Rotation Rate of Mercury

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Rotation Rate of Mercury

• Lab 9

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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
• 11 resonance not possible because orbit very
  eccentric

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Mercurys 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

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23 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 2176
  days, for the mark to get back to the same
  position.

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Mercury spins on its axis every 59 days But
the length of a day on Mercury is about three
times this
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In two revolutions of Mercury around the Sun, the
planet rotates three times on its axis
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Explanation

• 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 32
  spin-orbit resonance in Mercury's motion
• Resonance just means that two characteristic
  timeshere Mercury's day and yearare 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 11

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Explanation of Mercurys Rotation

• The 32 spin-orbit resonances didnt occur by
  chance.
• Tidal forces due to the Suns 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 32 spin-orbit resonance.

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Doppler Shift

• 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

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2 kinds of velocity

• 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

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Calculate!

• 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

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Detailed handbook

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