cubinator

I've reorganized my code to be a lot neater in general, and generate more useful information. Instead of storing every possible scenario, it runs the general occultation calculation in a function, and checks each time whether the error is the smallest it's seen. Only then does it append the data onto an array of scenarios. So I can run through 1 million combinations of parameters while only storing (and having to look at) 1400 progressively-smaller ones. This should allow me to run the calculation at a high resolution without worry of slowing MATLAB to a halt or generating gigabytes of garbage data. I've also added a couple new calculated parameters that should allow me to write an intuitive visualization of the occultation from all three locations that clearly shows the error in the calculation, and eventually could let you see the parallax with your own eyes! - if my math and our observational accuracy is good enough.

12 of them stacked together is a mile.

Looks like the front fell off. That is a big thing.

The issue I'm having with the errors is that they are out of order. For instance, at the rightmost low point on the latest graph, the errors are, in rad/1000: CA t2 -.2234 CA t4 .0608 MN t1 .1004 MN t2 .0212 MN t3 -.0044 MN t4 .0553 UK t1 .739 UK t4 -.6674 Some are positive, meaning the event is predicted later than observed, and some are negative, meaning the event is predicted earlier. Notice how CA t2 is negative and CA t4 is positive. t2 looks like this: And t4 looks like this: So if we are measuring the Moon-Mars center distance at those times, t2 will be smaller than 1 Moon radius (negative error) and t4 will be greater (positive error). Mars' angular size was estimated earlier to be around 20 arcseconds, which is around 0.1 rad/1000, close to the size of this difference in error. I need to implement a better estimate of Mars' angular size that takes into account the offset path behind the Moon and the variable Moon angular rate, and use that to estimate the error. I also need to make a code that, instead of saving every worthless value, only saves the 'good' sets of parameters as it's sweeping through. These changes should make it easier for me to find good estimates of everything, AND easier to make visualizations of the event - like the MS Paint drawings above, but with actual data! If I calculate the occultation path for each location, I might also be able to constrain the estimate to cases where Mars has the same angular size between all locations. Hmm, maybe I should look back at trying to find an analytical solution...

Update: It crawled to a halt as I expected it would. This is how far it got: It got through about 2% of one value of Moon distance. You can see it sort of shallow out a bit, but it's not enough to know if there's a better estimate elsewhere. I'll see what this data says. As you can see, there is a lot of calculation effort that is not ultimately needed.

I'm going to leave the code running at a high resolution overnight and see if it doesn't grind to a crawl. In the likely case that this doesn't magically produce all the answers, I will need to find a way to sort out the good tries from the bad.

I wonder what things they think should be improved for future extraplanetary rotorcraft, what weaknesses they see in Ingenuity after its resounding success.

I bet they'll be able to look at the pictures of the sampling event and figure out which rocks in it they picked up and which ones they didn't.

What an amazing sequence of hand-offs of the spacecraft! It's great to see it safe and sound.

That doesn't add up to me. A higher parachute deployment should result in a longer descent. Perhaps they mean the parachute deployed at 5000 ft at the time when they expected it to still be at 20000 ft? Without telemetry I can't say.

Fantastic landing!

I'd love to try to grab my own as it comes closer, but it looks like it'll be cloudy.

I think you can have some structure that bends and twists to orient itself. Radiation pressure from the star is plenty for attitude control on arrival.

I've just found out that my 3D printer prints everything about 1.5% too tall, which is pretty amusing.

The report itself lays out several concrete recommendations on how to use existing and already-planned infrastructure, such as Earth-observing satellites and aviation data, to gather actual scientific data on unidentified phenomena, and recommends implementation of a more standardized reporting system. I am imagining something similar to the meteor and satellite reentry reporting forms, one of which I once used myself to report an unusual group of high-altitude objects I couldn't identify.

Falcon 9 takes 40 minutes from start of fueling to launch. Is that faster than taking an average business jet across the gulf? They are even coming out with supersonic ones...

I'd be interested to hear about all the abiotic processes that can produce that molecule.

Thought this was for Starship for a second before the tweet loaded and nearly fell out of my chair.

Perhaps any life that is capable of crossing the intergalactic void at will is not quite 'as we know it'.

Relax, and enjoy the pretty spirals along the way. We might all be in elliptical galaxies by that time.

We will eventually fall into it anyway, as far as I know.

This is getting very exciting! I introduced Moon's distance and angular speed to the sweep, and have been repeatedly running it with tweaked ranges of values. I can minimize the upper limit of the error I see, but the lower limit of the error seems to keep hovering at about 0.065 degrees, no matter what I do! What I expect from this script is that the error between the two most distant locations will be around the angular diameter of Mars (which is a little smaller than the distance between the horizontal lines and zero). Since I'm plotting the sum of all the errors, it makes sense that the plateau might be around 8 times that size. I still need to do some work to try to find the best minimization of the individual observations rather than the sum, because some of these combinations of errors don't make much sense. However, it's good enough that I have numbers that I can start to crudely mash together: I take the physical distance between CA at its t2 and UK at its t4 as a baseline...(8931.7 km) I subtract the angular error between t4UK and t2CA...(0.0103 deg for the point on the left above and 0.00518 deg for the point on the right) and now I have Mars appearing in a different place in the sky between CA and UK. Divide baseline by sine of the error and... The point on the left says Mars is 49,786,510 km away, and the point on the right says Mars is 98,801,991 km away! Neither of these are quite correct, but the true value (82 million km, "what NASA wants you to think", etc.) is between these two, which is extremely promising!

Also, as a heads-up: There will be another occultation of Mars coming up on Sept. 16th! This one will happen during the daytime, and the Moon will only be a thin crescent, so if you're planning to observe this one, be VERY CAREFUL as the Sun will only be about 20 degrees away! If you accidentally look at the Sun through any unprotected magnifying equipment like binoculars or a telescope your eye tissue will come out of it looking like a fried egg! I'd recommend setting up such that you and all your equipment are in the shadow of a large building or structure to your west, so that the Sun only moves deeper into the shadow and you have no chance of pointing at it. This one's probably not so useful for making parallax measurements, as Mars is so much farther away, but it's an interesting chance to get to see a planet during the daytime. I'll probably set up if it's clear and maybe grab an angular size measurement if I can, but besides that I'll just sit back and enjoy the show!

This plot shows the deviation from observed conditions for scenarios sweeping over the Moon's 2D position in space, the Moon's direction of motion, Mars' position relative to the Moon, and Mars' direction of motion: That's 5 dimensions. The error displayed is obtained by measuring the angular distance between Mars and the Moon's center for each observer at their recorded times. This distance then has the Moon's angular radius (as observed) subtracted from it. The new value is added up between all of the observations. A value close to zero means Mars was very close to the edge of the Moon at all recorded times for that scenario. As you can see, there are not any very close scenarios in the above sweep. I think this is because of some differences in other Moon-related parameters currently kept constant. I have the Earth-Moon distance set at the value it was measured at in September 2018. As we know, the Moon moves around a bit, so it's quite likely it was at a different distance in December 2023. I think the bigger difference, though, is the angular speed of the Moon, which I have set as its average based on the sidereal period. When the Moon is close to Earth it speeds up, and when it is far it slows down, and according to Kepler's second law and orbital values from Wikipedia I calculated that the angular speed at apoapsis is 0.7999 what it is at periapsis. So I really should know how close the Moon was to apoapsis or periapsis in order to know its angular speed. By playing around with the Moon's distance and angular speed values (specifically, making the Moon more distant and slowing it down), I can reduce the amount of error. The two horizontal lines are where I think I should be in order to start seeing parallax with Mars. There are a couple ways I could go about this. One is to increase the number of dimensions to sweep from 5 to 7, including the Moon's distance and angular speed. This would increase the computation time and possibly give me multiple combinations of observation-matching results, which may give the distance to Mars but muddle the actual distance to the Moon. The other thing I could do is measure the Moon's apoapsis and periapsis myself by photographing the Moon over the course of a month and measuring the angular size and position in the sky. This would give me a more complete measurement of the Moon's orbit and let me get a better idea of its state during the occultation. Given that it is currently cloudy, I'm going to see about getting a start on Option 1.

I'm more surprised that the thing grew to that size in 40 years.