studies on the utilization of solar sail in lunar-transfer trajectory zhao yuhui 1,2, liu lin 1,2 1....

STUDIES ON THE UTILIZATION OF SOLAR SAIL

IN LUNAR-TRANSFER TRAJECTORYZhao Yuhui1,2, Liu Lin1,2

1. Astronomy Department, Nanjing University, Nanjing, 210093,China2. Institute of Space Environment and Astrodynamics, Nanjing University,

Nanjing, 210093, China

南京大学空间环境与航天动力学研究所Institute of Space Environment and Astronautics, Nanjing University

Outline

I. Primary TrajectoryII. The orbit under real ‘dynamical model’III. The acceleration due to light pressureIV. Numerical simulations and resultsV. Conclusions


Introduction


1C C

Introduction


1L

Introduction

Hohmann transfer: shorter transfer time, larger fuel consumption

Use the instability of : energy- saving, long time consumption

Reasonable use of light pressure: this paper studies


The force due to light pressure

surface pressure: relative to the mass area ration

conservative central repulsive force:It doesn’t accelerate or decelerate moving bodies continuously. Therefore, the normal direction of the solar sail usually point in a particular direction in order to use light pressure to guide a probe and save energy consumption.

/S m

Introduction


Earth gravity filedLunar gravity field

Earth parking orbit

H ＝200km

T ＝ 12h

T ＝ 24h

T ＝ 48h

Transfer orbit

Transfer orbit

The edge of Moon gravity field

co-two body problem


Primary Trajectory

Co-tow Body Problem (Hohmann Transfer)

Earth parking orbit: 200km-height circular orbit T=12 hour orbit T=24 hour orbit T=48 hour orbit

Transfer orbit: from earth parking orbit to the 300km high point above north pole of the moon

Orbit around moon: 300km×200km lunar polar orbit we consider the two primaries separately, central gravitations in each gravitational field are:

is used to calculate the accelerations.

3

3' '

'

e

m

GMF r

rGM

F rr

2 2 1( )v GMr a


• The kinematical equations are:

• Earth’s central gravity acceleration:

• Lunar central gravity acceleration:

• The acceleration due to :

• Solar gravity perturbing acceleration:

1 2 3 4

0 0 0 0 0: ,

r F F F F F

t r t r r t r

The orbit under ‘real dynamical model’

1 3eGM

F rr

2J

2 33( )m m

mm m

r r rF GM

r r r

3 2( )( )xF R R

4 33( )s ss

s s

r r rF GM

r r r


• Acceleration due to light pressure:

Generally this doesn’t accelerate or decelerate a probe

continuously in space exploration.

• Continuously accelerating:When the normal direction of the solar sail is along the

bisector between the direction of the probe from the sun

and the direction of motion of the probe

The acceleration due to light pressure

2

2

(1 )( )( )

( ) ( )s s

ss s

r rSF

m r r r r


• Acceleration due to light pressure:2

*5 2( )( ) cos ( )s s

sss

r rS rF

m r r rr r

The acceleration due to light pressure

* 0 * 1/21 190 ,cos ( ) ( ),cos ( cos ) 0

2 2 2s

s

r r r

r r r


• five simulation models:• 1) hohmann transfer orbits when the sun and the moon

are on two sides of the earth• 2) takes the light pressure into account on the basis of 1)• 3) hohmann transfer orbits when the sun and the moon

are on the same side of the earth• 4) takes the light pressure into account on the basis of 3)• 5) a transfer orbit ‘only’ guided by light pressure

Numerical Simulations


• trajectory:

Model 1)-4) (4 times impulse)

200km-height circular orbit GT0 orbit GEO orbit

transfer orbit 300km×200km lunar polar orbit

Model 5) (4 times impulse)

200km-height circular orbit GT0 orbit apogee=100,000km transfer orbit 300km×200km lunar polar orbit


By light pressure only


• Initial conditions:

Choose the time that the position of the sun and the moon meets the above requirements during March 2007 as the launch time, and the normal direction of the solar sail in model 2),4),5) points the particular direction given above to accelerate the probes continuously.

Suppose of the earth’s

It’s about

11/ 10S m


1t, 25m 25mm S


Results:



• Analysis:

1),2)and 3),4): The relative position of the 3 bodies have effects on the acceleration due to light pressure and energy-saving.

2),4),5): The effect of light pressure used in a hohmann transfer is not obvious because of the short transfer time while a reasonable use will achieve energy saving along with a not very long transfer time.



Conclusions Acceleration due to light pressure is effected by the relative position of the moon and the sun, and has a slight effect in hohmann transfer orbit. However, if light pressure is reasonably used, energy saving could be actually realized with not too much time consumption by adjusting the solar sail’s normal direction to point a particular direction. This kind of orbits has applications and perspective in deep space exploration, it’s an alternative ‘propellant’ to guide a deep space detector

studies on the utilization of solar sail in lunar-transfer trajectory zhao yuhui 1,2, liu lin 1,2 1....

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