You Can Weigh Jupiter

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You Can Weigh Jupiter
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How Do We Measure Mass?

• Only one way gravity!
• By measuring interactions between two objects, we
  can infer their mass

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Johannes Kepler

• Keplers Harmonic Law
• T2 a2
• T orbital period (Earth years)
• a distance from the sun (AU)
• Purely empirical he tried numbers until it
  worked

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Issac Newton

• More general version of Keplers Harmonic Law
• T2 a3/M
• T orbital period (Earth years) a distance
  from the sun (AU) M mass of central body (in
  terms of solar masses)
• Rearrange for mass M a3/T2
• This can now be applied to any pair of bodies,
  not just the sun and planets
• Actually, M should be (Mm) but m is negligible

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Jupiter and Its Moons

• Jupiter has four very bright moons Galilean
  Satellites
• Io, Europa, Ganymede, Callisto
• Discovered by Galileo in 1610

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Motion of the Moons

• Most of the planets in the solar system lie
  within the same plane
• We see Jupiters moons oscillate from one side to
  the other
• Animation
• We can use this motion to calculate the weight of
  the planet

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Simple Harmonic Motion

• The motion of the moons around Jupiter as seen
  from Earth creates a sinusoidal curve
• This curve has a period and an amplitude that you
  can measure

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What This Looks Like In Astronomy

• By measuring the distance of the moon from
  Jupiter (R) and noting the date, you will come up
  with a curve for one of the moons

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How Do We Get Jupiters Mass?

• By measuring the moons period (T) and its
  distance from the planet (a), you will be able to
  calculate M, the mass of Jupiter
• A few reminders
• Convert the period into Earth years divide by
  365.25
• Make sure you have the period in days before
  converting to Earth years
• Convert the distance into AUs divide by 1050
• Remember to record cloudy skies in the correct
  time slot dont just ignore them!

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Choosing Your Observation Interval

• When choosing the observation interval, you want
  to choose something smaller than the period of
  the moon you are looking at
• Sidereal Periods
• Io 1.8 days
• Europa 3.6 days
• Ganymede 7.2 days
• Callisto 16.7 days

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Basic Lab Procedure

• Go to one of the computers and open up the Clea
  JUPITER lab
• Pick a moon to observe and choose an appropriate
  interval
• Click on your moon and record the R value and
  whether its traveling east or west
• Plot your curve as you go make sure you have
  enough data to measure the period before you stop!