Geoscience Reference
In-Depth Information
sampling at 100 ms
diffraction pattern
1.2
1
TNO:
Radius = 1.5 km
Distance = 43 AU
Shadow Velocity
= 25.24 km/s
0.8
0.6
target star (A0):
T = 9790 K
point source
0.4
0.2
0
-10
-5
0
5
10
Central Distance (km)
Fig. 4. Diffraction pattern and detector's response. Target star: A0 (black body at
9,790 K), point source. TNO: radius 1.5 km, 43 AU away, shadow velocity 25.24 km/s.
Filter: 400-800 nm band-pass. The diffraction pattern through the center is shown as
the dash curve. Response at a sampling rate of 100 ms is shown as nine small squares. A
set of light curves will fill the solid line if all possible sampling phases are considered.
here. Shadow velocity, however, is a free input parameter here. It can be
related to the angular separation from the opposition with a general (circu-
lar or non-circular) Keplerian orbit assumed. That velocity is a function of
TNO orbital elements and the two-dimensional TNO phase angle. Its dis-
persion can thus be related to a distribution in the orbital elements. There
are some interesting relations between a random impact parameter and
the distribution of geometric occultation duration. Given a spherical object
with its circular shadow, this distribution can be calculated analytically.
A simulation is shown in Fig. 5 (the rightmost solid line with eccentricity
e
= 0) where a target star of point source is assumed. A few more two-
dimensional cases were studied. An ellipse with certain orientation is similar
to a circle basically. An ellipse of certain size with random orientation has
an eccentricity-dependent distribution. Its geometric occultation duration is
dominated by the size of its minor axis. Figure 5 shows the cumulated prob-
ability with respect to the normalized occultation duration. (For an ellipse,
it is normalized with respect to its major axis where it has the longest occul-
tation duration.) Geometric rectangular shadows were analyzed as well.
Two folding points relate to its length and its width respectively as can be
