Is there any relation between orbital motion and spin motion?

[cooper607]

hi guys, i have a question about the orbit-spin relationship of the celestial objects. for example in our solar system i understand the orbital period becomes lengthy for the planets more distant than the sun, it's logical, but what happens with their spinning motion..? i don't understand why Mercury spins for around 175.97 days and Venus for 243 days while Earth for 24 hours! and Mars for somewhat more than 24 hours! why does they differ so abruptly in spin ? also someone please explain me tidal/gravitational lock...
regards

 

[D H]

For the Jupiter, Saturn, and Neptune, the rotation axes are fairly close to aligned with the orbital plane. These giant planets grew by first forming as a terrestrial-sized planet and then sweeping up dust and gas to become a giant. The gas and dust moved at slower than orbital speed. Those giant planets were somewhat akin to a snowball rolling down a hill, growing bigger and bigger as it accumulates snow. The rolling motion -- that's the planet's rotation (as opposed to its orbit).

Uranus is an outlier amongst the giant planets. It's tilted at 97.8° with respect to the orbital plane. One explanation is that something very big smacked into Uranus during the formation of the planets.


For the terrestrial sized planets, their rotational motion is pretty much (1) random and (2) unconnected with orbital motion. Ignoring tidal locking, the rotation of a terrestrial-sized planet is dominated by the last few things that smacked into the planet during the planet's formation. The consensus view on how terrestrial-sized planets form is that the form by fractal aggregation. Little tiny particles of dust collide with one another, in pairs, and sometimes stick to form a slightly bigger (but still tiny) dust particle. These collide and stick, in pairs, with other particles, eventually building up to form little tiny rocks. These collide and stick, in pairs, to form boulders. And so on. Eventually you get a planet. Almost all of the angular momentum comes from the last few collisions. The angular momentum from when the planet was tiny is pretty much washed out, and the orientation is pretty much random.

For Mercury and Venus one cannot ignore tidal locking. Mercury is essentially tidally locked to the Sun. Strictly speaking, tidal locking means that the orbital and rotational periods are the same. Mercury is in a 3:2 resonance, but that's because the 1:1 resonance (true tidal locking) is not as advantageous energy-wise as is the 3:2 resonance. The angular momentum Mercury has been stolen by the Sun. Mercury lost it's original angular momentum rather quickly because Mercury is so close to the Sun.

Venus is, in a sense, also tidally locked to the Sun. Venus (the solid part of Venus) rotates less than one rotation per orbit, and the rotation is retrograde. Venus also has a very thick atmosphere. Parts of this atmosphere rotate much, much faster than does the solid part of Venus, and this atmospheric rotation is retrograde to Venus' body rotation. In other words, Venus' upper atmosphere has a prograde rotation with respect to Venus' orbit. Generalizing tidal locking to mean "the state that the planet (or moon) is one once the primary is done toying around with the planet (or moon)", then Venus too is tidally locked. It's rotation is permanent, or nearly so. (The Sun will engulf Venus when the Sun goes into it's red giant phase, five billion years in the future. So Venus' rotational behavior is not quite permanent.)


So what is "tidal locking"? The gravitational field of the Sun acting on a planet, or of a planet acting on a moon, is not uniform. Gravity is a 1/r² force, per Newton's law of gravitation. This means that the gravitational acceleration of a planet toward the Sun / a moon toward a planet varies over the volume of the planet / moon. The primary (Sun in the case of a planet, a planet in the case of a moon) exerts a torque on the secondary (the planet or the moon). This "gravity gradient torque" (google that term) is roughly a 1/r³ torque. This means that planets close to the Sun are subject to a huge torque compared to those further away. This also means that gravity gradient torque can be a problem for satellites orbiting the Earth, particularly those in low Earth orbit. It's a rather big problem for the International Space Station.

In addition to applying a torque to the secondary non-uniform gravitational field does something else to the planet or moon. It squeezes them. You are familiar with the ocean tides. You may not know this, but the Moon and Sun also result in Earth tides (google that term, and also "solid body tide"). The solid Earth isn't quite as solid as you think. You oscillate up and down by less than a meter every 12 hours because the Moon and Sun squeeze the Earth a tiny bit. The body tides exerted by the Earth on the Moon are much larger than the paltry sub-meter Earth tides that the Moon exerts on us. They were much, much bigger 4.5 billion years ago when the Moon was much closer to the Earth than it is now.

If the secondary is not tidally locked (1:1 resonance), the rotation of the secondary will not match the orbit. The axis along against the object is squeezed varies. The secondary is never perfectly elastic, so some of that changing squeezing will result in heating. The object heats up, and does so asymmetrically. The thermal radiation is asymmetric, so it can carry angular momentum away from the secondary. There's yet another effect. The non-spherical shape into which the secondary is squeezed in turn feeds back into the torque that the primary exerts on the secondary. Put it all together and the secondary eventually settles into a rotation that is in some kind of resonance with the orbital rate. For a nearly circular orbit, the most favored resonance is 1:1, true tidal lock.

 

[cooper607]

oh thanks/////that was really very detailed and helpful

 

[Igottaknow]

For the Jupiter, Saturn, and Neptune, the rotation axes are fairly close to aligned with the orbital plane. These giant planets grew by first forming as a terrestrial-sized planet and then sweeping up dust and gas to become a giant. The gas and dust moved at slower than orbital speed. Those giant planets were somewhat akin to a snowball rolling down a hill, growing bigger and bigger as it accumulates snow. The rolling motion -- that's the planet's rotation (as opposed to its orbit).

Uranus is an outlier amongst the giant planets. It's tilted at 97.8° with respect to the orbital plane. One explanation is that something very big smacked into Uranus during the formation of the planets.


For the terrestrial sized planets, their rotational motion is pretty much (1) random and (2) unconnected with orbital motion. Ignoring tidal locking, the rotation of a terrestrial-sized planet is dominated by the last few things that smacked into the planet during the planet's formation. The consensus view on how terrestrial-sized planets form is that the form by fractal aggregation. Little tiny particles of dust collide with one another, in pairs, and sometimes stick to form a slightly bigger (but still tiny) dust particle. These collide and stick, in pairs, with other particles, eventually building up to form little tiny rocks. These collide and stick, in pairs, to form boulders. And so on. Eventually you get a planet. Almost all of the angular momentum comes from the last few collisions. The angular momentum from when the planet was tiny is pretty much washed out, and the orientation is pretty much random.

For Mercury and Venus one cannot ignore tidal locking. Mercury is essentially tidally locked to the Sun. Strictly speaking, tidal locking means that the orbital and rotational periods are the same. Mercury is in a 3:2 resonance, but that's because the 1:1 resonance (true tidal locking) is not as advantageous energy-wise as is the 3:2 resonance. The angular momentum Mercury has been stolen by the Sun. Mercury lost it's original angular momentum rather quickly because Mercury is so close to the Sun.

Venus is, in a sense, also tidally locked to the Sun. Venus (the solid part of Venus) rotates less than one rotation per orbit, and the rotation is retrograde. Venus also has a very thick atmosphere. Parts of this atmosphere rotate much, much faster than does the solid part of Venus, and this atmospheric rotation is retrograde to Venus' body rotation. In other words, Venus' upper atmosphere has a prograde rotation with respect to Venus' orbit. Generalizing tidal locking to mean "the state that the planet (or moon) is one once the primary is done toying around with the planet (or moon)", then Venus too is tidally locked. It's rotation is permanent, or nearly so. (The Sun will engulf Venus when the Sun goes into it's red giant phase, five billion years in the future. So Venus' rotational behavior is not quite permanent.)


So what is "tidal locking"? The gravitational field of the Sun acting on a planet, or of a planet acting on a moon, is not uniform. Gravity is a 1/r² force, per Newton's law of gravitation. This means that the gravitational acceleration of a planet toward the Sun / a moon toward a planet varies over the volume of the planet / moon. The primary (Sun in the case of a planet, a planet in the case of a moon) exerts a torque on the secondary (the planet or the moon). This "gravity gradient torque" (google that term) is roughly a 1/r³ torque. This means that planets close to the Sun are subject to a huge torque compared to those further away. This also means that gravity gradient torque can be a problem for satellites orbiting the Earth, particularly those in low Earth orbit. It's a rather big problem for the International Space Station.

In addition to applying a torque to the secondary non-uniform gravitational field does something else to the planet or moon. It squeezes them. You are familiar with the ocean tides. You may not know this, but the Moon and Sun also result in Earth tides (google that term, and also "solid body tide"). The solid Earth isn't quite as solid as you think. You oscillate up and down by less than a meter every 12 hours because the Moon and Sun squeeze the Earth a tiny bit. The body tides exerted by the Earth on the Moon are much larger than the paltry sub-meter Earth tides that the Moon exerts on us. They were much, much bigger 4.5 billion years ago when the Moon was much closer to the Earth than it is now.

If the secondary is not tidally locked (1:1 resonance), the rotation of the secondary will not match the orbit. The axis along against the object is squeezed varies. The secondary is never perfectly elastic, so some of that changing squeezing will result in heating. The object heats up, and does so asymmetrically. The thermal radiation is asymmetric, so it can carry angular momentum away from the secondary. There's yet another effect. The non-spherical shape into which the secondary is squeezed in turn feeds back into the torque that the primary exerts on the secondary. Put it all together and the secondary eventually settles into a rotation that is in some kind of resonance with the orbital rate. For a nearly circular orbit, the most favored resonance is 1:1, true tidal lock.

Just a quick question. This is a great explanation by the way but I was wondering about one thing that wasn't really addressed here. The difference in the spin rates for mercury and venus compared to Earth is huge in relation to the distances they are from the sun. We are comparing a few hours to hundreds of days, but their distances are not the same ratio (spin related to distance from the sun). One thing I thought I might see in an answer to the main question is the effect that the moon has had on the Earth over its lifetime. It has actually slowed Earth's spin (I think). The theory of the moons formation is that a planet the size of Mars crashed into Earth and the moon was formed from that collision and at that same time set the Earth's current spin in motion which back then would have been much more rapid than it is today.

 

[Janus]

Just a quick question. This is a great explanation by the way but I was wondering about one thing that wasn't really addressed here. The difference in the spin rates for mercury and venus compared to Earth is huge in relation to the distances they are from the sun. We are comparing a few hours to hundreds of days, but their distances are not the same ratio (spin related to distance from the sun).

There are a lot of factors that determine how fast tidal locking will occur, but one in particular is that the distance from the Sun causes a difference that is proportional to the distance to the power of 6. All else being equal, a planet twice as far away would take 64 times longer to become tidally locked.