Visibility of solar flaring region from Jupiter

[SmartKB]

I numerically calculated the following numbers with an error of 1 degree.

The geocentric longitude of the Sun on 25 November 1999 at 00:00 UT was 243.52 degrees.

On this date, from sunspot number 8771, an M2.0 class of flare started occurring at 18:59 hours and ended at 19:29 hours. This sunspot was located at S15W40.

On this date, the ecliptic longitude of Jupiter was 32.92 degrees and its geocentric longitude was 26.20 degrees.

I would like to know whether the solar flares from the flaring region be visible from Jupiter.

Help me to understand the geometry of the alignment of the location of the sunspot 8771 w.r.t. the Jupiter.

[Philalethes]

At such distances, you can essentially treat the visible disk of Sol as an orthographic projection (i.e. a perspective projection at infinite distance). To sanity check that assumption, let's use the geometry outlined in this StackExchange answer to get an idea of how much of the surface we'd be seeing at that distance:

Here R_% is the percentage of the area of the entire surface we see (the first term is a division by two since we can't possibly see more than half), r is the radius of the object we're looking at (1 Solar radius in this case), and H is the distance from the observer to the surface of the object. Using Skyfield and JPL's DE422 ephemeris, I get a distance from Jupiter to Sol of ~742 million km on that date, while the Solar radius is ~700,000 km; subtract the latter from the former to get H, so let's round H down to ~741 million km to be generous. Calculating this we find the area we see to be 49.95%, indeed virtually half the surface. If we repeat the same procedure from Earth, we get 49.76%, also practically the entire half we're looking at.

So, the reason for this assumption is that we can then essentially just offset by the longitudes in question (the Solar equator is somewhat tilted too, ~7.25°, but there's no need to account for that unless we find out that we're at an edge case). Now, what we want to find out is essentially the heliocentric elongation between Earth and Jupiter, i.e. the angle between the two as seen from Sol, because if the sum of this angle and the western longitude of the sunspot is smaller than 90°, then we can then conclude that the sunspot would be visible from Jupiter too (I assume you've already worked out more or less that Jupiter is slightly "behind" Earth in their orbits at that date).

To calculate this angle there are two options: either use the respective distances from Earth and Jupiter to Sol and use the law of sines to calculate the phase angle of Jupiter as seen from Earth, and then automatically you have the heliocentric elongation between the two since you already know the angle between the two (the difference in their longitudes, but note that you should use the ecliptic longitude here for both), or simply use something like Skyfield again as I will do to make those calculations simpler. If you were to do both you'd find a small difference due to Jupiter not being exactly at 0° of ecliptic latitude, but it's close enough; you should get an angle of ~30° (~29.4° when I use Skyfield, ~30.4° when using trigonometry and the distances).

That means that with the sunspot being ~40° W (Solar "west") and Jupiter being ~30° "behind" us in terms of heliocentric elongation, the sum of these two is roughly where Jupiter would observe the sunspot, i.e. at ~70° W, well within bounds of the visible disk, but nearing the limb.

As an addendum, here's a diagram of the situation; sizes are not to scale, but I tried to preserve some semblance of the relative distances of Earth and Jupiter:

Edited May 13, 2023 by Philalethes
updated diagram with projection + small correction

[SmartKB]

This is in continuation of the calculated numbers of the sunspot designated AR8771 for 25 November 1999 at 00:00 UT. 

I found that during 25-26 November 1999, AR8771 shifted from S15W40 through S15W51 (26 November 1999). The numbers worked out previously reveal that on 25 November, AR 8771 being at ~70 W can be seen from Jupiter.

On 26 November 1999 00:00 UT, the ecliptic longitude (Deg.) of the Earth was 62.283^o, of Jupiter was 32.831^o; and, the heliocentric elongation was ~29.5^o. Now, AR8771 as seen from Jupiter will be at ~80.5^o [29.5^o + 51^o], right?.

Since during 25-26 November 1999, the position of AR8771 as seen from Jupiter was ~70^o and ~81^o, and these numbers being less than 90^o, the discussion allows me to conclude that AR8771 is visible from Jupiter throughout the period (25-26 Nov.), right, thank you.

Edited May 30, 2023 by SmartKB
Changed 26 November 1999 to 26 November 1999 00:00 UT

[Philalethes]

6 hours ago, SmartKB said:

This is in continuation of the calculated numbers of the sunspot designated AR8771 for 25 November 1999 at 00:00 UT. 

I found that during 25-26 November 1999, AR8771 shifted from S15W40 through S15W51 (26 November 1999). The numbers worked out previously reveal that on 25 November, AR 8771 being at ~70 W can be seen from Jupiter.

On 26 November 1999 00:00 UT, the ecliptic longitude (Deg.) of the Earth was 62.283^o, of Jupiter was 32.831^o; and, the heliocentric elongation was ~29.5^o. Now, AR8771 as seen from Jupiter will be at ~80.5^o [29.5^o + 51^o], right?.

Since during 25-26 November 1999, the position of AR8771 as seen from Jupiter was ~70^o and ~81^o, and these numbers being less than 90^o, the discussion allows me to conclude that AR8771 is visible from Jupiter throughout the period (25-26 Nov.), right, thank you.

Yeah, that sounds about right to me; even though Earth orbits faster than Jupiter, the rotational speed of Sol will dominate, so over the course of just a single day there's not going to be much of a difference. You can also reference e.g. this diagram to get a sense of how much rotation takes place per day at a given latitude, that way you don't need to account for the longitude as seen from Earth on the second day:

At a latitude of ~15° S we'd thus expect a movement of ~14.4° per day, so the stated change of ~11° seems plausible; I see in the archive that that is indeed what was registered, and I'd guess the difference is mostly due to how the position of the region is determined from day to day (just a couple of days later its longitude increased 15° in a single day, so it definitely varies). Earth's orbit will also account for ~1° per day of difference.

From Jupiter I would guess that on the second day (November 26) the overall movement of the region would likely be a bit further along than assumed, i.e. closer to the expected movement of ~14.4°, and thus would be closer to around ~84° W. Here I've overlaid a grid based on that day on the image from the archive to see more precisely where the different parts of the region was located:

Each blue line here is 10°, with all the smaller lines representing 1° each. As you can see the estimated 40° W seems to be somewhere around the middle of the two spots. Then we look at the day after:

In fact, I would argue here that the middle point between the two spots that define the region has clearly shifted more than 11°, as the middle seems to be around ~53° rather than 51°. If you just look at e.g. the center of the large spot on the left you also see that it moves from ~35° to ~48°, in agreement with this. So the region seems to have shifted ~13°, which is very close to what you'd expect at that latitude as seen from Earth (~14.4° - ~1° = ~13.4°).

Since the orbital period of Jupiter is 11.86 times that of Earth (~11.86 years), then that single degree would be 0.084 degrees instead, which is negligible; thus the middle of the region would likely be around ~84° W as mentioned earlier. Note however that the spot on the right would be virtually at the limb, at ~89°, so it would be less visible. The left spot would be at around ~79°. I haven't looked at the details of the flares in question, but even at the limb flares from the region would most certainly be possible to see.

For comparison you can e.g. look at 3110 that had an M-flare a couple of hours ago, which is located at ~89° W now. As you can see from the images above the longitudes between 80-90° aren't that readily visible, but it's possible to make them out, and flaring from there is typically clearly visible.

Edited May 30, 2023 by Philalethes
clarification

[SmartKB]

This is still in continuation of the previous clarifications.

On November 26, 1999, from AR8778 (located at S14E10) arise an M-class 6.0 flare at 1338 hours and continued up to 1348 hours.

On this date (November 26, 1999 13:38 hours), the heliocentric ecliptic coordinates of the Earth was 63.853 degrees at r = 0.987 A.U.
Heliocentric ecliptic coordinates of the Jupiter was 33.016683 degrees at r = 4.961 A.U.

On this date, the percentage of the Sun seen from the Jupiter is 49.953%; seen from the Earth is 49.998%; and, thus, during this instant also, we can see almost the entire half of the Sun from both the Jupiter and the Earth.

However, the heliocentric elongation being 30.836 degrees (say, approx. 31 degrees) and AR8778 being located at S14E10 means that this AR will be located beyond the disk, and, hence, won't be visible from the Jupiter and the Earth as well, right?

[Jesterface23]

This would of been the view of region 8778 from Jupiter,

[Philalethes]

6 hours ago, SmartKB said:

This is still in continuation of the previous clarifications.

On November 26, 1999, from AR8778 (located at S14E10) arise an M-class 6.0 flare at 1338 hours and continued up to 1348 hours.

On this date (November 26, 1999 13:38 hours), the heliocentric ecliptic coordinates of the Earth was 63.853 degrees at r = 0.987 A.U.
Heliocentric ecliptic coordinates of the Jupiter was 33.016683 degrees at r = 4.961 A.U.

On this date, the percentage of the Sun seen from the Jupiter is 49.953%; seen from the Earth is 49.998%; and, thus, during this instant also, we can see almost the entire half of the Sun from both the Jupiter and the Earth.

However, the heliocentric elongation being 30.836 degrees (say, approx. 31 degrees) and AR8778 being located at S14E10 means that this AR will be located beyond the disk, and, hence, won't be visible from the Jupiter and the Earth as well, right?

The conclusion there doesn't sound quite right. As Jesterface shows above, you see roughly where the region would be located. Making the same simplifications as above, consider how the AR would look to be at 10E from Earth (i.e. clearly visible, slightly to the left of the central meridian by 10 degrees), and thus if Jupiter is ~31° behind us in orbit, then the same region would appear around 21W (i.e. to the right of the central meridian by ~21 degrees, as roughly seen in the above image).

So the region would be visible from both Earth and Jupiter, and not beyond the disk.

[SmartKB]

The following URL's provide the view of the Sun with overlay of the latitude/longitude grids. The previous discussions along with the images available, as follows, have helped me to understand the scenarios.

The AR on November 25, 1999 is available at: https://www.solarmonitor.org/full_disk.php?date=19991125&type=ysxt_flter&indexnum=1

The AR on November 26, 1999 is available at: https://www.solarmonitor.org/full_disk.php?date=19991126&type=ysxt_flter&region=

Thank you all for your generous time and availability.