Институт Космических Исследований
Space Research Institute
Solar sailing in vicinity of Sun-Earth collinear libration points.
Denis Novikov
Phone +7(095) 333-11-00
Fax +7(095) 913-30-40
e-mail: dnovikovt@iki.rssi.ru
Space Research Institute (IKI)
117997, 84/32 Profsoyuznaya Str, Moscow, Russia
Phone +7(095) 333-52-12
Fax +7(095) 913-30-40
www.iki.rssi.ru
Институт Космических Исследований
Space Research Institute
Abstraction.
For space weather studies it is very effective to put spacecraft into vicinity of L1
libration point. With the use of solar sails it is possible to control the motion of the spacecraft
including shift the orbit further from the Earth. The possibilities of this approach are
considered and results are presented.
Earth-Synchronous Heliocentric Orbital Motion Using Solar Sails
Well known example of the Earth- Synchronous spacecraft (s/c) heliocentric orbital
motion is the case when s/c is positioned in L1 or L2 solar-terrestrial libration points. In these
cases s/c is moving around the Sun with the same period as the Earth being either 1.5 mln. km
closer (L1) or further (L2) to the Sun than the Earth and situated on Sun-Earth line. It is
possible because Earth in this case is decreasing (L1) or increasing (L2) the Sun gravity field
acceleration to the extent required by necessity to keep orbital period of the s/c equal to Earth
one.
Similar effect can be reached by use of solar sails. Using them in the vicinity of L1
libration point one can reach additional decreasing effect of solar gravity acceleration thus
allowing to shift s/c Earth-Synchronous position closer to the Sun than L1 point.
Suppose we intend to shift s/c closer to the Sun than the Earth orbit of a radius by d
distance keeping the same Earth heliocentric orbital angular rate .
For motion along this more close to the Sun circular orbit the required heliocentric
acceleration is to be:
Wr   2 (a  d ) .
If s/c is positioned on Sun-Earth line then the acceleration produced by the Earth
gravity field force is:
WE  
E
d2
,
where  is the Earth gravitational constant, the acceleration produced by Sun gravity field is:
WS 
S
(a  d ) 2
,
the required acceleration to be produced by solar radiation pressure is
WP   F
S
,
m
where F is solar radiation pressure, S - s/c cross-section area, m - s/c mass.
DENIS NOVIKOV
2
Институт Космических Исследований
Space Research Institute
Then the formula is valid:
 2 (a  d ) 
S
(a  d )
2

E
d
2
F
S
.
m
Using the following values of parameters:
S = 132712517,
E = 398.6,
a = 149597.81 tds. km,
2
 a  N
F  4.5 10 
 2 (for full photons absorption),
ad  m
6
and the above formula one can calculate the required solar radiation acceleration Wr and
required m/S ratio for solar sails.
Some results of such calculations may be presented by the following table:
d,
Wr,
tds km
m/s2
m
, kg/m2
S
1500
0

2000
-0.0001333
0.03468
2500
-0.0002306
0.02018
3000
-0.0003118
0.01502
4000
-0.0004560
0.01042
The case given in the above table supposes that solar radiation is fully absorbed by the solar
sails, i.e. the reflectivity coefficient is equal zero. From effectiveness point of view it is the
worst case. The best case is full reflectivity of sail surface, when acceleration produced by
solar radiation pressure is two times higher. Accordingly the maximum allowed mass to
cross-section area ratio is two times higher than given in the table figures.
DENIS NOVIKOV
3
Институт Космических Исследований
Space Research Institute
Scheme of solar sail.
Full ideal reflection.
photons
photons
transparent liquid crystal film
mirror reflecting layer
Liquid crystal film with
a mirror reflecting layer.
Solar radiation pressure
2
 a  N
F  9  10 

2
ad  m
6
Full absorption.
photons
fully non transparent liquid crystal film
Solar radiation pressure
2
 a  N
F  4.5  10 

2
ad  m
6
Fully diffused reflection.
photons
Solar radiation pressure
2
 a  N
F  6  10  6 
 2
ad  m
DENIS NOVIKOV
4
Институт Космических Исследований
Space Research Institute
The orbit around the libration point.
Methods and Tools to Launch spacecraft onto Trajectory in L1 Point Vicinity.
It was shown that there are methods to launch s/c onto trajectory in vicinity of collinear solarterrestrial libration points L1, L2 using only one impulse on parking orbit. In this case the
maximum amplitude of orbit around libration point is realized reaching 750 tds km for the
cases when perigee of transfer orbit is in proximity of ecliptic plane and up to 1 mln. km in
the other cases.
DENIS NOVIKOV
5
Институт Космических Исследований
Space Research Institute
The injecting V impulse for all these cases is about 3200 m/s for 200 km altitude circular
parking orbit. To form the near libration point orbit with lower amplitude one needs to apply
additional impulse. This impulse reaches its maximum value equal 300 m/s when this
amplitude is to be equal zero. The value of this impulse is linearly depending amplitude
reaching zero value when amplitude is maximum value.
There is alternative way to decrease the amplitude by use of Lunar gravity assist maneuver.
Taking into account the small mass of the s/c it seems most attractive to use passenger or semi
passenger mode of launch.
High elliptic parking orbits can be considered for such approach. From list of such orbits
those which are used for comparatively regular launches of dedicated payloads are worth full
to be explored. Examples of the mentioned orbits are the ones for “Molniya” and “Oko” s/c.
These orbits are high elliptical half-day period orbits. Despite big angle of its perigee-apogee
lines with respect to the ecliptic plane (perigee is comparatively far from ecliptic plane) it is
still possible to use them as intermediate parking orbits for injection s/c to transfer trajectory
to libration points.
Required V for injection s/c to transfer orbit is 680 m/s for the mentioned half-day period
orbit. The other example of candidate parking orbit is geostationary transfer orbit. For this
case V is 750 m/s.
Advantage of this orbit is the fact that the perigee if the transfer orbit is close to the ecliptic
plane for this case what allows applying Moon gravity assist maneuver for decreasing the near
libration point orbit amplitude. Thus taking into account not excluded requirements to apply
V impulses for construction zero-amplitude libration orbit and unavoidable correction
maneuvers the total V is to be taken about
750+300+50= 1100 m/s.
It means that for hydrazine as propellant with specific impulse 2200 m/s the mass of
propellant is to be about 40 percent of s/c initial mass.
DENIS NOVIKOV
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