Pop goes the planets!

Question

So, you have eight planets in the solar system. Mars, Saturn, etc etc. **What would happen to poor old Earth if, for some yet unknown law, some handwavium, or that statement, the aliens did it, if every other planet but Earth just went "Pop?"[1]

All of the moons, all of the speed, acceleration, etc etc, stayed the same, just that every planet, except Earth, is gone?

What I mean is that, lets say we have planet X in the solar system, and that X has one moon. When planet X goes pop, its moon just keeps on going on to whatever direction/acceleration it was moving. If that makes sense?

Main Question: What would happen to Earth if this happened?

Bonus Questions:

1. Is Planet Poppin' even possible?

Edit

-Bonus 2 removed

[1] I mean that the planets just pop out of existence, as if they were never there in the first place.

Answer 1

Not a lot...at first

The sun's gravity outweighs the gravity of every planet combined by a factor of more than 1,000. At the time of your birth, the doctor/midwife who delivered you had more of a gravitational influence on you than Jupiter did, and Jupiter is more massive than all other planets combined. Our orbit would be essentially unchanged, so the sudden and mysterious vanishment of all the planets besides Earth would have virtually no immediate impact.

Immediate impact, I said. Things get interesting quickly, though.

Without the planets around, you've got a lot of loose rock knocking about, and Earth is suddenly the second-largest target in the solar system (after the sun). It would take a LOT more calculating time than I have access to to predict what would happen to all of those moons, asteroids and comets, and it would depend a lot on where everything was in its orbit at the time. However...

Impacts. We'd see a lot of 'em, between the moons that used to be circling gas giants, especially, but also between asteroids and other bodies that used to be stabilised by Jupiter's gravity. Chances of Earth getting off scott free are slim to none, and if you think the dinosaurs had a bad day, imagine taking an Io between the eyes.

Bonus 1 Is Planet Poppin' even possible?

Nope. Not by any laws of physics that we currently know. All that mass and energy has to go somewhere.

Bonus 2 What would happen to society if this happened?

I'd imagine a lot of new religions would be founded.

Answer 2

Planet Earth would simply keep moving in its orbit around the Sun. In fact, it would do so more smoothly as the gravitational perturbations from other planets would do longer happen.

The moons of the planets that vanished would move in tangential paths to their original orbits around their planet. The moons around, say, the planet Saturn would initially move as a cloud of moons that will expand the moon's orbital velocities add to their solar velocity (this is the velocity of the Saturn planet-moons system around the Sun). Similarly, the swarm of particles that make up Saturn's rings will move outwards from their orbit around the now vanished planet.

What will be left is a bunch of former moons and a cloud of ring particles, mainly, following Saturn's old orbit, but which will be dispersed due to their velocity differences resulting from the relative positions to each other when Saturn vanished.

Deimos and Phobos will be a pair of moons following what had been Mars' orbit, but each moon will have its own orbit around the Sun. Possibly over time they will become widely separated. This will depend on their positions relative to each other at the moment when Mars went Pop!

Bonus Question:

There is no known physical mechanism to explain why the other planets of the solar system would instantaneously vanish as if they had never existed.

Suspect the work of extremely technologically advanced aliens. Or Mr Mxyzpltk moonlighting from his usual employment in DC's Superman comics. Joking aside, but whatever could cause planets to vanish without any trace involving physical phenomena beyond anything we currently understand.

Answer 3

I will try to consider the possibilities, but I haven't done calculations, so might I'am wrong:

The instantaneous displacement of planets (into nonexistence or far away) would be impossible, since it would violate the local energy conservation. If a mischievous god still performs it as a miracle, the following might would happen: Some moons have small orbital velocity compared to their mother planet (eg. Mars: 24 km/s and Phobos 2.1 km/s) so they would orbit on a roughly similar curve as their bygone mother had. But others have larger (eg. Jupiter 13 km/s and Io 17.3 km/s) So their course would greatly depend on their orbital phase at the moment of the planet displacement. They could come close to us, get placed on higher and lover orbits, or may even deorbit and fall into the Sun. The exact outcome would depend on the date of the event, and have to be determined using N-body simulation, and it could be anything from almost nothing to the destruction of the Earth.

The conversion of all planetary mas into photons would be impossible too (as suggested by AlexP), since it would violate lepton and barion number conservation. But if handwaving aliens would do it, (for example by annihilating all their particles with it's antiparticle one by one.) the conversion of the Jupiter alone would mean 3.2e+44 Joules. Even if this wouldn't be a total conversion, and some energy would be carried away by neutrinos and other neutral particles, this energy is the output of the Sun during more than 10e+17 seconds. Since the Jupiter is about 3-6 AU away from us, we would have an nukeflash about 10e+16 times brighter than the Sun. (depending on our orbital phase) The Mars would have a 10000 times lower absolute luminosity, but can be as close as 0.5 AU from us... So, I think, we would all die. And the moons would get vaporized, melted, or shattered... (could be easily calculated too.)