# Calculating distance of comet C/2019 Y4 (ATLAS)

SO, I decided I would take some pictures of the comet C/2019 Y4 last night. Afterwards, I thought I would try and do a rough estimation of distance based on my observations. I don't have any fancy measuring tools, so a few approximations were made, but my result was way off. I've clearly done something wrong and was hoping someone could point out where I have gone wrong and correct me.

So, I basically layered my first picture over the second in photoshop and marked the start and end position over the course of 1 hour.

I apologise for the poor photo, the exposures were short and I haven't done any processing as I was only interested in the position.

So,to me, it looks like it has moved approximately he same distance as the 2 stars to the right. These are TYC 4360-0254-1 and TYC 4360-1679-1 according to Sky Safari Pro.

I used the measurement tool in the app to measure the distance in arc-minutes, which gave me 1'55.1"

I converted this into degrees using Google, which gave me 0.0258333333 degrees.

I then decided to work out the approximate distance between my start and end points by using my latitude to work out the speed the earth was rotating (cos(latitude) x 1670) which I found HERE.

My latitude is approx 50.82N, so I got my speed at 1055.04km. I used that as a distance. I now have a triangle with a base of 1055.04km and a top angle of 0.02583 degrees.

I turned this into a right-angle triangle by putting a line down the middle. I can now work out all 3 angles. I have 90, 0.010129 (half the original angle) and 89.987 (90-0.010129) I also have an opposite, adjacent and hypotenuse. I only know the adjacent which is half my original distance (527.52km), and I want to find the Opposite.

Using SOHCAHTOA, I can say tan(89) = opp/adj, thus opp = 527.52 x tan(89.987) which gives me 2,324,974.545km.

Sky safari gives a distance of 153.1 million km.

So where did I go wrong? Was it because of poor approximations? I know that the linear distance for the adjacent side isn't quite accurate because of earth curve, and I know the comet was also moving, and I know my measurement of the start and end position wasn't too accurate, but I was hoping to at least get within 10%, so I think I must have gone wrong somewhere in my method, rather than poor approximations.

I do hope I have put enough effort in for this to be considered a good question. I have tried re-measuring and double checking, but if there is any other info people need, then by all means, ask and I'll do what I can

EDIT

Because of the comment by barrycarter, I realised I had forgotten the movement of earth itself. As this is approximately 107207km/h, I included this in my calculations and ended up overshooting and getting 238,577,507km.

So, I made tiny adjustments to my parallax angle, and if I change this slightly, then I get very different answers.

Based on that, is it possible my crude measurement of the parallax angle is to blame?

• I cant help with the question, but it's nice to see people having a go at things like this. Plus, I think it's a well written question, easy to understand and follow. I hope you get an answer as I'd be interested to try this myself! Commented Apr 7, 2020 at 14:34
• Try using HORIZONS (ssd.jpl.nasa.gov/horizons.cgi) to verify your positions as a start. Also remember the Earth revolves around the Sun at about 100,000 km/h (if I did the math right), which may be a much bigger factor.
– user21
Commented Apr 7, 2020 at 15:03
• @barrycarter Ahhh! I forgot to include the movement of Earth too! but would it make much difference? I also just need distance travelled, rather than knowing my exact start positions
– MCG
Commented Apr 7, 2020 at 15:16
• @barrycarter I took your comment into account and have updated the question
– MCG
Commented Apr 7, 2020 at 15:30
• To answer your last question, yes. Remember that tangent grows very rapidly near 90 degrees (to infinity), so even small errors in measurement can lead to large changes in value. I believe there was a Greek astronomer who did the exact same thing and miscalculated the distance to the moon
– user21
Commented Apr 7, 2020 at 16:13

It appears that you are doing a simple parallax calculation, using a baseline obtained from the Earth's rotation over an hour. You appear to be neglecting the most significant change, the motion of the comet.

If you plot the position of C/2019 Y4 in SkySafari, you will see that around this date the comet's location against the star background shifts about 37 arc minutes per day, or a bit over 1.5 arc minutes per hour. The location is based on the orbital elements of the comet (MPEC 2020-C76), but also includes the effect of the Earth moving in its orbit, as mentioned in the comments.

There is no simple way of determining the distance of a solar system object from two position measurements alone. A rough estimate of the orbital elements requires at least three position and time measurements; the MPC orbital elements referenced above are based on many observations over several months.

• I did mention that I know the comet is also moving, but I thought over the time of an hour it wouldn't have so much of an effect to put me too far off. If you look at my edit, I did take the comet into accoutn and re-calculate
– MCG
Commented Apr 7, 2020 at 18:08
• Saying that, +1 for the tips on how to get better measurements. I was just seeing if I could do it!
– MCG
Commented Apr 7, 2020 at 18:11
• I don't know how you tried to compensate for the comet's motion, but if you are still doing a parallax calculation, where is the apex of your triangle? Commented Apr 7, 2020 at 19:18
• I didn't compensate for the comet's motion. I was hoping over the course of an hour at that distance it wouldn't make too much of a difference. The Apex I suppose would have been the location of the comet during the first observation
– MCG
Commented Apr 7, 2020 at 20:24
• Ok. I was responding to your comment that you "took the comet into account and re-calculate." Knowing the correct distance from SkySafari, you can check that the actual parallax is about 2 orders of magnitude smaller than the comet motion you neglected. Commented Apr 7, 2020 at 21:21

The issue that you have is that

1. You are moving. The biggest component of your velocity is the orbit of the Earth around the sun (about 30km/s). The Earth is also rotating, and this, of course makes all the stars move across the sky, but they all move together. Your motion due to the rotation of the earth is probably less than 0.3km/s
2. The comet is moving. It is in an elliptical orbit around the sun and is moving at orbital speeds (10s of km/s)
3. You only have two observations and they are very close together in time.

Because the comet is moving at a similar speed to the Earth, you would need to determine the orbit of the comet, you can't find only its distance. Orbital determination requires a minimum of three observations, and for most mortals, you need a software package to do the calculations for you (unless you are Carl Fredrick Gauss, of course)

To accurately determine the orbit you should get a series of observations over a longer period of time and use something like find_orb to determine the orbit.

• Thanks for the response. I was able to get within 10% once I decided to do pixel counting between the stat and finish position of the comet and take the angular separation from that. So I'm gonna take it as a win there! I understand I'll never get it accurate, but was hoping to get something approximate. I know there were a lot of things I didn't factor in, which I did try to make clear in the post, but I hoped they wouldn't make a huge difference
– MCG
Commented Apr 7, 2020 at 18:13
• Unfortunately, England doesn't have clear skies too often so these opportunities to do this are few and far between!
– MCG
Commented Apr 7, 2020 at 18:14
• Same here. I have only had two decent views of C/2019 Y4, and one observation where I might have barely seen it, in the past month. Last night was hazy with a near full Moon, so there was no chance. Commented Apr 7, 2020 at 21:25