Environmental Engineering Reference
In-Depth Information
useful time it can send power to a single location on the ground is
D
T
¼
TA
=
2
pR
e
¼
100
:
7 min
ð
807
=
2
pR
e
Þ¼
2
:
034 min
;
ð
5
:
4
Þ
with
T
the orbital period,
R
o
¼
R
e
þ
A
¼
7164 km, altitude
A
¼
807 km [61], taking
R
e
2.034min is clearly too short a
time for useful power transfer, so the orbit should be adjusted to a higher altitude.
This will require a larger antenna to keep the same resolution on the ground. To get a
useful time, let us choose 2.034 h, 60 times longer. We can
find the new orbit radius
R
0
o
¼
¼
6357 km for the polar radius of the earth.
D
T
¼
A
0
tomake the period
T
0
¼
R
>
þ
D
60
2.034min
¼
2.034 h by using Keplers
e
law
2
3
ðTÞ
=ðR
o
Þ
¼
constant
:
ð
5
:
5
Þ
To
nd the new parameters
T
0
,
A
0
,
R
0
o
such that
T
0
/
60, setting
R
0
o
/R
o
¼
D
D
T
¼
x
,
and
R
e
/
R
o
¼
a
¼
0.887 we take the ratio based on Equation 5.4, and using
Equation 5.5:
T
0
=D
T
0
=
A
0
=
x
3
=
2
x
3
=
2
D
T
¼
60
¼ð
T
Þð
A
Þ¼
½ð
x
a
Þ=ð
1
a
Þ ¼
ð
x
0
:
887
Þ=
0
:
113
;
or
ð
5
:
6
Þ
x
3
=
2
:
¼
ð
x
:
Þ:
ð
:
Þ
6
78
0
887
5
6a
The solution to this numerical equation is
x
2.55, corresponding to orbit radius
R
0
o
¼
2.875
R
e
,
A
0
¼
11 918 km, and period
T
0
¼
1.875
R
e
¼
6.83 h. These numbers
T
0
¼
return
2.03 h using Equation 5.4. (A slight change tomake the period 6.0 hwill
be assumed below, to give exactly four orbits per day.)
We are pursuing a design of a solar power satellite based on scaling the
properties of the Radarsat, and have found that to make the time the satellite
is in view of a particular location long enough to transfer a signi
cant amount of
energy, we have had to make altitude
A
D
11 918 km versus the 807 km, an
increase by 14.8. (This altitude is about 1/3 of the geosynchronous orbit at
36 300 km mentioned in Figure 5.7.) The new orbit is not assured of being
sun-synchronous, but we will assume that it is [62], or can be adjusted to become
sun-synchronous, (For example, if the period
T
0
is adjusted to 6 h from 6.83 h,
then the satellite will make exactly four earth orbits per day.) The sun will always
be approximately at right angles to the track of the satellite, so that the vertical
solar cell panels in Figure 5.8 will be reasonably oriented to absorb light from the
sun year-round. In the larger orbit we have assumed, there will be no period of
eclipse, realizing that the orbit radius is now 2.9 earth radii. The width of the
ground that can be accessed is about
A
[
R
e
/(
A
¼
þ
R
e
)]
¼
0.655
R
e
¼
0.655
6357
2600 mi. If the satellite is above New York, its power could be tapped in
locations 1300 miles to the west, which would include Chicago and a bit more.
Even so, we are insisting on resolution to restrict the incoming energy to a
receiving region 1309m in diameter. This requirement will make the transmitting
antenna large in dimension, but still could contain only the 10 240 elements in the
Radarsat, the elements would be more widely spaced.
km
¼
