# Do planets lose energy while rotating?

When a planet rotates/spins, is it true that the planet loses energy? If this is true, then where does this energy lost by the planet go? My confusion may be in the basic understanding of the mechanism. When I imagine a planet rotating, what I think is either of the two things may happen -

1. The planet already has energy within the system, which is lost when the planet rotates. OR
2. The planet rotates because it receives energy from the outside.

So which one of the above actually happen?

This is what I think may happen. If I am wrong, please correct me.

• This might be an entirely different question, but doesn't rotation cause stress or strain on a physical body, some of which is converted to heat? Aug 24 at 13:08
• @BarryCarter How so? Aug 25 at 15:23
• @JasonGoemaat I thought things like conservation of angular momentum only applied in theory, not in practice. When a ball is rotating, the atoms in the ball are going at many different velocities. The electric force keeps them together, but the ball must deform slightly, which changes it shape, and the process repeats. I think that's how stress and strain work. Even if you use a spring without breaking it, every use weakens in slightly (I think) Aug 25 at 16:22
• @BarryCarter: Angular momentum is absolutely conserved. Has to be, by Noether's theorem, since the universe is rotation-invariant. There's no preferential direction. Aug 26 at 14:04

The energy a rotating planet has is derived from the rotation the initial interstellar cloud of gas and dust had prior to it flattening into a protostellar disk.

The rotation of a planet is bound by the laws of angular momentum. Alone, without any other influences, the rate of rotation will remain constant for ever. However, some planets have moons & these will affect the planet's rate of rotation. Earth's rotation rate is slowing due to the Moon, particularly through the action of tides. During the era of the dinosaurs a day of Earth was went from 19 21 hours (620 Ma ago) to 23 hours (65 Ma ago), now its 24 hours. I'll let others who are more knowledgeable about this than me comment on how a star might affect the rotation of planets orbiting it.

• Also the star itself does inflict tides on the planets. On Earth 1/3 of the tide is caused by the Sun. As such, moons are not a prerequisite for loss of spin rotation. Solar tides will gradually lead to a longer year as the spin's angular momentum is thus transferred into orbital angular momentum. See this question: astronomy.stackexchange.com/questions/18283/… Aug 23 at 19:18
• The moon is tidally locked to Earth. Most of the Jovian moons are tidally locked. If a moon orbiting a planet can lose its angular momentum then a planet orbiting a star can as well, although the process seems to be a lot slower. Aug 24 at 2:15
• @AdamChalcraft - Also see Mercury's 3:2 spin-orbit resonance (which is the result of the same effect on an eccentric orbit instead of a circular one).
– TLW
Aug 24 at 4:38
• Be aware that time to tidal lock scales, to a first approximation, with the sixth (6th) power of the orbital radius (SMA).
– TLW
Aug 24 at 4:43
• @planetmaker A planet without a star is called a rogue planet - it just needs to be big enough to be of "planetary mass", which is big enough to become roughly spherical, but not so big it turns into a star. Aug 24 at 14:01

In addition to the interaction with other bodies (moons, other planets, stars) as described in another answer, you also have gravitational waves produced by spinning body that isn't perfectly symmetrical. Which the earth isn't. Those waves carry some energy and angular momentum with them, which means the planet loses it.

Mind, that contribution is tiny. It's relevant only for extremly dense and massive bodies, so it wouldn't matter to a planet. But it is an effect.

• Even the gravitational radiation due to Earth's orbital motion around the Sun is tiny. According to physics.stackexchange.com/a/412990/123208 it's ~196 watts. It'd be interesting to compare the gravitational radiation due to the Earth's rotation to that of the orbit of the Earth & Moon about their barycentre. Aug 24 at 16:56
• So on the order of... a race between losing energy to gravitational waves and theoretical proton decay? Aug 24 at 22:56
• It's on the time scale of "way too long to matter", yes. For the earth specifically, it would've long since been swalloed by the sun as it expands into a red giant. Aug 25 at 13:28

In addition to tidal/gravitational effects, a planet might lose energy also due to electromagnetic emission, provided that the planet has a magnetic field and if the magnetic field dipole moment is not aligned to the rotation axis (this is indeed the case for the Earth, the "magnetic axis" is tilted by about 11°).

The component of the dipole orthogonal to the rotation axis, due to rotation, will radiate electromagnetic waves. The radiated power by such a dipole is (in far field condition, assuming an ideal dipole) proportional to $$m^2 \omega^4$$, where $$m$$ is the dipole moment and $$\omega$$ the angular velocity. A good reference on this is, for example, D. J. Griffiths Introduction to Electrodynamics, Chapter 11 "Radiation".

There is an exercise in the same book in which one is asked to compute such emitted power in the case of the Earth, just to find out that such power is really tiny - of the order of few $$\mu\text{W}$$.

Well, kenetic energy is of at least three types. Translational energy, rotational energy, and vibrational energy. As energy is neither created nor distroyed, the planet really does not lose energy, rather transfers it to other bodies. If it is in some sort of debrie field, it might impart its rotational energy into other masses which would show up as translational energy. Think of playing billards. If a ball hits another ball off center, you will see that the hit ball has both rotational energy and translational energy. Eventually, drag will dissipate into heat energy (which is just kinetic [translational and vibrational] energy of the molecules).