation of the earth - no, both "move" at the same rate. Due to proper motion - sure, but again that depends on speed of object.

Object twice as far away moving at twice the speed will again subtend the same angle (as it will cross twice the length).

 

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13 hours ago, Robindonne said:

Well, it should be possible if you calculate a bit more then just the movement on one night.    Over a longer period, and with some very very delicate equipment, you have to be able to make a sort of estimation.   But you’ll need some comparable objects incl their data.  Its also late here, and english is not my main language, so sorry if it all sounds a bit off

This is in effect what was done in transit instruments but rather than measure the edge to edge transit times they initially used a cross wire defining the center of the field of view to time transits.  

Regards Andrew 

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  • 3 weeks later...

If you had a planet with a distant star lined up immediately behind it, then due to parallax, as the earth turned slightly the apparent position of the planet would change more then the position of the star, and the star would peep out from behind the planet.  However the distances are so great and the angles so small that it would be very hard (impossible??) to measure.  However the parallax effect of the earth going round the sun can certainly be used to measure stellar distances.

 

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On 27/09/2020 at 03:25, Sunshine said:

I am aware that the movement is due to earths rotation but, technically a much more distant object should move slower across the field of view, no?

Mars sometimes moves retrograde, sometimes like the other planets. Polaris won't cross the EP at all...

Olly

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On 27/09/2020 at 02:25, Sunshine said:

would a planet cover the distance faster than a much more distant object? I am aware that the movement is due to earths rotation but, technically a much more distant object should move slower across the field of view, no?.

No.  I think you are confusing the apparent movement of an object across the eyepiece due to the earth's rotation with change in the apparent position of nearby and distant objects with a change in observing location (parallax). You can demonstrate the difference with your finger held out  in front of your face. If you focus on your finger and rotate your head so your finger moves across the field you will see the finger stays in the same position relative to objects in the distance. If you move your head from side to side though the finger moves relative to the distant object.

The observed change in position of a fixed object with time from one side of the eyepiece is almost entirely due to a change  in the viewing angle, not due to the effect of a change in viewing position (parallax).  eg , if a planet is at the same position as a distant star at one side of the eyepiece, they will still be at the same position relative to each other when they get to the other side of the eyepiece field to a degree of precision you could possibly expect to measure, (ignoring any effect of the relative orbital motion of the earth and planet). 

In parallax measurements you change your viewing location significantly relative to the nearer object (eg from one side of earths orbit to the other) and then the relative position of  nearby and distant objects does change.

Robin

Edited by robin_astro
clarity
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