# Why does the Earth lose rotational velocity in the vacuum of space?

I think it is a well-known fact here that the Earth is slowly losing rotational velocity over time (some 1.4 milliseconds of the day are gained per hundred years). Eventually, this means that the Earth will become tidally locked with the Sun, meaning that one face of the Earth will always face the Sun and one will face away, much like our relationship with our own moon.

My question may perhaps be more related to physics, but why does the Earth lose rotational velocity? We know from Newton's laws that an object in motion stays in motion unless acted upon by an outside force. Well, what is the outside force? Is it the Sun's pull on us? Is it the Moon's pull? Is it another planet?

One of your instincts was correct; it is indeed the influence of the Moon.

Wikipedia notes:

Over millions of years, the rotation is significantly slowed by gravitational interactions with the Moon; both rotational energy and angular momentum are being slowly transferred to the Moon: see tidal acceleration.

And here is the general case of a satellite influencing the rotation of the primary:

Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite (e.g. the Moon), and the primary planet that it orbits (e.g. Earth). The acceleration causes a gradual recession of a satellite in a prograde orbit away from the primary, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking of the smaller first, and later the larger body. The Earth–Moon system is the best studied case.

Pictorially it is described here: The fact that the tidal bulge is moved relative to the Moon causes a torque between the two bodies, leading to the slowing of Earth's rotation and the recession of the Moon. As torque is related to angular acceleration $\alpha$ via the relation $$\tau=I \alpha \to \alpha=\frac{\tau}{I}$$ and torque is defined as $$\tau = r F \sin \theta$$ where $I$ is inertia, we can calculate the angular acceleration if we know the tidal forces at work.

• Very thorough, thank you very much. Just to be clear though, we are indeed outside of the gravitational influence of every other planet, correct? Dec 23, 2014 at 19:38
• @TomSterkenburg Well, every object in the universe influences every other object, so the answer is actually no. But besides the Sun, the Moon has the greatest impact of any other body on the Earth. Dec 24, 2014 at 14:36
• The influence the other bodies have on earth is so minimal, that the sun will have gone through its red giant phase and either swallowed earth or ejected it before any noticeable difference would appear. Aug 5, 2016 at 6:16
• Yeah, my impression is that neither the Moon nor the Sun is made of vacuum. Thus the question is based on a fallacy. Aug 6, 2016 at 2:43

Explanation in non technical jargon: Think of yourself (Earth) sitting with your arms tucked close to your chest on a rotating piano stool. If you were to extend your arms, the rotation speed of the stool seat will slow down. Now, because the location on Earth directly under the moon is pulled toward the moon, the radius of the Earth is extended (stretched)towards the direction of the moon, for the same reason as you, on the rotaing piano stool, slow down as you extend your arms away from your body, thereby increasing the radius of your body or the piano stool. Technically, you and the Earth are obeying the law of "conservation of angular momentum": Mass x speed x radius of a rotating body is constant. Should the radius of the body increase, its rotational speed must decrease in order to hold constant the value of its original angular momentum.

Another factor slowing Earth rotation is the part of ocean movement caused by the moon's gravity, i.e. tides. The sliding of the ocean water over the Earth's rotating surface acts like a brake, furthering the decrease in Earth rotation rate. Even if the Earth were without large expanses of water--oceans--its rotation rate would still decrease, but not as much.