A day of problems: Vikram Lander, Saturn’s day length, and solving for 42

By on September 9, 2019 in

Sometimes Mondays are just full of problems, and this Monday is no different. In this episode we look at 3 issues in science: the problematic hard landing of Vikram, the problem of solving for Saturn’s rotation, and the difficulty of finding the 3 numbers that when cubed and summed provide a problem with an answer of 42.

Play

Links

Vikram Landing on the moon

Saturn’s ill defined Day

The problem that 42 answers

Transcript

Last Friday, after we had recorded our daily episode, the Indian Space Research Organisation, or ISRO, attempted to land their Vikram lunar lander on the southern polar region of the moon. With the lander still more than 2km from surface, all contact was lost, and pundits all across social media saw in the telemetry indications that the mission was going to fast and off course. Over the weekend, ISRO scientists and engineers have worked hard to see if they could find their lander and if possible make communications. So far, there has been radio silence, but the little lander was found by the Chandrayaan-2 orbiter. While we don’t have an image to share with you at this time, an ISRO official has been quoted by the India Times as saying “It had a hard-landing very close to the planned site as per the images sent by the on-board camera of the orbiter. The lander is there as a single piece, not broken into pieces. It’s in a tilted position.”

At this time, ISRO continues to try and make contact, but the reality is, space is hard, and in all likelihood, we will not hear from this spacecraft. India is nonetheless to be commended for all the accomplished. Their orbiter is performing well, and will continue to do science from its unique orbit.

I also want to point you to video of the Indian Prime Minister Modi comforting the heartbroken chief Sivan of ISRO first with a handshake and then with a grandfatherly, back thumbing hug of compassion when the head of ISRO breaks into tears. While there are often matters of Inidan politics I don’t agree with, this single act of kindness is something everyone can learn from. In a moment of failure, and in a global community where NASA’s motto that “Failure is not an option” permeates everyt hing, we have come to expect our aerospace engineers and politicians to meet failure with promises to investigate and an air that someone will be held responsible. The reality is, sometimes shit just happens and a spacecraft lands hard and off target. We need to accept that failure is part of exploration, and learn from it and move on out into the solar system.

Space is sometimes hard in really unexpected ways. For me, one of the biggest “How do we not know this yet?” quandaries is the rate of Saturn’s rotation. That’s right, even after 100s of years of ground-based observations all those 100s of orbits made by Cassini, we still don’t precisely know how fast Saturn rotates. This is a complex problem with it having a cloud layer that rotates at different rates at different places and as we can see here on Earth, the rates cloud circle the Earth isn’t a precise indicator of how fast a world spins. With Jupiter, we by-passed these cloud related issues by looking at it’s electromagnetic field and measuring radio emissions. Saturn’s field, however, isn’t as strong, and early work by Voyager 1 and 2 could only really Saturn rotates somewhere around every 10 hours and 40 minutes which isn’t bad… but when Cassini looked to refine that measurement, it found a difference of 6 minutes between its measurements the Voyagers measurements… indicating radio emission wasn’t a nice clean reflection of rotation and more physics is needed to sort what is going on. Well, that new physics may have been found. In a new paper in the Journal of Geophysical Research: Space Physics, a team from Birmingham-Southern College has pointed out that the tilt of Saturn may lead to seasonal variations in radio emission. Ultraviolet Sunlight hitting Saturn’s atmosphere can affect the distribution of plasma, and that plasma in turn can drag on the fields generating the radio emission we see. This effect can explain why we see Saturn’s radio emission change seasonally, and this model offers us clue toward how to finally figure out how long a day is on Saturn.

From one weird problem to another, I would like to introduce you to the math problem many of you never knew you could be amused by. 

For reasons that I can’t explain, mathematicians in 1954 set out to learn what 3 whole-numbers, when cubed, would add up to numbers 1 to 100. The numbers they added together could be positive or negative. This makes sense since 2 cubed + 3 cubed + 4 cubed is 99, and to get anything smaller than 99, something is going to need to be subtracted.

Well, apparently, since 1954, people have been plugging away on this problem, and as of this year only two numbers, 33 and 42, remained unsolved. Inspired by a youtube video on Numberphile, Andrew Booker solved for 33 earlier this year, and that left the Douglas Adam’s Quote requiring number 42 as the only solution that lacked an equation, and in math’s Life the Universe, and Everything can’t easily be cubed. What can be cubed are numbers, and the thing that can cube them are supercomputers. Booker, determined to see this problem finished, reached out to MIT mathematician Andrew Sutherland. Sutherland is an expert in massively parallel computation, and together they enlisted the aid of the Charity Engine, an initiative to use unused CPU cycles on home computers to solve problems. With the help of more than 1million hours of computing spread across 500,000 volunteered computers, Andrew and Andrew were able to find those three numbers that can be cubed and summed to get 42. 

Ready for the answer? I’m not sure I’m ready to try and say this, but here goes:

Negative 80 quadrillion 538 trillion 738 billion 812 million 075 thousand 974 … cubed

Plus 80 quadrillion 435 trillion 758 billion 145 million 817 thousand 515 cubed

PLUS 12 quadrillion 602 trillion 123 billion 297 million 335 thousand 631 cubed 

Is… 42.

And there you have it. Here is to hoping all the mice are happy to finally know the question 42 is the answer to.

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  1. Daily Space 9/09/2019 | Citizen Science - September 9, 2019

    […] We have the post and transcript over here – https://cosmoquest.org/x/dailyspace/2019/09/09/a-day-of-problems-vikram-lander-saturns-day-length-an&#8230; […]