Is the Earth Getting Heavier?

By Dave Goldberg

Except for the occasional earthquake or volcano eruption, the Earth seems like a fairly stable place. But if you believe that YOU COULD NOT BE MORE WRONG. We are under constant bombardment. From space! And how does all of this cosmic debris affect the earth? In this week's "Ask a Physicist" we'll find out.

Jehal90 (Jesper to his friends) asked:

　

Considering that planet Earth is being bombarded with energy from the sun, approximately how much mass does our planet gain from sunlight in say, a million years?

This is a fun question because it connects almost directly (and somewhat surprisingly) with how the Higgs works. We're all familiar with Einstein's great equation, E=mc², but the Higgs particle gives mass to others by virtue of the fact that the equation can be inverted:

m=E/c²

Just as you can get energy out of annihilating mass, you can also create mass from whole cloth by producing energy. If you pour enough energy into the earth in the form of sunbeams, presumably the earth will get more and more massive, right? Wrong, but to understand why, we need a strict accounting of where all of the energy goes.

The Sun is Falling Apart
As you probably know, the sun is a mass of incandescent gas, a gigantic nuclear furnace. There's no question that the sun is losing mass over time. It radiates at a rate of about about 4x10²⁶ W. To make that much energy, huge amounts of hydrogen are fused into a huge (but slightly smaller) amount of helium, with a deficit of about 4 billion kilograms every second, or about 370 billion tons a day.

We don't see most of that. The earth is a very tiny target (unlike, say, a Dyson Sphere). If we covered the whole earth with perfect solar panels, we'd only gain about 2 kilograms each second, or about 60,000 tons a year. That's still quite a lot, but we don't get to keep it, contrary to Jesper's working assumption. For the most part, energy in equals energy out.

When these two effects aren't in balance, we get global warming, and while that spells disaster for people, it has only the most marginal effect on the mass of the planet. An increase of 1 degree Celsius throughout the entire atmosphere only adds about 60 tons to the terrestrial scale.

But Jesper's question got me thinking. There are a lot of other effects that feed the earth.

We would, in principle, get a much bigger deposit from the Solar Wind. One of the dangers of being an astronaut is that the sun (and space generally, but let's focus on the local problems) is throwing out protons and electrons at speeds of several hundred kilometers per second. The sun is blowing off enough material that if the earth were still around in a few trillion years (it won’t be), we'd slowly spiral away as the sun loses its gravitational pull.

For our purposes, we're much more concerned about what happens to all of that wind. If we didn't have a giant magnet in the middle of the earth, about 20,000 tons a year of high energy charged particles would fly through the atmosphere, knocking out most of our technology.

Fortunately, we do have a magnet to deflect the solar wind, which means that we get beautiful Aurora Borealis rather than stone age technology.

Small Stuff in Space
So if the sun isn't feeding earth, what is?

I'll tell you what it's not (at least for the most part): big giant rocks from space.

As io9 readers, you undoubtedly know the ostensible odds of successfully navigating an asteroid belt. The reality is far different. Even in the heart of the asteroid belt, large asteroids are about a million miles away from one another. In our region of the solar system, large objects are even less common. A kilometer scale meteor only hits the earth every half million years or so.

But there is a lot of smaller stuff out there, on the scale of pebbles and grains of dust, basically the detritus left over from the formation of the solar system. As the earth flies around in its orbit, it gobbles them up.

Roughly 40,000 tons of material fall to earth every year. Supposing it were uniform, that would mean that the radius of the earth is growing by about 0.02 nanometers every year, roughly a billion times slower than the continents are moving.

Of course, every now and again we get a whopping huge event. Those kilometer scale meteors? They can deliver a couple of billion tons of material all at once and in spectacularly explosive fashion.

So yes, the earth is definitely gaining weight, or would, except for the fact that it has a slow leak.

We’re Also Evaporating
                      The Sun Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune

Behold! The Solar System! Take a good look, and you may notice that the outer planets (Jupiter, Saturn, Uranus, and Neptune. Nuts to you, Pluto) are giants, with huge envelopes of gas and ice. The inner planets, including us, are also rocky and quite small.

Why is that?

Because it's hot in the inner solar system, and if you heat up gas, it tends to fly around fast enough to achieve escape velocity from its home planet. The lighter the gas, the quicker it boils away, and hydrogen is the lightest of them all. We lose about 3 kg of hydrogen per second, which if you do the mass comes out to about 100,000 tons per year. Incidentally, though it's a slow leak, but only for now. As the sun heats up, the pounds are just going to melt off the planet.

Put another way, Jesper asked a great question because he got it exactly wrong. The sunlight isn't really bloating the earth at all. Gaea may have a hearty appetite, but when nature calls, she calls collect.

Dave Goldberg is a Physics Professor at Drexel University
http://io9.com/is-the-earth-gaining-weight-512456481