How can I estimate the motion of Pluto using telescope and camera observations?

In summary, the conversation is discussing the process of estimating the motion of Pluto using a telescope and camera. The main points include the use of the image scale of the telescope and the resolution of the camera, the calculation of resolution using the equation \theta=\frac{1.22\lambda}{D}, and the comparison of the measured distance with the resolution limit to determine if Pluto's motion is resolved. There is also a discussion about using a ruler or image overlay to measure the distance moved by Pluto, and a question about the dimensions of a galaxy in a picture taken by the telescope.
  • #1
big man
254
1
Hi guys,

I've been having trouble with this problem and would appreciate just some direction to assist me.

I have to estimate the motion of Pluto in "/hour from observations given that the telescope is a 14inch f/11 with an AP7 CCD camera with pixels 24microns on a side.

Now we have two pictures of Pluto at epochs separated by a little more than half an hour. I assume that since the resolution of the camera is given you'd have to measure something on the picture. The other though I had was that you would need to find the image scale of the telescope (which I've done).

Image scale = [tex]d\theta/ds[/tex] = [tex]206265/F[/tex] = 52.7" per mm.

Where F is the focal length determined by the formula f=F/D.

I swear I have to use the image scale of the telescope and the resolution of the camera together to get any further in this problem, but like I said I don't really have a clue.

Thanks for any help you might be able to give
 
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  • #2
big man said:
I swear I have to use the image scale of the telescope and the resolution of the camera together to get any further in this problem

I'm not sure why you think you would need the resolution to get the answer. If the separation of the object in the two images is greater than your resolution limit, then all you should need is the image scale and a ruler.
 
  • #3
well haha like I said I didn't really have any idea. I just thought that since he gave us the information on the camera we would somehow need to incorporate it into the calculation. So then would I just find the distance moved by Pluto on the picture in maybe 40 minutes and then multiply that by the image scale?
 
  • #4
big man said:
well haha like I said I didn't really have any idea. I just thought that since he gave us the information on the camera we would somehow need to incorporate it into the calculation. So then would I just find the distance moved by Pluto on the picture in maybe 40 minutes and then multiply that by the image scale?

Don't forget that you want the rate of motion, not the absolute motion (i.e. you have to divide by the time interval).

I suppose you could calculate the resolution and compare to the separation you measure to verify that it's beyond the limit. It should be obvious from direct comparison of the images, however.
 
  • #5
yeah sorry my phrasing wasn't too good there, I meant the rate of motion when I said the distance traveled in 40 minutes.

Thanks again for your explaining this stuff to me.

It takes me a little longer than most people to understand this Astronomy stuff haha : )
 
  • #6
Wait sorry for re-opening this Spacetiger, but I was just looking at the images and you can JUST see Pluto move a little. Sorry I thought I remembered it being more pronounced than that, but it is a very small movement. It's maybe a millimeter if you're lucky, but that estimation has a great deal of uncertainty...
 
  • #7
big man said:
Wait sorry for re-opening this Spacetiger, but I was just looking at the images and you can JUST see Pluto move a little. Sorry I thought I remembered it being more pronounced than that, but it is a very small movement. It's maybe a millimeter if you're lucky, but that estimation has a great deal of uncertainty...

Are you overlaying the images? If the apparent motion is noticably larger than the background stars, then it's probably resolved, but again, you can just do the calculation and see for yourself. Do you know the equation for calculating resolution?
 
  • #8
I'm actually blinking the images using the CLEA software we have, but they could easily be overlayed.

I've attached one of the pictures with Pluto circled so you can see what it looks like.

For the resolution of the camera wouldn't it just be the dimension of the picture divided the dimension of a single pixel??

ie Res = Dimension/(24*24 microns)
 

Attachments

  • PlutoC1.jpg
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  • #9
big man said:
For the resolution of the camera wouldn't it just be the dimension of the picture divided the dimension of a single pixel??

Pixel sizes are often chosen to roughly correspond with the resolution limit, but they don't determine it. Try this:

[tex]\theta=\frac{1.22\lambda}{D}[/tex]

where [itex]\lambda[/itex] is the wavelength of the light, D is the diameter of the telescope's aperture, and [itex]\theta[/itex] is the minimum angle that can be resolved.
 
  • #10
ahh k so you mean the smallest resolvable angle by the telescope.
Well I estimated it as 2.4*10^-6 radians (or 8.26*10^-3 minutes of arc) so yeah now I just compare that to the distance measured on the picture. Like you said it is obvious that it's resolved, but I guess it would be better to demonstrate it with the above calculation.

I was thinking that a better way to find the distance moved by Pluto would be to overlay the images and then use photoshop to find the x,y co-ordinates of pixels. Using that you can use the right-angle formula to determine the resultant change in position in terms of pixels and then multiple by 24 microns to get the distance moved. Can that be done or should I just use a ruler??

Thanks again for your assistance
 
  • #11
Just an additional question spacetiger and then this is it haha : )

I took a picture of a galaxy which is meant to be of size 10.2 x 9.5 arcmin (M74) and it fits perfectly in the middle of the picture taken by the ccd on the telescope. But the thing is the field of view of the telescope is 10 arcmin. So wouldn't the dimension with 10.2 arcmin be slightly truncated?

I've attached the pic.
 

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  • M74-R.jpg
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  • #12
big man said:
ahh k so you mean the smallest resolvable angle by the telescope.
Well I estimated it as 2.4*10^-6 radians (or 8.26*10^-3 minutes of arc) so yeah now I just compare that to the distance measured on the picture. Like you said it is obvious that it's resolved, but I guess it would be better to demonstrate it with the above calculation.

If that's the number, then your resolution limit is likely determined by atmospheric turbulence. Normal telescopes can't resolve below a few arcseconds.


I was thinking that a better way to find the distance moved by Pluto would be to overlay the images and then use photoshop to find the x,y co-ordinates of pixels. Using that you can use the right-angle formula to determine the resultant change in position in terms of pixels and then multiple by 24 microns to get the distance moved. Can that be done or should I just use a ruler??

Either way is fine.
 
  • #13
big man said:
I took a picture of a galaxy which is meant to be of size 10.2 x 9.5 arcmin (M74) and it fits perfectly in the middle of the picture taken by the ccd on the telescope. But the thing is the field of view of the telescope is 10 arcmin. So wouldn't the dimension with 10.2 arcmin be slightly truncated?

It's hard to say. Either number could be an approximation or misnormalization. I wouldn't worry about it.
 
  • #14
Thanks a lot for your help Spacetiger. I really appreciate it and now I know more about telescopes which is good :).

Thanks again
 

1. What is the estimated distance traveled by Pluto in one orbit around the sun?

The estimated distance traveled by Pluto in one orbit around the sun is approximately 7.5 billion kilometers.

2. How long does it take for Pluto to complete one orbit around the sun?

It takes Pluto approximately 248 Earth years to complete one orbit around the sun.

3. What is the estimated speed of Pluto in its orbit around the sun?

The estimated speed of Pluto in its orbit around the sun is about 17 kilometers per second.

4. How does the orbit of Pluto differ from the orbits of other planets in our solar system?

The orbit of Pluto differs from the orbits of other planets in our solar system in several ways. Firstly, it has a highly elliptical orbit, meaning it is more elongated and less circular compared to other planets. Secondly, its orbit is inclined, which means it is tilted at an angle compared to the rest of the planets. Lastly, Pluto's orbit is not in the same plane as the other planets, making it unique in its path around the sun.

5. How accurate are the estimates for the motion of Pluto?

The estimates for the motion of Pluto are constantly being refined and updated as technology and research progress. Currently, the estimates are considered to be highly accurate, with a margin of error of only a few kilometers per second. However, as our understanding of the universe continues to improve, these estimates may become even more precise in the future.

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