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Rotation Rate of Mercury. Lab 9. Mercury. Closest planet to Sun, ~ 0.4 AU Very small, even Ganymede is larger Very eccentric orbit ~0.308 - 0.467 AU Sidereal rotational period = 58.7 days (rotation is the length of time for an object to spin once on its axis )

Rotation Rate of Mercury

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Rotation Rate of Mercury

Lab 9

- Closest planet to Sun, ~ 0.4 AU
- Very small, even Ganymede is larger
- Very eccentric orbit ~0.308 - 0.467 AU
- Sidereal rotational period = 58.7 days (rotation is the length of time for an object to spin once on its axis )
- Mercury has rotation of three times every two orbits
- Sidereal year = 88 days
- 1:1 resonance not possible because orbit very eccentric

- It takes Mercury about 59 Earth days to spin once on its axis (the rotation period), and about 88 Earth days to complete one orbit about the Sun
- However, the length of the day on Mercury (sunrise to sunrise) is 176 Earth days

- A point initially pointing toward the Sun will point in the same direction after one rotation (59 days or 2/3 of the orbital period), but that point will no longer be directed toward the Sun
- It takes three rotations of the planet during two orbits of the planet about the Sun, or 88 x 2=176 days, for the mark to get back to the same position.

Mercury

spins

on its

axis

every

59 days

But the

length

of a day

on

Mercury

is about

three

times this

- Rotation period of Mercury is 59 days, which is exactly two-thirds of the planet's orbital period
- Because there are exactly three rotations for every two revolutions, we say that there is a 3:2 spin-orbit resonance in Mercury's motion
- Resonance just means that two characteristic times—here Mercury's day and year—are related to each other in a simple way
- A simpler example of a spin-orbit resonance is the Moon's orbit around Earth
- This rotation is synchronous with the revolution, so the resonance is said to be 1:1

- The 3:2 spin-orbit resonances didn’t occur by chance.
- Tidal forces due to the Sun’s gravity are responsible in a very subtle way.
- Tidal forces try to synchronize the rotation rate with the instantaneous orbital speed.
- But tidal forces decrease with distance, so the perihelion distance won out.
- At perihelion the rotation rate and orbital speed is the same, but not so at other points, so we end up with this 3:2 spin-orbit resonance.

- object that is moving away from you has a longer wavelength than it had when it was emitted - a redshift
- object that is moving towards you has a shorter wavelength than it had when it was emitted - a blueshift

- 2 motions of Mercury produce Doppler shift
- Orbital velocity
- Rotation on its axis

- Edge of planet rotating towards us has an orbital velocity faster than the rest of the planet
- So echo of pulse has a higher frequency

- Edge of planet rotating away from us has an orbital velocity slower than the rest of the planet
- So echo of pulse has a lower frequency
- Difference in echoes can be calculated to give rotational velocity of surface of Mercury
- From that we can calculate period of rotation

- http://www.phys.unt.edu/courses/Astronomy/mercury.pdf