SNAP L2 Orbit Scattering Angles for near Ecliptic Pole Pointings

Patrick Jelinsky

02/20/2004

Introduction

This is an addendum to the 1/26/2003 SNAP Tech note "SNAP L2 Orbit
Scattering Angles" \[Ref 2\]. Only pointing directions within 20 or 25
of the ecliptic poles were used to determine the sun, earth, and moon
scattering angles.

# Halo Orbit

Reference 1 showed that the best L2 halo orbit had an amplitude out of
the ecliptic plane (Z direction) of 55,000 km. This orbit was used to
analyze the potential angles that the sun, earth, and moon could have
with SNAP.

The analysis was run with 24 pointing directions with the Z axis within
of the north ecliptic pole and 24 pointing directions with the Z axis
within of the south ecliptic pole. For each pointing direction the
observatory was rotated about the Z axis with the sun to x axis angle in
the range of 45 at 11 locations. The orbit was run for 1 year and one
location on the orbit per day was analyzed. Therefore about 192,720
pointing orientations were checked. For each of these orientations, the
sun, earth, and moon vectors in the local SNAP coordinates were
recorded.

Figure 1 shows the result of the analysis for the Z axis within 20 of
the pole. The dots are the results of the analysis and the lines are the
recommended scattering angle bounds. The points for the boundary are
given in Table 1. is the rotation about the Z axis and is the rotation
about the Y axis.

![](media/image1.wmf){width="5.895833333333333in"
height="2.2680555555555557in"}

Figure 1 Earth, Moon, and Sun angles for a halo orbit with the Z axis
within 20 of the poles. The dots are the results of the analysis and the
lines are the recommended scattering angle bounds.

Table 1 Halo Orbit ( = 20) Scattering Angle Boundary Points

+-----------+-----------+-----------+-----------+-----------+-----------+
| ## Earth  |           | ## Moon   |           | ## Sun    |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| **()**    | **()**    | **()**    | **()**    | **()**    | **()**    |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -70.9     | 0.0       | -85.8     | 0.0       | -45.0     | -20.0     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -65.4     | 22.3      | -70.1     | 24.0      | -45.0     | 20.0      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 65.4      | 22.3      | 70.1      | 24.0      | 45.0      | 20.0      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 70.9      | 0.0       | 85.8      | 0.0       | 45.0      | -20.0     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 65.4      | -22.3     | 70.1      | -24.0     |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -65.4     | -22.3     | -70.1     | -24.0     |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+

Figure 2 shows the result of the analysis for the Z axis within 25 of
the poles. The dots are the results of the analysis and the lines are
the recommended scattering angle bounds. The points for the boundary are
given in Table 2. is the rotation about the Z axis and is the rotation
about the Y axis.

![](media/image2.wmf){width="5.944444444444445in"
height="2.1958333333333333in"}

Figure 2 Earth, Moon, and Sun angles for a halo orbit with the Z axis
within 25° of the poles. The dots are the results of the analysis and
the lines are the recommended scattering angle bounds.

Table 2 Halo Orbit ( = 25°) Scattering Angle Boundary Points

+-----------+-----------+-----------+-----------+-----------+-----------+
| ## Earth  |           | ## Moon   |           | ## Sun    |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| **()**    | **()**    | **()**    | **()**    | **()**    | **()**    |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -70.9     | 0.0       | -85.8     | 0.0       | -45.0     | -25.0     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -64.0     | 27.2      | -66.0     | 29.0      | -45.0     | 25.0      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 64.0      | 27.2      | 66.0      | 29.0      | 45.0      | 25.0      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 70.9      | 0.0       | 85.8      | 0.0       | 45.0      | -25.0     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 64.0      | -27.2     | 66.0      | -29.0     |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -64.0     | -27.2     | -66.0     | -29.0     |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+

Lissajous Orbit

Reference 1 showed that the best L2 lissajous orbit had an amplitude out
of the plane (Z direction) of about 264,000 km and an amplitude in the Y
direction equal to the amplitude in the Z direction. This orbit was used
to analyze the potential angles that the sun, earth and moon could have
with SNAP.

The analysis was run with 24 pointing directions with the Z axis within
of the north ecliptic pole and 24 pointing directions with the Z axis
within of the south ecliptic pole. For each pointing direction the
observatory was rotated about the Z axis with the sun to x axis angle in
the range of 45 at 11 locations. The orbit was run for 6.8 years and one
location on the orbit per day was analyzed. Therefore about 1,310,496
pointing orientations were checked. For each of these orientations, the
sun, earth, and moon vectors in the local SNAP coordinates were
recorded.

Figure 3 shows the result of the analysis for the Z axis within 20 of
the pole. The dots are the results of the analysis and the lines are the
recommended scattering angle bounds. The points for the boundary are
given in Table 3. is the rotation about the Z axis and is the rotation
about the Y axis.

![](media/image3.wmf){width="5.960416666666666in"
height="2.2979166666666666in"}

Figure 3 Earth, Moon, and Sun angles for a lissajous orbit with the Z
axis within 20° of the poles. The dots are the results of the analysis
and the lines are the recommended scattering angle bounds.

Table 3 Lissajous Orbit ( = 20°) Scattering Angle Boundary Points

+-----------+-----------+-----------+-----------+-----------+-----------+
| ## Earth  |           | ## Moon   |           | ## Sun    |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| **()**    | **()**    | **()**    | **()**    | **()**    | **()**    |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -57.4     | 0.0       | -71.3     | 0.0       | -45.0     | -20.0     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -52.4     | 30.6      | -58.0     | 36.1      | -45.0     | 20.0      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 52.4      | 30.6      | 58.0      | 36.1      | 45.0      | 20.0      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 57.4      | 0.0       | 71.3      | 0.0       | 45.0      | -20.0     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 52.4      | -30.6     | 58.0      | -36.1     |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -52.4     | -30.6     | -58.0     | -36.1     |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+

Figure 4 shows the result of the analysis for the Z axis within 25 of
the pole. The dots are the results of the analysis and the lines are the
recommended scattering angle bounds. The points for the boundary are
given in Table 4. is the rotation about the Z axis and is the rotation
about the Y axis.

![](media/image4.wmf){width="5.920138888888889in"
height="2.154166666666667in"}

Figure 4 Earth, Moon, and Sun angles for a lissajous orbit with the Z
axis within 25° of the Poles. The dots are the results of the analysis
and the lines are the recommended scattering angle bounds.

Table 4 Lissajous Orbit ( = 25°) Scattering Angle Boundary Points

+-----------+-----------+-----------+-----------+-----------+-----------+
| ## Earth  |           | ## Moon   |           | ## Sun    |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| **()**    | **()**    | **()**    | **()**    | **()**    | **()**    |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -58.0     | 0.0       | -70.9     | 0.0       | -45.0     | -25.0     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -51.4     | 35.6      | -58.2     | 41.1      | -45.0     | 25.0      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 51.4      | 35.6      | 58.2      | 41.1      | 45.0      | 25.0      |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 58.0      | 0.0       | 70.9      | 0.0       | 45.0      | -25.0     |
+-----------+-----------+-----------+-----------+-----------+-----------+
| 51.4      | -35.6     | 58.2      | -41.1     |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+
| -51.4     | -35.6     | -58.2     | -41.1     |           |           |
+-----------+-----------+-----------+-----------+-----------+-----------+

# Conclusion

The bounds for the angles for the Earth, Moon, and Sun are given in the
tables and can be used in the stray light analysis of SNAP.

The lissajous orbit has a slight advantage over the halo orbit since the
stray light from the earth and moon should be easier to control. The
stray light from the sun should be the same for both. In the lissajous
orbit the earth will have about 28% and the moon 43% of the flux of the
respective objects in the halo orbit. This is since the disks are less
illuminated. The angles of the earth and moon for the lissajous orbit
are also closer to the X axis by about 12.

# References

1.  SNAP Tech Note \# TBD, SNAP L2 Orbit Eclipse/Antenna Study, P.
    Jelinsky

2.  SNAP Tech Note \# TBD, SNAP L2 Scattering Angles, P. Jelinsky