Is the Moon moving away from the Earth?

Question posed by Robin

The Moon is currently^[1] 368,976 km away from the Earth, and measurements show that its average distance is increasing by about 3.8 cm every year.

How do we know?

The distance from the Earth to the Moon is currently measured by bouncing laser light off special reflectors that were left there by astronauts on the Apollo 11, 14 and 15 lunar missions. We know how fast laser light travels (light speed, funnily enough!) and we can time how long it takes for a beam of light to get to the Moon and back. If you know how fast something's travelling and how long it takes to get there, you can work out how far it went quite easily:

Maybe you remember this equation from school: \( speed = \frac{distance}{time} \) ?

Well, we can rearrange that to get \( distance = speed \times time \), and then plug in the numbers. Light travels at the blistering speed of 299,792,458 metres per second, so it's just a case of multiplying that by half of the time (in seconds) recorded by the scientists who fire lasers at the Moon (half, because they measure the time from when they fire it to the time they receive its reflection, which means it's gone to the Moon and back in that time).

The photograph below is of an observatory in Wettzell, Germany, which is one of the sites tasked with (among other things) firing lasers at the Moon for distance measuring purposes.

Wettzell Laser Ranging System, H. Raab (CC BY-SA 3.0), via Wikimedia Commons

Why is the Moon moving away from us?

It's not because we smell.

You are probably aware that the Earth keeps the Moon in orbit via a force called gravity. What many people don't realise is that the Moon also attracts the Earth with its gravity: it's a mutual thing.

You can see one of the effects that the Moon has on Earth when you go to the seaside- over the course of a day, the sea rises and falls (we call this a tide). Sea tides are caused by the water on the surface of the Earth being attracted by the Moon's gravity, and actually being dragged into a bulge that rises above the Earth's surface^[2].

Whilst all this is happening, the Earth is rotating. Friction between the Earth's surface and the ocean means that the tidal bulge caused by the Moon's gravity is dragged around the Earth, and the bulge ends up pointing slightly ahead of the Moon in its orbit, rather than directly at it.

Now, because the Earth's oceans are made up of water, and water has mass, the water itself exerts a gravitational pull on everything else - including the Moon. Just as the water is dragged around by the Earth's spin, the water pulls the Moon sideways a little in its orbit. This means that the Moon actually speeds up a tiny bit in its orbit around the Earth.

As the Moon starts to move faster, its orbit becomes wider, and it moves a little bit further away from the Earth.

Will this happen forever?

Gravity has less of an effect the further away you are, so as the Moon recedes from the Earth, the effect that each body has on the other reduces slightly, so the tidal bulge isn't quite as big, and the tug that the Moon feels from it is smaller too.

In addition, as the Earth's rotation is slowed by tidal effects, the ocean tides aren't pulled as far or as fast in front of the Moon, so the effect of this is lessened.

As a result, these changes - the Moon speeding up and getting further away - will happen slower and slower over time.

What goes up must come down

To speed something up in its orbit you need energy, and energy can't just pop up out of nowhere: if something gains energy something else must be losing it. So as the Moon speeds up, what's slowing down?

The energy that speeds the Moon up comes from the tidal bulge of Earth's water dragging the Moon along in its orbit. The tidal bulge is able to do this as it has been dragged ahead of the Moon by the rotation of the Earth: as the Moon speeds up and its orbital distance is increased, the Earth's rotation slows down a little: our day is becoming longer by about two milliseconds every hundred years.

Although we quite often use the word 'tides' to refer to the effect of the Moon on bodies of water on the Earth, tidal forces actually affect the whole of a planet or satellite. Even on the Earth the effect of the Moon is measurable, with the Earth's rocky surface being squeezed or stretched a number of centimetres by the effect of the Moon's gravity.

Relevant posts:

• You now know that the Earth's rotation is slowing down, but... will it stop completely?
• Some other posts about the Moon
• A few posts about gravity
• More posts about tides.

Have a question about this topic? Comment below! Got an astronomy related question of your own? Ask it here.

Footnotes:

1. By 'currently' I mean literally while writing this post. The Moon's orbit around the Earth isn't circular - it's an ellipse - so the distance between the two goes up and down over the course of a month, and that's before we even take into account any other things that might make a difference. That's not the subject of this post, though, hence being stuck down in this footnote. Before you go back up to the main article, try this link to see how far apart the Moon and the Earth are right now. [back]
2. This might be a good time to go and have a quick read about how the Moon causes tides. [back]