Gottem. :)

And now for the segue into a shower thought - so the first thing night side would notice is the Moon disappearing (if it's in the night sky), but after that, how long before effects begin to suggest something is seriously wrong on the day side. Something tells me it will be sooner than the morning.
- I'd assume after 8 minutes the people on the day side would notice and all media would blow up, so hopefully you'd be asleep and wouldn't have to worry :)
  
  worry
  I, for one, welcome the inexplicable annihilation of the sun
  
  But all the solar panels will stop working so there will be no electricity. Batteries would run out and any other source of energy would be destroyed by people who started a cult worshipping the Sun hoping it would reappear
  So no social media on the part of the Earth that would notice the disappearance of the sun. The other side wouldnt have any problems with electricity since they wouldnt have the Sun-worshipping cult
- The ocean would revolt.
- Cool writing prompt: Elusive Dawn
- I wonder how long till everyone was dead. And what would be the last living species.
  
  My guess is that bacteria down in the crust near thermal vents would live the longest. Thousnands of years if they are able to follow the heat down.
  Figure bunkered people might make it a few months depending on their power source and ability to withstand dropping pressure. Not sure how long it would take for the atmosphere to freeze. Government bunker that is vacuum proof with a reactor might make it a decade.
- The first measurable thing that would happen is that we would stop orbiting the sun, since (counter to what my 12-year-old ufo-believing self thought) gravity also travels at the speed of light.

But not by much longer. People on the other side of the world or connected to satellites monitoring sunspots would notice pretty much immediately after the light ceases to reach the earth and would tell everyone else over the internet
- And even if you're not connected at the moment, the moon will go dark.
  
  Good one! If the moon wasn't visible at the time and you were just sitting outside say at midnight, I wonder if you would notice anything different.
- yeah but everybody else would be sleeping so it would still take longer
- Most of us sleep at night and don't check our info-hose feeds until we wake up.
  
  What's sleep?
  looks at time that says 23:27
- Only if you believe in magic box or “radio”
- No dude, it's only a difference of 1.3 seconds, faster then the Internet unfortunately.
  
  the other side of the world wouldn't notice there suddenly being no light anymore if there wasn't light in the first place.
  they would notice that the moon disappeared though
- Ok, first thing, did you not understand the image is a joke? Secondly, you have failed so badly at trying to use logic. And you'd notice it everywhere on the earth, both because of the moon and also just light scattering, it would become darker than ever before. And as said, most people would be asleep on the dark side, which is obvious. And it's not like the astronomers etc. have some kind of worldwide siren to get everyone's attention, most people wouldn't notice it for a while, even if they posted about it online.

Wouldn't the planet rapidly start to cool? I think we'd be dead by morning
- Atmosphere would hold the heat for a bit, the real issues will begin with food shortages because the crops won't grow
  
  Yeah but how long is a bit? Also, without the gravity center of our solar system, how long would it take for all the planets to start drifting off into the void?
- The core is still hot. If we bury ourselves deep underground, there is a chance the humanity could survive for thousands of years without a sun. If not humanity, then some sort of life will survive long enough for future archeologists to find it millions of years later.
  But don't quite me on this; I'm simply reciting from memory something I read in National Geographic or a similar publication 10-20 years ago. IDK how true this actually is.
  
  We would need enough advance notice to prepare for massively farming mushrooms or something underground to eat. Canned food will run out in a few years, even military MREs have a shelf life. A few lucky people might survive a generation, but there's a minimal breeding stock requirement to avoid degeneration from inbreeding. Extremely long odds, I think the human race would only survive this event in a sci-fi fantasy story.
  
  If we bury ourselves deep
  Fuck you I'm going underground
  
  Yeah, something will live, but I was more thinking surface life.
- Doesn't the earth itself provide a significant amount of heat from the core? I'm sure I read somewhere that for something like every 10 meters down you dig, the temperature raises by 1° celcius. So maybe we'd not notice a temperature drop so quickly?
  
  The surface would eventually freeze over. But some life would almost definitely survive deep underground and underwater, near geothermal vents not unlike those that hosted the first lifeforms on Earth. And, maybe, in some billions or trillions of years, Earth would stray near another star system, get captured by its gravity and slowly thaw out, restarting the evolution of life.
  
  Not sure how quick exactly, but the earth doesn't provide enough heat, not even close. Kurzgesagt has a video on a similar subject, without the ~~trillions~~ 1.7e17 Watts showering the earth every second we'd get awfully cold awfully quick. They are talking about slowly moving away from the sun, but they conclude it would get real icy
- The moon also doesn't emit it's own light. It would take longer for the moon to "disappear" than it would for the sun but it wouldn't be the whole night.
  
  I agree with you, but also... I'm not sure that I'd notice that I could see the moon a few minutes ago and now I can't (unless I happened to be looking at it as it happened)... I feel like that is something that could be happening every single night and I've never noticed.
  The sun disappearing is like... Super noticeable by comparison.
  
  The moon is just a few light-seconds away from earth; that's why they could have conversations with ground control during the moon landings. Moon will go dark a few seconds after the sun.
- Wherever you live on the Earth's surface starts cooling every night and gets warmed up again the next day. It wouldn't cool any faster if the sun went away, it would just keep cooling at the normal rate until everything was frozen. But I doubt it would take more than a week or two, depending on where you live.
  
  Yeah, but that's with petawatts being blasted on the other side of the earth every second, wouldn't the loss of that make the whole system cool down faster, including the side the sun doesn't touch? I'm thinking it'd be like having food on a hot plate, bottom is very hot, the top is less hot. But if you take the food off the plate the whole thing rapidly goes to room temp. I honestly have no idea, just conjecture tbh.
- False; no sun = no morning!
  
  So extremely cloudy mornings = no morning? lol just kidding.

https://xkcd.com/1391/
- That's a good way to infinite wishes.

i mean, if the moon is up there, the light first has to bounce off of the moon, and then back to earth, so yes, it would most definitely take longer...
- the light first has to bounce off of the moon, and then back to earth
  That's a second, more or less.
  
  that is still one second longer so.
- This reminds me of Inconstant Moon by Larry Niven! Time for a reread.

I wonder if we would feel the sudden disappearance of the centripetal force of the sun's gravity.
- After 8 minutes
- http://scienceprimer.com/lunar-and-solar-tides
  Yes, the tidal effect of the sun would disappear, and that would probably make the oceans all fucky suddenly (after an 8 minutes lag).
  
  Does gravity travel at the speed of light?
- After 8 minutes, almost certainly
- Gravity isn't a force, strictly speaking. Objects move along geodesics in spacetime (that's basically a straight line along a curved surface), and gravity bends spacetime, and therefore also these geodesics, around massive objects. So you don't actually get accelerated by gravity, that's why you don't feel anything during free fall. What we perceive as the force of gravity pushing us down, is the solid ground accelerating us upwards, when following the geodesic would have us fall instead.
  So when the sun disappears, the geodesic that used to spiral around the sun suddenly straightens out, and the neutral movement, the new free fall, has the earth continuing in a straight line. You wouldn't be able to feel that. What the other person said about tidal forces is true tho, it would likely cause worldwide tsunamis

I wonder how long it would take before you would feel it becoming colder
- If you ever experienced a solar eclipse, you will feel drastically how much the temperature changes.
  
  Even the difference between standing in shade and standing in direct sunlight on a sunny day is noticeable.
- Forget colder, I kind of feel like we're missing out on not hearing the sun thanks to space

In a sane world this would earn you a dunce hat. In this one it will earn you a position in the gubmint.
- Is a position on the gubmint good or bad?
  
  Well, the U.S. government is the greatest freakshow on the planet right now.
  Would you like to be in it? If so, a position can be yours for as low as $2.5m. Hurry up while vacancies last.

But will we feel the shift in gravity/inertia as the planet starts moving straight?
- This is the cutting-edge of my understanding so if I'm wrong somebody call me out, but I think because gravity is warping space-time and not actually pulling anything, we wouldn't feel an inertia change. Our inertia would be maintained, but the space-time we're going through would suddenly be shaped different, so we'd follow a new path
  
  The part you're missing is that earth isn't a point in space. That's why there's tides caused by the sun (which are different than tides caused by the moon)
  A person wouldn't feel the difference, but the tides would slosh back when the solar gravity stops effecting them.
  
  So would all the other planets, so there'd be a non-zero chance we'd smack into one of them. Most likely though we'd become a very, very cold rogue planet.
- yes, after 8 minutes
  
  I know gravity moves at the speed of light. I'm just referring to the slight pull of the gravity and the sudden shift to traveling straight off instead of a circle.
- I really doubt we would notice, because if so we would already be feeling different during day and night. The sun pulls us toward the sky during the daytime and toward the ground at night. Also toward the east at sunrise and the west at sunset. But none of this seems noticeable.
  
  We are in "free fall" around the Sun so that's why we don't feel its pull of gravity.
  You would similarly feel weightless if you were in an orbit around Earth.

If it happens at night it will probably take 5 or 6 seconds longer for people to start seeing the first messages on the internet

Teacher: I meant the global we. So it would average out to 8 minutes.
- Someone at day will inform sun is missing to the people on night
  
  A person can't inform others faster than the speed of light.

What about gravity? I know I read something about this once, but is gravity also limited to the speed of light?
- Yeah, we'll feel it after 8 minutes all right :-)
  Gravity travels at the speed of light.
  
  Does it? In my experience alcohol can delay gravity
- Yep, it is. We'd stay in our orbit of the sun for 8 minutes after it vanished too
- From what I know, particles that have a mass greater than 0 move below the speed of light and can never reach it. Particles that have no mass (every force is transferred via particles) move at the speed of light. So there is no way to have anything that is faster than the speed of light, not even forces.
  
  But do we know that gravity is a force transfered by a particle yet?

The telephone: "Am I a joke to you?"
- Who would leave their sound on in the middle of the night?

That's boring.
Can we just have the reverse, like a "When Day Breaks" scenario? At least its fun.

The real question is if the earth becomes a rogue planet or if Jupiter captures most/all of the remaining solar system. Jupiter is technically a failed star, so could it finally get it's glowup from being the sun's understudy and keep us all together until we fall into the gravitational well of a new star?
- If the sun just disappears, I doubt even having another sun would keep everything from flying off to fuck knows where. Jupiter, by comparison, is beyond hope. The Barycenter is far from Jupiter.
  
  Only two ways to find out. Time to fire up universe sandbox, cause I'm fresh out of the ability to delete the sun in the production environment.

I believe we'd still be warm for those 8 minutes. We have an 8 minute grace period before having to do anything, then enough time to add sweaters faster than earth cools.
- I was forced to calculate the black body temperature and radiation for the Earth, back in college by hand.
  I decided for fun to zero out the sun from the equation to see what would happen.
  My math came out to about -32°C average surface temperature.
  Earth would become an ice planet.
  I think you'd uh, need a bit more than a sweater in those conditions 😅
  
  It's sweaters all the way down. You have time to order from China shipped by boat before -32C happens. You're just being a "save the sun" hippy climate alarmist /s. Energy company shareholders would benefit from high demand, so saving the sun is just selfish of you :P
  
  People live in those temperatures in places like remote Russia, right?
  https://en.m.wikipedia.org/wiki/Oymyakon
  
  So.
  The Antarctic. Roughly. Everywhere. Including the equator cuz that’s not a thing anymore.
  Are there any places that would be “warm” for any reason if you recall?
  Like, I assume the oceans would survive until the core stops and the planet truly dies?
- it's because light takes 8 minutes to get from the sun to us. and since gravity also travels at the speed of light our orbit would only change after 8 minutes.

For further reading, see Galaxias by Stephen Baxter.