When Would Planets Go Dark if the Sun Went Out?

[mopc]

TL;DR Summary

If the Sunlight lets say would go off, exactly how long would astronomers on Earth still see sunlight reflected on the surface of Mercury, Venus, Mars, the asteroids, Jupiter Saturn, etc.?

If the Sunlight lets say would go off, exactly how long would astronomers on Earth still see sunlight reflected on the surface of Mercury, Venus, Mars, the asteroids, Jupiter Saturn, etc.?

I mean Sun goes dark at 0:00 from the point of view of Earth-based observers. At that exact moment, if they looked at Venus and Mercury, would they still see a few minutes of sunlight reflecting off their surfaces? And the outer planets Jupiter Saturn, Neptune, Pluto?
Or would we just see everything going dark at the same time?

Because if we see the Sun going dark at 0:00, tht means it went dark at 23:52'. Then Mercury and Venus must have gone dark a few minutes later, like 23h53 for Mercury and 23h55 for Venus , but thats in imaginary absoute time, we would see Venus going dark depending on how far Venus is from us + light speed, supposing the Solar System is in the arrangement of today, at what times would we see from Earth the surface of each planet going dark?

 

[Ibix]

You seem to understand how to do the calculation, so all you need is the current locations of the planets. This page discusses data sources, including NASA's Horizons database. I think you just want to set Ephemeris Type to Vector Table, Edit the Coordinate Center to be the sun (you can search for @sun - sorry PF user sun, I can't work out how not to ping you while typing that), Edit the date range, then generate the table for each Target Body. Read off the x,y,z values and apply Pythagoras to get distances, then divide by 300,000 km/s to get delays in seconds.

The first link discusses some python libraries that may make that easier if you know some programming.

 

[Drakkith]

I mean Sun goes dark at 0:00 from the point of view of Earth-based observers. At that exact moment, if they looked at Venus and Mercury, would they still see a few minutes of sunlight reflecting off their surfaces? And the outer planets Jupiter Saturn, Neptune, Pluto?
Or would we just see everything going dark at the same time?

We would see the Sun go out first, then the planets would go dark. This is because sunlight from the Sun travels a straight line to us and thus a shorter distance than the sunlight that ends up getting reflected from each planet to us. The time taken would be the sum of the distances from the Sun to a planet and then from the planet to Earth divided by the speed of light. For example, Mercury and Venus would taken anywhere from an extra few seconds to an extra minute or two depending on where they are in their orbits (rough guess, I haven't done the math). The planets outside of Earth's orbit would also show some variability based on our orbital positions.