What would happen if Venus and Earth collided?

Question

The first thing we would need to consider is that Earth has already been hit by a protoplanet half its size 4.5 billion years ago, meaning the Earth may have a chance of staying intact after the collision.

The next thing we would need to think about is the Moon. The impact would have a gigantic force and may disrupt the Moon's orbit, which would lead to two possibilities: either it would collide with the Earth-Venus body, or it would get ejected into space, without any planet to orbit. It may even start orbiting the Sun. The Earth could get completely destroyed, but again, it went through that before.

I also am wondering if it might disrupt any of the planets in any way, and if Earth's orbit might be changed. Thanks for answering the question!

Answer 1

This is the kind of thing that computer simulations are done for, but I am not aware of any that were specifically for a Venus-sized body hitting the earth.

The specific details would depend very much on the velocity and angle of the impact. But, in general, as the two planets approached, tidal forces would deform both planets in the hours before collision, causing significant heating. The collision would liquify and splatter both planets, but also probably slow down their relative velocities so that most of the matter of both planets would form a spinning cloud of giant droplets and later coalesce. The moon would be caught up in the cloud and might end up combined with one composite planet. Or you could end up with a planet plus a moon, with some of the current moon in the planet and some of both planets in the new moon.

Be aware that this is not the sort of thing that can "just happen". The orbits of Venus and earth are stable on long time scales. But simulations have been done showing that there could (with very low probability) be collisions between inner planets, billions of years from now if instabilities slowly built up in their orbits. But they ran numerous simulations and only had a few near misses far in the simulated future.

This article shows simulations of collisions that are more unequal, and more similar to the moon-creating collision. But the fluidic, gravity-controlled nature would be the same.

Answer 2

The outcome of a Venus - Earth collision depends on the impact speed. At a relatively low speed, the matter is likely to condense to form a new planet. But if the speed is high enough the planets will be totally disrupted and the matter will disperse. We can calculate this speed from the gravitational binding energy. For a spherical body of uniform density, this is

$$U = -\frac{3GM^2}{5R}$$

where $G$ is the gravitational constant, $M$ is the mass of the body, and $R$ is its radius.

Real planets don't have uniform density. They have dense cores, and their actual binding energy is somewhat higher, but the above formula gives a reasonable rough approximation.

Notice that the GBE (gravitational binding energy) is negative. If two planets collide with kinetic energy equal to the negative of the sum of their GBE they will become totally unbound. So we just need to solve for $v$ in

$$-\frac12( M_{Venus}+M_{Earth})v^2 = U_{Venus}+U_{Earth}$$

This results in $v\approx8.384\,\rm km/s$, which I calculated using this Python script.

By way of comparison, the mean orbital speed of Earth is $29.78\,\rm km/s$ and of Venus is $35.02\,\rm km/s$. A smooth Hohmann transfer ellipse from the current Venus orbit would meet Earth at a relative speed of $2.495\,\rm km/s$, well below the disruption speed. However, if Venus were on a Solar System escape trajectory and it collided with Earth, the relative speed could easily be higher than the Earth's orbital speed.

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As Mark Foskey mentions, a collision between Venus and Earth is quite unlikely. However, there is a chance that interaction between Jupiter and Mercury will disrupt the inner Solar System before the Sun becomes a red giant.

From Wikipedia:

Mercury–Jupiter 1:1 perihelion-precession resonance

The planet Mercury is especially susceptible to Jupiter's influence because of a small celestial coincidence: Mercury's perihelion, the point where it gets closest to the Sun, precesses at a rate of about 1.5 degrees every 1,000 years, and Jupiter's perihelion precesses only a little slower.

At one point, the two may fall into sync, at which time Jupiter's constant gravitational tugs could accumulate and pull Mercury off course with 1–2% probability, 3–4 billion years into the future. This could eject it from the Solar System altogether or send it on a collision course with Venus, the Sun, or Earth.

If inner system disruption doesn't occur, Mercury and Venus will likely get swallowed when the Sun expands. Earth may survive the Sun's early red giant phase, but eventually it too will probably succumb.

It's difficult to make solid predictions about such far future events. We don't know exactly how the Solar System will respond as the Sun sheds mass. By the time the Sun becomes a white dwarf it will have roughly 50% of the mass it had when it was a new main sequence star.