Galileo movie of Io.

Volcanoes of Io

Summary
The student determines the height, velocity, and range for volcanoes on Io and compare the results to geysers on Earth

Background and Theory
Io is the most geologically active world in our solar system. In fact, the surface of Io is so active that it is the only solid surface in our solar system without any impact craters. Io is resurfaced in under a million years and the entire crust is recycled in about 10 million years. That means that over the age of the solar system, the crust of Io has been completely recycled over 400 times.

The mechanism for this intense amount of resurfacing is volcanism. Io's volcanism dwarfs all other worlds in our solar system. Volcanoes were first discovered on Io when the Voyager spacecrafts flew past in 1979 and detected eight volcanoes in eruption. The Galileo spacecraft now in orbit around Jupiter has discovered more volcanoes and continues to monitor the eruptions on Io. The size of the eruptions is immense, some hurtling material higher and farther than any terrestrial volcano. The difference is due to the lower gravity of Io plus the fact that it does not have an atmosphere.

Procedure
  1. The first image that follows was taken by Voyager 2 of the volcano Prometheus. The second image is of the Ra Patera volcano taken by the Galileo spacecraft.

    For each of the images determine the maximum height of the volcano above the surface of Io. To do this, you must first calculate the image scale. The radius of Io is 1820 km. For the image of Prometheus, you may assume that 1/4 of the disk is being shown. Your task is much easier and more accurate for Ra Patera as most of the disk of Io is displayed.

    PrometheusRa Patera
    Prometheus Ra Patera
    Full scale picture of Ra Patera

    Height of Prometheus:

    Height of Ra Patera:

    Note: your values should be between 75 and 100 km; otherwise, you have made an error.

    In the following calculations, be careful about units.

  2. From the height of the volcano's plume, you can approximate the velocity that the material left the volcano using the equation:

    height = (velocity)2 / 2g

    or
    velocity = square root (2g x height)

    where the height is measured in meters, the velocity in meters per second, and g is the acceleration due to gravity for the surface of Io. Values of g are given for a few solar system worlds in Table 1. Also given in this table is the escape velocity (Vescape) of the planet. Objects moving faster than Vescape can escape the gravitational pull of the planet.

    Table 1: Values of g for some solar system objects.
    Planetg
    (m/s2)    		 Vescape
    (km/s)
    Vesta0.23 0.35
    Io1.81 2.6
    Earth9.81 11.2
    Determine the velocity of the material ejected from the surface of Io for these two volcanoes. Show all work here.

    Prometheus

     

     

     

     

     

     

    Ra Patera

     

     

     

     

     

     

  3. Randy Johnson (ex-Mariner) can throw a fastball about 150 km/hr. How does the velocity of the volcanoes on Io compare to his fastball? Be quantitative: state how many times faster or slower. Show all work here.

    Prometheus

     

     

     

     

     

     

    Ra Patera

     

     

     

     

     

     

  4. The Yellowstone geyser Old Faithful (which in some respects resembles Io's volcanoes more than some other terrestrial volcanoes such as Mt. St. Helens) spews steam to a height of about 61 meters (200 feet) with a velocity of about 50 m/s. If Old Faithful were transported to Io, it would spew steam at about 350 m/s. How high would Old Faithful reach on Io? Show all work here.

     

     

     

     

     

     

  5. If a volcano with the same velocity as Prometheus were to occur on the asteroid Vesta, describe what would happen to the particles ejected by the volcano.

     

     

     

     

     

     

  6. The following image is a "Mercator Map" of Io. The largest volcano on Io, named Pele (named after the Hawaiian goddess, not the soccer player), is the most conspicuous object visible to the left of center of this image (grid 4 right, 3 down from upper left-hand side).
    Assume that the height of the image shows the full diameter of Io, determine the scale of the image. Then, using criteria of your choosing, calculate how far the material is being thrown from the central vent of Pele. Be sure to show all work here and to mention briefly what criteria you used.

    Mercator Projection Map of Io
    Mercator Projection Map of Io

     

     

     

     

     

     

  7. If you know the range of the plume of Pele, you can determine its minimum velocity from:

    range = (velocityminimum)2 / g

    or
    velocityminimum = square root (g x range)

    Determine the minimum velocity of material being ejected from Pele

     

     

     

     

     

     

  8. How high would Pele be able to throw material on Earth? Don't forget to scale down its velocity.

     

     

     

     

     

     

  9. Compare the following two shots of Io: one from Voyager 1979 and one from Galileo 1996. How many differences (changes) do you see between these two images taken nearly 20 years apart? Mark an "X" on one of the shots indicating where changes have occurred. Try to find at least 5 changes.

    Voyager and Galileo images of Io

Take a look at this image of Io for one of the most spectacular images of a moon you will ever see!