7 replies to this topic

[Marcin_78]

I was toying with the site ssd.jpl.nasa.gov/horizons/app.html#/ again and in a spreadsheet I made a chart for angular size cycles for Jupiter, Mars and Saturn rings in the years 2023-2075. Each cycle is represented by 3 parts: opposition + two solar elongations of 60 degrees.

 

By opposition I mean the biggest solar elongation in each cycle (on the NASA site the solar elongation never reaches 180 degrees – it's probably calculated for 3 dimensions, not just 2).

 

I calculated each size of the Saturn rings as 2.2x angular size of the plain Saturn. The rings are actually slightly bigger than this, but I didn't want to overstate them.

 

The results are quite interesting (click to enlarge):

 

 

Here's a chart only for the years 2023-2036, so it's easier to see some details:

 

 

The charts confirm my (short) personal experience and what I've read on the net (including this forum) about observing planets in the long run, but there are also some surprising cases:

 
1. Mars is usually very small and disappointing. Oppositions are rare. The best oppositions are very rare.
2. Jupiter is clearly the best when close to opposition. When it's far from opposition the Saturn rings are often bigger.
3. Saturn, as far as the rings are concerned, is always “good enough”, even far from opposition. The best oppositions are very rare, but they are not all that different from average oppositions.
4. In some years (most notably in 2064) the size of Jupiter at opposition is smaller than the size of Saturn rings at Saturn opposition.

 

If anybody is interested, below there are screenshots how I gathered the needed data. I chose a location as close to my location as possible, but it's not really important as far as angular sizes of planets are concerned.

 

 

 

In order to identify oppositions and solar elongations of 60 degrees and then to combine the results into one chart I had to come up with some specific spreadsheet formulas, but to me it was fun.

 

Clear skies!

Edited by Marcin_78, 30 March 2024 - 08:13 AM.

[johnfgibson]

The jaggedness of the plots is unnatural. They should be smooth, since they represent the motions of planets evolving continuously in time under a smooth sum-of-inverse-square law. 

 

Did you use a time interval of six months to make the plot? Can you do it again with a one-month interval? Or a one-week interval?

 

If you can't change the interval you could send me the time series data and I can interpolate it with a Fourier series. 10 to 1 it'll change some of your conclusions about the relative sizes of Jupiter and Saturn's rings.

Edited by johnfgibson, 30 March 2024 - 09:43 AM.

[Marcin_78]

The jaggedness of the plots is unnatural. They should be smooth, since they represent the motions of planets evolving continuously in time under a smooth sum-of-inverse-square law. 

 

Did you use a time interval of six months to make the plot? Can you do it again with a one-month interval? Or a one-week interval?

 

If you can't change the interval you could send me the time series data and I can interpolate it with a Fourier series. 10 to 1 it'll change some of your conclusions about the relative sizes of Jupiter and Saturn's rings.

Theoretically I could do 1 day interval, but for as many as 53 years (2023-2075) that would mean 58035 different positions on the chart (53 * 365 * 3 planets, not counting the additional days from the leap years). My chart for the 53 years was made out of only 373 positions (153 for Saturn, 146 for Jupiter and 74 for Mars).

 

The idea to represent each cycle by only 3 parts (interval of 120 degrees of solar elongation angle) was aimed at limiting the amount of data needed to draw a chart, but the end result is quite similar to a day-by-day chart:

 

 

The ignored/flattened part of each cycle (the bottom part) is the least important one because a planet is very small then anyway.

 

My conclusions about the relative sizes of Jupiter and Saturn's rings wouldn't change even if I used a smooth chart.

Edited by Marcin_78, 30 March 2024 - 11:46 AM.

[MikiBee]

Theoretically I could do 1 day interval, but for as many as 53 years (2023-2075) that would mean 58035 different positions on the chart (53 * 365 * 3 planets, not counting the additional days from the leap years). My chart for the 53 years was made out of only 373 positions (153 for Saturn, 146 for Jupiter and 74 for Mars).

 

The idea to represent each cycle by only 3 parts (interval of 120 degrees of solar elongation angle) was aimed at limiting the amount of data needed to draw a chart, but the end result is quite similar to a day-by-day chart:

 
Jupiter 2023-24.jpg

 

The ignored/flattened part of each cycle (the bottom part) is the least important one because a planet is very small then anyway.

 

My conclusions about the relative sizes of Jupiter and Saturn's rings wouldn't change even if I used a smooth chart.

Nice work, but I think it would be worth smoothing the curves by having more data points. I am sure you don't need to do any manual inputs, it all comes from these publicly available datasets. There are a few good raw data sites out there. Often, I do similar stuff as I love visualizations...

[MikiBee]

This is some of my work, a 12 year cycle of Jupiter oppositions. A couple of perihelic oppositions of Jupiter are behind us, now Big Jove will get smaller at oppositions for the next few years...

 

Edited by MikiBee, 30 March 2024 - 01:12 PM.

[Mark Gingrich]

 

3. Saturn, as far as the rings are concerned, is always “good enough”, even far from opposition. The best oppositions are very rare, but they are not all that different from average oppositions.

Yes, but Saturn's rings effectively vanish -- irrespective of their angular width -- on those occasions when Earth crosses the ring plane.  The particular dates within your chosen time span are as follows:

 

23 March 2025

15 October 2038

2 April 2039

9 July 2039

5 May 2054

31 August 2054

1 February 2055

25 August 2068

 

... which I've unabashedly snitched from Jean Meeus's Astronomical Tables of the Sun, Moon and Planets, 3rd edition, page 60.

[Marcin_78]

OK, I prepared smooth charts, with intervals of 10 days and no solar elongation cutoff.

 

 

The 10-day intervals mean that in the worst case I missed an opposition by only 5 days.

 

This time I also included the whole year 2075 (previously I accidentally set a limit for the X axis at the value 2075 instead of 2076, so the last year was lost).

 

Click to enlarge.

 

 

 

The better charts are surprisingly similar to my previous charts even at the bottom parts of the cycles. Even the asymmetrical bottom parts for the Mars cycles were roughly correct.

 

This chart for the 53 years was made out of exactly 5808 positions (1936 days * 3 planets). The number of days is equal to the number of data lines in my spreadsheet, but it can be calculated this way:
(53 years * 365 days + 13 additional days from leap years) / 10 days = 1935.8

 

The number 1935.8 has to be rounded up because the first date of the chart is 2023.01.01, not 2023.01.10.

Edited by Marcin_78, 01 April 2024 - 05:45 AM.

[MikiBee]

OK, I prepared smooth charts, with intervals of 10 days and no solar elongation cutoff.

 
Horizons System - 3.jpg

 

The 10-day intervals mean that in the worst case I missed an opposition by only 5 days.

 

This time I also included the whole year 2075 (previously I accidentally set a limit for the X axis at the value 2075 instead of 2076, so the last year was lost).

 

The better charts are surprisingly similar to my previous charts even at the bottom parts of the cycles. Even the asymmetrical bottom parts for the Mars cycles were roughly correct.

 

This chart for the 53 years was made out of exactly 5808 positions (1936 days * 3 planets). The number of days is equal to the number of data lines in my spreadsheet, but it can be calculated this way:
(53 years * 365 days + 13 additional days from leap years) / 10 days = 1935.8

 

The number 1935.8 has to be rounded up because the first date of the chart is 2023.01.01, not 2023.01.10.

Great work, Mars oppositions are of special interest considering its highly elliptical orbit. It's really cool to see that Mars' perihelic oppositions sometimes come in pairs as it happens in the 2060's.

 

Years ago I analyzed various periodicities of Mars' synodic revolutions but cannot find my visual. I vaguely remember something like 78 years. Maybe another set of perihelic oppositions added to the first chart would "uncover" that...

Edited by MikiBee, 01 April 2024 - 07:34 PM.