Why doesn't the earth spiral into the sun?

janvd

Hi all!

If space isn't a true vacuum, why doesn't our earth lose its speed due to friction?
I know that it's a near vacuum outside our atmosphere and the friction would be almost negligable. But in the course of a billion years, shouldn't it have an effect?
Why aren't we slowing down because of this? or are we?

Drakkith

It does lose energy. It's just so small as to have almost no effect. Even over a billion years.

Bandersnatch

Hi janvd.

It really is negligible.

Consider the scales here. 4,5 billion (10⁹) years might sound like a lot of time, but the Earth is a seriously hefty lump of rock. It weighs 6*10²⁴kg. It takes a lot to slow down such a juggernaut.

Let's compare the densities of Earth:
5,5 * 10⁶ g/m³ (or, five and a half tons per cubic metre)
and vacuum:
3*1,5 * 10^-24 g/m³ (or, three hydrogen atoms per cubic metre)

The Earth travels at 30 km/s through space, so each second it hits:

(∏*36*10¹² m²) {Earth cross-section} * (3*10⁷ m) {distance travelled in 1 second} * (3*1,5 * 10^-24 g/m³) {density of vacuum} = 0,015 grams of matter.

multiply that by Earth's age:
0,015 * 4,5*10⁹ {years} * 365 {days in a year} * 24 {hours in a day} * 3600 {seconds in an hour} = 2 * 10¹² kg

Or, the Earth managed to hit some two billion tons of hydrogen during its life so far*.
Compare that to Earth's total mass: 6 000 000 000 000 billion tons.
That's 3 trillion times more.

Quite negligible, I'd say.


*that's of course assuming there has always been the same density of dust in vacuum, which is obviously not true, but is not a terribly bad approximation for this kind of calculations.


Additionally, it's worth noting that tidal effects of the Sun have much more significant effect on Earth, transferring its rotational angular momentum into its orbital angular momentum(which translates to increasing orbit radius). So overall, the Earth is actually spiralling outwards.

Drakkith

Not to mention the Sun is losing mass over time, leading to less gravity, also causing us to move outwards from it.

janvd

Thanks for the replies!

xAxis

I doubt with such a low density we can even call it a "friction".
Other forces probably have comparable or greater effect. For instance, constant bombardment of photons from sun, magnetic fields interactions, gravity from other planets...