And even if you're not connected at the moment, the moon will go dark.

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.

Only if you believe in magic box or “radio”

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 :)

Someone at day will inform sun is missing to the people on night

Yeah, we'll feel it after 8 minutes all right :-)

Gravity travels at the speed of light.

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.

Yep, it is. We'd stay in our orbit of the sun for 8 minutes after it vanished too

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.

Atmosphere would hold the heat for a bit, the real issues will begin with food shortages because the crops won't grow

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 light first has to bounce off of the moon, and then back to earth

That's a second, more or less.

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).

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 😅