Untitled Document

Procedures

Open Saturn images in HOU-IP.
- Zoom the image to 2.
- Check log scaling
- Select desired pallet and adjust scaling as desired.
- Click Data Tools, Image Info to get the exact date and time the image was taken.
Use a planetarium program such as TheSky to identify Saturn's moons.
- Reset the planetarium program to the site location, date, and time the Saturn image was taken.
- Find and center Saturn. Click on the moons until you locate Titan.
- Match the moon pattern in the planetarium program to the Saturn image to identify Titan.
Use HOU-IP's Axes tool to find the centers of Saturn and Titan:
- Click Data Tools, Image Info. Record date and time of image into your log.
- Click Data Tools, Axes. Use your cursor to make a box around Saturn. From the Results box, record center (x, y) pixel coordinates to your log.
- Click Data Tools, Axes. Use your cursor to make a box around Titan. From the Results box, record center (x,y) pixel coordinates to your log.
- Repeat this process for all 19 images.
Use distance formula to calculate orbital distances (in pixels) for Titan:
- For each image plug the coordinates for the center of Saturn and the center of Titan into the distance formula and calculate.
- Or plug the coordinates for Saturn and Titan into the distance formula calculator in Excel.
- Record calculated distance in log for each image.
From log, enter data for each image into Excel spreadsheet.
- Image number
- Date image was photographed
- Time image was photographed
- Orbital distance of Titan from Saturn in pixels.
- Note: Other columns will be automatically calculated by Excel.
Using the graph as a reference, adjust phase angle, period, and amplitude (pink boxes) for the cosine curve (pink line) until it matches Titan curve.
- As a first guess, set amplitude value to the largest distance value measured for Titan.
- Phase value ranges from 0 to 6.28 and is used to shift cosine curve left or right. Start at 0. Increase phase angle value by .5's until it approximates the slope of the left side of Titan's curve.
- Period values widen / narrow the distance between peaks in the cosine curve. Increase or decrease the period value for the cosine curve so that it passes through Titan curve data points for both days.
- Move back and forth between the phase angle, period, and amplitude boxes, adjustmenting values to minimize differences between the two curves.
- The closer S(r-rcalc)^2 is to zero, the better the fit of the curves. (S(r-rcalc)^2 is the sum of the squares of the differences between the curves)
- When no changes can be made to phase angle, period, or amplitude that will decrease S(r-rcalc)^2 you have determined the period and orbital radius (in pixels) for Titan. Record your values for amplitude and period.
Determine image plate scale:
- Using Astro Photo program, enter CCD type, method of focus, type telescope, focal reducer size, and type binning.
- Use Pixel Coverage calculation to get plate scale (2.9 '/pxl).
Calculate orbital radius.
- Convert amplitude (A) from pixels to arc seconds by multiplying it by the plate scale (2.9). This gives the angular width of Titan's orbit: q' = A x 2.9'/pxl
- Convert arc seconds to radians:
  qdeg = q' x 1deg / 3600'
  qrad = qdeg x prad / 180deg
- Use Geometric geocentric eliptical coordinates (r :) from TheSky to find the distance from Earth to Saturn for Jan 10, 2001. Convert from AU to km.
  d = 8.533379AU x 1.496 x 10^8 km/AU = 1.277 x 10^9 km
- Use small angle formula to find the orbital radius of Titan by using angular width qrad and the distance from Earth to Saturn (d) in km:
  D = d x qrad
- Our value for Titan's orbital radius:
  D = 1,287,000 km

HOU Home	Mass of Saturn	Links & Contacts	CFHS Home

	Measured Value	Accepted Value
Orbital Period of Titan	284.7 hrs	284 hrs
Orbital Radius of Titan	1.29 x 10^6 km	1.22 x 10^6 km

Period of Titan