Lab04: Jupitor and its moon

• The first accurate determination of the speed of light (c) was made in 1676 by Danish astronomer Ole Roemer
• Roemer obtained a value of c = 2.14 x 10^8 meters per second, which is 70% of today's value of c = 3.00 x 10^8 meters per second
• Roemer's determination showed that light had a finite speed and was not instantaneous, as many people had thought before him
• Roemer was not initially trying to find the speed of light, his original goal was to see if the orbiting moons of Jupiter could be used to find the longitude of places on earth

  
• Jupiter's moons

  • Galileo discovered 4 moons in 1610
  • Moons orbit Jupiter with remarkable regularity

  
• Ephemeris


  A table of predictions of the positions of celestial objects at given times
• Eclipse


  The disappearance or reappearance of the moons as they pass into Jupiter's shadow

  
• Eclipses of Jupiter's moons were considered an important way to tell time precisely, especially for navigation at sea

  
• Latitude


  The angular distance north or south of the equator
• Longitude

  The angular distance east or west of the prime meridian
• Determining longitude was a major challenge for maritime societies for centuries due to the lack of a reliable sea-going clock
• Knowing the difference between local time and time at the prime meridian allows determination of longitude
• After several weeks nothing is visible on any horizon. It is an hour before dawn and you want to know your position.
• Polaris


  The North Star, used to determine latitude
• Sextant sighting of Polaris shows it is 47 above the horizon, so your latitude is 47N
• When you left London you set your watch to the clock at the Greenwich Observatory and you haven't reset it. The watch shows the time in London.
• The sun should have risen very close to 6:00 am, but your watch shows 8:00 am. The two hour difference between the time the sun tells (local time = 6 am) and what your watch shows (Greenwich Mean Time = 8 am) represents your longitude.
• A one hour difference would indicate that you were 15 West of the prime meridian. Two hours means you are 30 West, and that is your longitude.
• Your position is 47N latitude and 30W longitude.
• If your watch kept time to within one second and you marked the sun's rising to within one second, you would be within one mile of your true location in longitude. With a good sextant that is skillfully used and knowing how much Polaris is shifted from the NCP, your latitude position would similarly be about 1 mile in error.
• Galileo discovered Jupiter's moons a century and a half before Harrison's invention of a precise sea-going mechanical clock.

  
• The idea that Jupiter and its moons could be used as a clock for marine navigation seemed most attractive, and Galileo not only suggested this, but even designed a special telescope that made it easier to sight the moons at sea.

  
• Cassini had been timing the period of Io around Jupiter marking each orbit by when the moon left Jupiter's shadow. His data showed that when Jupiter and earth were close, the observed times of Io's eclipse agreed with those predicted by the ephemeris. But when Jupiter and earth were far apart, the observed eclipse times occurred 10 to 12 minutes later than predicted.

  
• Cassini originally deduced that this was a result of light taking a finite time to travel from Jupiter to earth. However he changed his mind, believing that light could not have a finite speed, and thought that something else was responsible for the errant timings.
• Roemer, however, agreed with Cassini's first interpretation of the data and used Cassini's work to determine the speed of light arriving at a value that was about 70% of the value of c that we accept today.
• Roemer is credited as the person to make the first modern measure of speed of light.
• The speed of light will be determined using a method developed in the 17th Century by Ole Roemer using data obtained by Giovanni Cassini.
• Observing the times of Io's eclipses when Jupiter is far from and near the earth

  1. Find two dates when the distances between Jupiter and earth are larger and smaller

  2. Observe and time an eclipse of Io on the far date

  3. Use the synodic period of Io to predict an eclipse several months later

  4. Observe and time the predicted eclipse

  5. Compare the predicted time to the observed time
• Synodic period


  The time it takes for a moon to repeat the same position relative to the planet and the observer

  
• In practice, dates about two months after conjunction and a month prior to opposition provide observing situations that allow Io's eclipses to be seen more easily.
• Giovanni Cassini observed the time when Io emerged from Jupiter's shadow. In this activity you will instead observe when Io enters the shadow.
• To get the exact time of an eclipse, you'll want to start with hour-long time intervals to get the moon close to eclipse and then set the time intervals shorter and shorter so that and you step forward you can see the exact moment when the moon passes into Jupiter's shadow and disappears.

  
• The different moons will appear different colors. Io can be identified by using the mouse to point the cursor at the moon and left clicking on it.

  
• The shadow of Jupiter is marked by two green lines, so that you can see when a moon is about to enter Jupiter's shadow.

  
• Universal Time is essentially the time at the Greenwich Meridian (5 hours ahead of Eastern Standard Time). Julian Day is just a running date that starts at noon Universal time and advances one unit every day.
• Naval Observatory (USNO) sites:
• Time in the simulation

  Shown in standard format (Month-Day-Year, and UT as Hours-Minutes-Seconds) and Julian Day (JD)
• Universal Time (UT)


  The time at the Greenwich Meridian (5 hours ahead of Eastern Standard Time)
• Julian Day (JD)


  A running date that starts at noon Universal time and advances one unit every day
• The fifth decimal place, 0.00001 JD, is about 0.8 seconds, or roughly 1 second