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Chapter 11: Problem 8

What is 3 -to- 2 spin-orbit coupling? How is the rotation period of an object exhibiting 3 -to- 2 spin-orbit coupling related to its orbital period? What aspects of Mercury's orbit cause it to exhibit 3-to- 2 spin-orbit coupling? What telescopic observations proved this?

Short Answer

Expert verified
3-to-2 spin-orbit coupling implies a body spins three times on its own axis for every two of its orbits. Consequently, the object's rotation period is 1.5 times its orbital period. Mercury's orbit exhibits this kind of coupling due to its elliptical orbit and solar tidal forces. Observational proof came from 1960's radar measurements and confirmed by spacecraft imaging.

Step by step solution

01

Understanding 3-to-2 Spin-Orbit Coupling

A 3-to-2 spin-orbit coupling means that for every two revolutions an object makes around a celestial body (its orbital period), it rotates three times around its axis (its rotation period). This state is also known as a spin-orbit resonance of 3:2 variation.
02

Relating Rotation and Orbital periods

Given the 3:2 spin-orbit coupling for an object, one can say that the object's rotation period is approximately 1.5 times its orbital period. This is simply understood by dividing the number of spins (3) by the number of orbits (2). In cases where the periods are in full synchronization, the object shows steady 'tidal locking' also called 'synchronous rotation', where the object rotates about its axis in exactly the same time it takes to orbit the other celestial body.
03

Mercury's Orbit and Spin-Orbit Coupling

Mercury exhibits a 3:2 spin-orbit coupling due to its elliptical orbit and solar tidal forces. Mercury's proximity to the Sun causes tidal bulging that efficiently dissipates orbital energy via heat. This has resulted in Mercury being in a 3:2 spin-orbit resonance with the Sun, causing its rotation period to be 1.5 times its orbital period.
04

Observational Evidence of Mercury's Spin-Orbit Coupling

Evidence of Mercury's 3:2 spin-orbit coupling was first obtained from radar observations in the 1960's. Prior to this, it was believed that Mercury was in a 1:1 spin-orbit coupling with the sun. The radar measurements showed that Mercury rotated three times for every two orbits around the sun. This was further proven by the images sent back by NASA's MESSENGER spacecraft.

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Most popular questions from this chapter

Why does the atmospheric pressure on Mars vary with the seasons? What is the relationship between this pressure variation and Martian dust storms?

Explain why Mercury does not have a substantial atmosphere.

What evidence do we have that the surface features on Mercury were not formed during recent geological history?

Figures 11-6b and \(11-6 c\) show a planet in synchronous rotation and Mercury with a 3 -to- 2 spin-orbit coupling, respectively. Stand up and demonstrate how planets move in each of these rotations by "orbiting" around a stationary classmate who represents our Sun. How would Mercury's motion be different if it had a 4-to-2 spin-orbit coupling instead?

The Mariner 2 spacecraft detected more microwave radiation when its instruments looked at the center of Venus's disk than when it looked at the edge, or limb, of the planet. (This effect is called limb darkening.) Explain how these observations show that the microwaves are emitted by the planet's surface rather than its atmosphere.
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