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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 )

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Mercury
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 )

  • Mercury has rotation of three times every two orbits

  • Sidereal year = 88 days

  • 1:1 resonance not possible because orbit very eccentric


Mercury s rotation
Mercury’s rotation

  • 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


2 3 resonance
2:3 resonance

  • 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.


Rotation rate of mercury

Mercury

spins

on its

axis

every

59 days

But the

length

of a day

on

Mercury

is about

three

times this



Explanation
Explanation rotates three times on its axis

  • 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


Explanation of mercury s rotation
Explanation of Mercury’s Rotation rotates three times on its axis

  • 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.


Doppler shift
Doppler Shift rotates three times on its axis

  • 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 kinds of velocity
2 kinds of velocity rotates three times on its axis

  • 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


Calculate
Calculate! rotates three times on its axis

  • 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


Detailed handbook
Detailed handbook rotates three times on its axis

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