Sunset on the Equator

Neil deGrasse Tyson made the following surprising tweet:

Of course that's not right due to the earth's axial tilt relative to the sun. To prove that, I decided to write a quick Frink program that will let us calculate the actual azimuth at which the sun sets at each day, as seen from a spot on the equator. (I'll arbitrarily choose a spot on the prime meridian, so it's easy to extrapolate the UTC times to any other spot in the world.)

The complete values are listed below, but the summary for 2012 is:

Most southerly sunset is 246.563° on 2012-12-21 18:02:19
Most northerly sunset is 293.438° on 2012-06-20 18:05:37

The sun sets as much as 23.437° south of due west.
The sun sets as much as 23.438° north of due west.

So the total variation around west spans almost 47 degrees, so his statement is quite wrong. He hasn't corrected the tweet in 24 hours. Let's see if he will.

(Note: He never corrected his incorrect tweet about how Coriolis forces affect a kicked football that I tried to get him to correct:

Update: See below about that tweet where my reply mysteriously disappeared.)

How about a wager, Neil? We'll fly to somewhere on the equator in December and measure the sun's azimuth at sunset. Whoever's wrong pays for the trip. Deal?

Or even a trip to a planetarium in which we could test this hypothesis? It'll be free for you if you're right.

Update: Censorship or Twitter Bug?

After writing this article and tweeting a link to Neil, I noticed that all of the replies to Neil's tweet that pointed out he was wrong had disappeared from the replies to his message. All the replies that didn't say he was wrong were still there. It's weird. I thought that he might have intentionally removed all replies that said he was wrong, but I later noticed that Twitter might limit displayed replies to 5. Is this the case? The weird thing is that it wasn't just the oldest or newest messages that weren't showing up, as timestamps prove. (We could test the "limit of 5" hypothesis by getting some of the people whose replies still show up to delete their replies, and see if any of the "you're wrong" replies then show up.)

I then found out through experimentation that an easy way to censor someone's replies is to block them, then unblock them. Their previous replies then magically disappear from the replies to your tweet, apparently forever! And no nasty "you have been blocked message" is visible to the people you censored, because Twitter doesn't tell you when you've been blocked, or unblocked. You'd only see the "you have been blocked" message if you tried to follow them again in the brief instant that they had you blocked. Even if they reply again to the same message after you've blocked-and-unblocked them, their new replies do not ever appear to show up as replies in the original tweet, as borne out by my experiments. The subsequent replies show up only in the sender's timeline as a disconnected message that others will only see if they're following the sender. That seems like a repeatable test to see if you've been blocked and unblocked. Can anyone corroborate this behavior?

By the way, I made a large list of reply tweets that I saw earlier as replies to Neil's tweet, but didn't show up a few hours later:

@cosmos4u @halfastro @fjselman @JfwellsPDX @agtmadcat @murli184 @LCTTA @heafnerj @numbakrunch @alee67 @Bondles @Suribot @jaynemharper @rickard_matt @billharder @FedoraPirate @CarneyFex @Canadaboy96 @Josh_Randel @eric_lobdell @aeliasen (my reply to his tweet, posting this article originally.)

All of these show that Twitter considers these to be "live" replies to Neil's original tweet. I saw a bunch of these in the replies at one time. However, a few hours later, they no longer showed up when you expand the replies to Neil's original tweet!

You'll see many more replies by searching for both names.

Later update: Testing with Twitter's mobile site shows more than 5 responses, but it only shows a fraction of the ones I've linked to above. Something is still wrong. Only 2 of the 19 people I list above who replied with corrections (@halfastro, @cosmos4u) have replies that show up. It shows 17 responses. If Twitter is limiting the number of responses to show, 17 is a very odd number. Hmmm...

What happens if any of the people listed above reply to Neil's original tweet again? If they've been blocked and unblocked, my tests seem to indicate that their replies will again fail to show up in his replies.

I also notice that no responses now show up to his earlier incorrect tweet about Coriolis forces even though my reply shows up as a valid reply if you go there directly, and there were other people telling him he was wrong at the same time. Is a pattern emerging?

I really don't want to think that Neil is intentionally removing replies from people who (correctly) point out his (mathematically demonstrable) errors. He's a great champion of science. Correcting your errors when you find them is utterly essential for the progress of science. I have great respect for people who admit their errors and make a learning experience out of it. Let's hope he corrects this mistake (and the Coriolis one, but I long ago gave up hope for that.)

I may be utterly wrong in all of this. It may be a Twitter bug, or a limitation, or a temporary glitch, or something subtle. I'll be glad to retract if proven wrong. I hope Neil will correct his proven errors, too.

"I would like to add something that's not essential to the science, but something I kind of believe, which is that you should not fool the layman when you're talking as a scientist. I am not trying to tell you what to do about cheating on your wife, or fooling your girlfriend, or something like that, when you're not trying to be a scientist, but just trying to be an ordinary human being. We'll leave those problems up to you and your rabbi. I'm talking about a specific, extra type of integrity that is not lying, but bending over backwards to show how you are maybe wrong, that you ought to have when acting as a scientist. And this is our responsibility as scientists, certainly to other scientists, and I think to laymen."
--Richard Feynman

(Appendix: About his incorrect Coriolis effect tweet that he never corrected: Read this part of the wikipedia article on the Coriolis Effect. In the northern hemisphere, the Coriolis effect due to the horizontal velocity of the ball always pushes the kick right, no matter which direction you kick in. The upward velocity component may accelerate the ball in the east-west direction, (up pushes it west,) but this tends to balance out due to equal upward and downward travel. But there's always the rightward component due to horizontal velocity. If the kick's more horizontal than straight up, it'll bend right, no matter which compass direction you kick it. Never left.)

Another Update: On 2013-04-17, Neil posted yet another tweet that was mathematically wrong. He claimed "The Sun is 1/2 of 1% as bright at Jupiter than at Mercury. But Jupiter is 300x bigger. All told, it receives 1.5x the Sun's energy". Screenshot below. (He's wrong. The correct answer is 4.75x, and the "300" figure comes out of nowhere). Do you see my replies when you go to the link above? My corrections are shown in the screenshot below, or are still active here: [1] [2] [3] [4]

Frink program

Here's the Frink program to calculate the sunset at the equator: TysonTweet.frink and the fabulous sun.frink astronomical library that powers it.

Sunset Tabulation