Herschel's Star Gages
General Description
This simulation illustrates William Herschel's methods of "star-gages"
by which he attempted to map out the shape of our galaxy in 1785. Herschel's
star gages (sic) relied on two important assumptions: that Herschel's
telescope (his "large 20 foot" with an 18.5 inch aperture) could see to the ends of the galaxy, and that within the
galactic system stars are distributed uniformly. If the first
assumption holds then the stars seen in the telescope all lie within a
conical region of space with the apex at the telescope and the base at
the edge of the galaxy. If the second assumption holds then the
number of stars seen in the telescope is proportional to the volume of
this cone. Since the volume of the cone is proportional to the cube
of its height, the distance to the galactic edge in any direction is proportional to
the cube root of the number of stars seen in that direction.
This simulation allows the user to use Herschel's method of star gages
to map out the shape of several artificial "star systems." One window shows
the view through a telescope, with a slider to rotate the telescope
around a fixed axis. Another window shows a 3D
view of the star system, showing either all of the stars in the system
or only those stars visible through the telescope. A third window
shows a plot of the star-gages. Plotting star-gages for many
different directions maps out a cross-section of the star system.
An optional slider allows the user to limit the distance
at which stars are visible, and a menu allows the user to
select from six different stars systems (some with stars distributed
uniformly, others with non-uniform distributions). These options let the user explore how violations of
Herschel's two fundamental assumptions invalidate his star-gage method.
Telescope View Frame
This frame shows the view through a telescope looking out from within
the star system.
- Telescope Options Menu
- Show Plot of Star Gages: show a plot of distance (as
determined by the star gage) versus direction angle.
- Show 3D View of Star System: show a 3D view of the star
system as seen from the outside.
- Limit Telescope Viewing Distance: reveals a slider that
allows the user to limit the distance to which stars are
visible in the telescope.
- System Menu
- Uniform 1: selects a star system in which stars are
distributed uniformly within a thin cylindrical disk, with
the telescope sweeping along the plane of the disk.
- Uniform 2: selects a star system in which stars are
distributed uniformly within a thin cylindrical disk, with
the telescope sweeping perpendicular to the plane of the disk.
- Uniform 3: selects a star system in which stars are
distributed uniformly within a flattened rectangular box,
with the telescope sweeping along the plane of greatest
extent.
- Nonuniform 1: as in Uniform 1 above, but with stars highly
concentrated near the center of the disk.
- Nonuniform 2: as in Uniform 2 above, but with stars highly
concentrated near the center of the disk.
- Nonuniform 3: as in Uniform 3 above, but with stars
concentrated near the center in one direction along the
plane of greatest extent, and near the
edge in the other direction along that plane.
- Activity Menu
- Open Handout (.pdf): opens an activity handout that
guides the user through the use of the simulation, in PDF
format. The document will open in the program you have
set as your default program for opening PDF files.
- Open Handout (.doc): opens the activity handout in
MS Word format.
- Open Handout (.tex): opens the LaTeX source code that
was used to produce the PDF handout.
- Visual Elements
- Black circle background: the telescope's field of view.
- White points: stars (more distant stars appear smaller).
- White text: N is the number of stars visible in the
telescope's field.
- Controls
- Angle: directional angle for pointing the telescope (in
degrees). The telescope is fixed within a given plane, so
it can only rotate about a single axis.
- d_max: an optional control that lets the user limit the
distance at which stars are visible through the telescope.
The distance unit is a stellar unit, which is the average
distance between neighboring stars in the stellar system.
Star System Frame
This frame shows a 3D view of the star system as seen from the
outside. The viewing angle can be changed by clicking and dragging
within the viewing panel.
- Star System Options Menu
- Show All Stars in System: show all the stars in the system.
Otherwise only the stars in the telescope's field of view are
displayed. If all stars are shown, the stars in the telescope's
field of view are highlighted (made larger and shown in red).
- Show Cone for Telescope's Field of View: displays a cone that
defines the telescope's field of view. Only stars within this cone
are visible. The height of the cone is set by the d_max value (see
above).
- Visual Elements
- White points: stars in the star system. If all stars are
shown then those visible through the telescope will be
highlighted.
- Red/blue points: stars visible through the
telescope. Colors indicate whether or not the telescopes sight
distance is limited (red for unlimited, blue for limited).
- Yellow cone: the region of space visible by the
telescope.
Star Gage Plot Frame
This frame shows a plot of the star gage results. Plotting the star
gages for a variety of angles will map out a cross section of the star
system, if Herschel's assumptions are valid.
- Visual Elements
- Red/blue points: star gage data with unlimited (red) or
limited (blue) sight distance. The distance from the
origin to the point (in stellar units) is derived by setting
the volume (in cubic stellar units) of the conical region of space visible to the telescope
(with apex at the telescope and base at the edge of the star
system) equal to the number of stars in the telescope's
field.
- Black circles: lines of constant distance from the
origin (in stellar units).
- Black radial lines: lines of constant orientation angle
for the telescope.
- Controls
- Plot Data Continuously: check this box to plot star gage data
continuously as the Angle slider in the Telescope View Frame is
moved.
- Plot: plot the star gage data for the current viewing angle
(if not plotting continuously).
- Clear: clear all star gage data from the plot.
Todd K. Timberlake (ttimberlake@berry.edu)