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Orbits Design for Remote Sensing SatelliteM.A. Zayan, F. Eltohamy

Nilesat Company+2012-3942832

[email protected]

1 1-4244-1488-1/08/$25.00 ©2008 IEEE.2 IEEEAC paper #1018, Version 4, Updated December 14,2007

Abstract —This paper is conducted to design and determine

satellite orbits for Earth observation missions, criteria for selecting orbits for remote-sensing satellites are considered.Data provided by the analysis of satellite orbits used for earth studies are generalized. Circular quasi-geosynchronous, sun-synchronous, regular, and other orbits

which permit regular coverage of the earth surface usingdetectors with constant parameters are considered, andrequirements for such orbits are formulated. A generalapproach to the evaluation of the node periods of rotation

and of orbital radius that meet those requirements isanalyzed and discussed. The orbital configuration of a

remote sensing satellite is designed to determine if baselineorbital parameters are appropriately specified to meet themission goal. An algorithm is developed and implemented

for remote sensing satellites orbits selection. A case study ischosen to verify, tune the results, and evaluate the performance.

TABLE OF CONTENTS

1. INTRODUCTION .................................................1 2. ORBIT PERTURBATIONS ...................................1 3. SUN-SYNCHRONOUS R EPEAT ORBITS ..............3 4. SIMULATION OF CASE STUDY...........................3

5. CONCLUSION.....................................................4 R EFERENCES......................................................... 4 BIOGRAPHY...........................................................4

1. INTRODUCTION

Remote sensing (RS), also called earth observation, refers toobtaining information about objects or areas at the Earth’ssurface without being in direct contact with the object or area. Most sensing devices record information about an

object by measuring an object’s transmission of electromagnetic energy from reflecting and radiatingsurfaces. Remote sensing techniques allow taking images of the earth surface in various wavelength region of theelectromagnetic spectrum (EMS). One of the major

characteristics of a remotely sensed image is the wavelengthregion it represents in the EMS. Some of the imagesrepresent reflected solar radiation in the visible and the near

infrared regions of the electromagnetic spectrum, others are

the measurements of the energy emitted by the earth surfaceitself i.e. in the thermal infrared wavelength region. Theenergy measured in the microwave region is the measure of relative return from the earth’s surface, where the energy istransmitted from the vehicle itself. This is known as active

remote sensing, since the energy source is provided by theremote sensing platform. Whereas the systems where theremote sensing measurements depend upon the externalenergy source, such as sun are referred to as passive remote

sensing systems. The orbital plane of the Earth Observationsatellite is commonly required to maintain a fixed angle(e.g.

30o) with respect to the mean Sun direction to ensureadequate illumination conditions for image data collection.The following sections discuss the orbit perturbations

forces, designing the orbit of remote sensing satellite andtaking a case study to verify paper approach.

2. ORBIT PERTURBATIONS

The orbital elements provide an excellent reference for

describing orbits, however there are other forces acting on asatellite that perturb it away from the nominal orbit. These

perturbations, or variations in the orbital elements, can beclassified based on how they affect the Keplerian elements.

Secular variations represent a linear variation in theelement, short-period variations are periodic in the elementwith a period less than the orbital period, and long-period

variations are those with a period greater than the orbital period. Because secular variations have long-term effects on

orbit prediction (the orbital elements affected continue toincrease or decrease), they will be discussed here for Earth-orbiting satellites. Precise orbit determination requires thatthe periodic variations be included as well.

Third-Body Perturbations

The gravitational forces of the Sun and the Moon cause

periodic variations in all of the orbital elements, but only thelongitude of the ascending node, argument of perigee, andmean anomaly experience secular variations. These secular

variations arise from a gyroscopic precession of the orbitabout the ecliptic pole. The secular variation in mean

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anomaly is much smaller than the mean motion and haslittle effect on the orbit, however the secular variations inlongitude of the ascending node and argument of perigee

are important, especially for high-altitude orbits.For nearly circular orbits the equations for the secular ratesof change resulting from the Sun and Moon areLongitude of the ascending node:

( ) nimoon /cos00338.0−=Ω

(1)

ni sun /)cos(00154.0−=Ω

(2)

Argument of perigee:

( ) nimoon /sin5400169.0 2−=ω

(3)

( ) ni sun /sin5400077.0 2−=ω

(4)

where i is the orbit inclination, n is the number of orbitrevolutions per day, and and are in degrees per day.

These equations are only approximate; they neglect thevariation caused by the changing orientation of the orbital

plane with respect to both the Moon's orbital plane and theecliptic plane.

Perturbations due to Non-spherical Earth

When developing the two-body equations of motion, weassumed the Earth was a spherically symmetrical,

homogeneous mass. In fact, the Earth is neither homogeneous nor spherical. The most dominant features area bulge at the equator, a slight pear shape, and flattening atthe poles. For a potential function of the Earth, we can find

a satellite's acceleration by taking the gradient of the potential function. The most widely used form of thegeopotential function depends on latitude and geopotentialcoefficients, J n, called the zonal coefficients.The potential generated by the non-spherical Earth causes

periodic variations in all the orbital elements. The dominanteffects, however, are secular variations in longitude of theascending node and argument of perigee because of theEarth's oblateness, represented by the J2 term in thegeopotential expansion. The rates of change of and due

to J2 are222

2 )1)((cos)/(5.12

−−−=Ω eia RnJ E J

(5)

222

7

14 )1)((cos1006474.2 −

−

−×−≈ eia 2222

2 )1)(sin54()/(75.02

−−−= eia RnJ E J ω (6)

2222

7

14 )1)(sin54(1003237.1 −

−

−−×≈ eia

where n is the mean motion in degrees/day, J 2 has the value0.00108263, R E is the Earth's equatorial radius, a is the

semi-major axis in kilometers, i is the inclination, e is theeccentricity, and and are in degrees/day. For satellites

in GEO and below, the J2 perturbations dominate; for satellites above GEO the Sun and Moon perturbationsdominate. The orbital plane Earth Observation satellite is

commonly required to maintain of a fixed angle(e.g. 30o)with respect t the mean Sun direction, to ensure adequateillumination conditions for image data collection.Considering the secular motion of the ascending node, aSun-Synchronous orbit may be obtained by adjusting the

inclination i in such a way that

Day/985647240.0SunD

=

•

α

Molniya orbits are designed so that the perturbations in

argument of perigee are zero. This conditions occurs whenthe term 4-5sin2i is equal to zero or, that is, when theinclination is either 63.4 or 116.6 degrees.

Perturbations from Atmospheric Drag

Drag is the resistance offered by a gas or liquid to a body

moving through it. A spacecraft is subjected to drag forceswhen moving through a planet's atmosphere. This drag isgreatest during launch and reentry, however, even a spacevehicle in low Earth orbit experiences some drag as it

moves through the Earth's thin upper atmosphere. In time,the action of drag on a space vehicle will cause it to spiral back into the atmosphere, eventually to disintegrate or burnup. If a space vehicle comes within 120 to 160 km of theEarth's surface, atmospheric drag will bring it down in a few

days, with final disintegration occurring at an altitude of about 80 km. Above approximately 600 km, on the other hand, drag is so weak that orbits usually last more than 10years - beyond a satellite's operational lifetime. The

deterioration of a spacecraft's orbit due to drag is calleddecay.The drag force F D on a body acts in the opposite directionof the velocity vector and is given by the equation

AvC F D D

2

2

1 ρ =

(8)

where C D is the drag coefficient, ρ is the air density, v is

the body's velocity, and A is the area of the body normal to

the flow.

For circular orbits we can approximate the changes in semi-major axis, period, and velocity per revolution using the

following equations:

ma AC a D

rev

2

2 ρ π −

=Δ

(9)

mV

a AC P D

rev

226 ρ π −=Δ

(10)

m

aV AC V D

rev

ρ π =Δ

(11)

where C D is the drag coefficient, is the air density, a is the

semi-major axis, P is the orbit period, and A, m and V are

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the satellite's area, mass, and velocity respectively. The term

m/(C D A), called the ballistic coefficient , is given as aconstant for most satellites. Drag effects are strongest for

satellites with low ballistic coefficients, this is, lightvehicles with large frontal areas.A rough estimate of a satellite's lifetime, L, due to drag can be computed from [1]

reva H L

Δ

−≈

(12)

where H is the atmospheric density scale height.

Perturbations from Solar Radiation

Solar radiation pressure causes periodic variations in all of the orbital elements. The magnitude of the acceleration inm/s2 arising from solar radiation pressure is

m

Aa

R

8105.4 −

×−=

(13)

where A is the cross-sectional area of the satellite exposedto the Sun and m is the mass of the satellite in kilograms.

For satellites below 800 km altitude, acceleration fromatmospheric drag is greater than that from solar radiation pressure; above 800 km, acceleration from solar radiation pressure is greater.

3. SUN-SYNCHRONOUS R EPEAT ORBITS

The orbital plane Earth Observation satellite is commonlyrequired to maintain of a fixed angle (e.g. 30o) with respect tthe mean Sun direction, to ensure adequate illumination

conditions for image data collection. Considering thesecular motion

3

2

3

2

2

2

10.083.1

,

cos)2/3(

−

•

==

=

−=Ω

t coefficien potential zonal J

a

GM nwith

ia

RnJ

Earth

o

Earth ft SecularDri

of the ascending node, a Sun-Synchronous orbit may beobtained by adjusting the inclination i in such a way that

DaySun /985647240.0 D

==Ω

••

α

for a given semi-major axis a. At the same time it isgenerally desirable to select the altitude in such a way theresulting ground track is repeated after a specified number

of days and orbits. Here “one orbit” refers to the time between subsequent nodal crossing, which is know as thedraconic orbit period. Due the secular perturbations

)cos31()4/3(

),cos51()4/3(

2

2

2

2

2

2

2

2

ia

RnJ nnn

ia

RnJ

o

ft SecularDri

−−=−=Δ

−−=

⊕

⊕•

ω

of the argument of perigee and he mean anomaly, thedraconic period

•

+

=

ω

π

n

2 TN

differs slightly from the Keplerian orbital period

oo n

2 T

π= .

In the case of the remote sensing satellite a Sun-synchronous orbit is preferred, for which the Greenwich

longitude

ΘΩ

−

of the ascending node equate crossing is repeated after K=3cycles and N=43 orbits, i.e.

D360.K T)..(N N −

•

Θ .

Determine the corresponding altitude and inclination of theorbit, tacking into account the above-mentioned secular

perturbations. For Sun-synchronous orbits

Day/360 T).( ND

≡

•

Θ

•

++=

=

ω Δπ nn ) Day. K /( N 2

Day ). N / K ( T

o

N

Ignoring the difference between draconic and Keplerian

orbital period )0( ≈+Δ

•

ω n , a first approximation of the

semi-major axis is obtained. From this, an approximate

value of the inclination can be determined from the

knowing secular rate

•

Ω of the ascending node. After

computing the perturbations )and n( •

ω Δ , a refined

value of no and the semi-major axis is obtained, which areused as input for a subsequent iteration. Starting from

Day).N/K ( TN = ,

the following flow chart describes the algorithm for computing the required Keplerian parameters for earthobserving satellites.

4. SIMULATION OF CASE STUDY Assume the case of the Remote Sensing Satellite a sun-synchronous orbit is required, for which the Greenwichlongitude of the ascending node equator crossing is repeated

after K=3 cycles (days) and N=43 orbits. The developedMatlab program determines the corresponding, semi major axis, altitude, inclination of the orbit. The result is verified by computing the Greenwich longitude of the ascending

node for N subsequent equator crossing (starting at an initial

value=0 without loss of generality). Convergence is

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achieved within 3 iteration, given the final solution of the

altitude h=774.99 km and i=98.5° for the parameters of the

satellite orbit. Taking into account the previous computed parameters of the satellite orbit to compute the motion of

the satellite relative to a ground station has longitude=+30°,

latitude e=+30°, and altitude=0.0 m. Assume the argument

of perigee =0, and the satellite crosses the equator at right

ascension=0 at the reference epoch 1.0 January 1997 and

predict its motion (elevation, azimuth, range) for a period of 3 days. The developed program is propagating the satelliteorbit during the specified period, using the secular

perturbations, conversion of the orbital elements to statevector elements and then compute the azimuth, elevationand range from the satellite position vector [3]. The program uses the ODE23 [5] function from Matlab libraryto integrate the acceleration and velocity every 1 minute to

get the state vector of the satellite and the correspondingAzimuth, Elevation and range. Although the lower order of ODE23 comparing ODE45 [3] the program givesacceptable accuracy of the trajectory with higher speed

process. Table 1 represents the iteration process sequences

and parameters values at each step. As shown in Figure 2, 3,the iteration process to get the inclination is presented andthe convergence process occurs in between step 2 and 3.

Figure 4 is verifying the algorithm process by representingthe Greenwich longitude of the ascending node for N subsequent equator crossing starts from zero longitude and

returns to zero after 43 orbits. The following Figures 5, 6, 7,9, 10 show the maximum elevation, the azimuth angle,ranging and the visibility time of the satellite. Figure 8 givesthe histogram graph of the elevation angle. The visibility

time is very small comparable to the day period. Theminimum elevation threshold should be considered withrespect to the operating band.

5. CONCLUSION

Satellite orbit parameters selection is very import issueduring mission analysis and design phase. According to therequired mission and tasks, the inclination parameter of thesatellite orbit is very critical issue. Based on the secular

drift, the orbit design could be achieved regarding the rateof change of the secular drift. The proposed orbit should be propagated to study and analysis all important events duringthe satellite life time. The orbital configuration of a remote

sensing satellite is designed to determine if baseline orbital parameters are appropriately specified to meet the mission

goal. An algorithm is developed and implemented for remote sensing satellites orbits selection. A case study ischosen to verify, tune the results, and evaluate the

performance. The simulated case study is propagated usingthe designed orbits to analysis, tune, enhance the proposedmission, and optimize the visibility time with ground track.The propagated model or the flight simulator has to include

all perturbated forces to get accurate simulation results. Thestrategy of the station keeping maneuver has to be has to betaken into account the happen events and orbits drift to keepthe satellite orbit in the desired window.

R EFERENCES

[1] http://www.braeunig.us/space/orbmech.htm.

[2] Maxwell Noton; Space Craft Navigation and Guidance

,”Advances in Industrial Control Series”, Springer-VerlageLondon Limited, 1998.

[3] Oliver Motenbruck, Eberhard Gill; “Satellite Orbit (Models, Methods, Application)”, Springer-VerlagHeidelburg New York (2000).

[4] Pocha, J. J. (Jehangir. J.); An Introduction to Mission

Design For Geostationary Satellites, Published by D. ReidelPublishing Company, Holland; 1987.

[5] MATLAB Soft Ware Package “The Technical Language of

Technical Computing”; Version 6.0.0.88 Release 12.

[6] A.F. Aly, M. Nguib Aly, M. E. Elshishtawy, M.A. Zayan;”Optimization Techniques for Orbit Estimation and

Determination to Control the Satellite Motion “, paper #164,Volume 5 Track 7.07 page 2231-2248, IEEE AC, 2002.

[7] Long A.C.; Mathematical Theory of the Goddard

Trajectory Determination System, Goddar Space FlightCenter; Greenbelt, Maryland (1989).

[8] Allgowe E. L., George K.; Numerical Continuation

Methods, SMC13, Springer Verlag, New York (1990).

[9] McCarthy J. J., Rowton S.; GEODYN ΙΙ Systems

Description, NASA Goddard Space Flight Center, 1993.

[10] Tapley B. D; Precision Orbit Determination for TOPEX/POSEIDON , 99, (1994).

BIOGRAPHY

Dr. Mohamed A. Zayan was born in 1969, He

received the B.Sc. in 1991, M.Sc. degree in

1998 in Digital Communication

Engineering, Faculty of Engineering, Alexandria

University, He received the Ph.D degree in 2004 in Satellite

Navigation and Guidance, Alexandria University. Currently, he is working as a Satellite Control Station

Manager Nilesat, Egypt.

Dr. Fawzy El-Tohamy Hassan Amer , B.Sc. in Electrical

Engineering, from MTC, Cairo, 1972, M.Sc. in Electrical

Engineering, from MTC Cairo, 1982, Ph.D. in Electrical

Engineering, from university of technology of Compigne,

France, 1986, Staff member in MTC, Cairo, Egypt .

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I f inew-iold=0

)R Jn

a.

3

2(cosi

22o

21

⊕

•−

−Ω

STOP

No T2n π=

0nnn

,0

Day/98564720.0

(K/N).Day[Day] T

:ConditionsInitial

o

ftSecularDri

N

=

=

=

=

•

•

Δ

ω

ΩD

32on

GMa Earth

=

START

ftSecularDriNo

2

2

2

2

2

2

2

2ftSecularDri

n) T/2(n

)icos31(a

RnJ)4/3(n

),icos51(a

RnJ)4/3(

•

⊕

⊕•

−

−

−

ω

Δ

ω

N O

Figure1. Orbits

Parameters Design

Flow Chat

YE S

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Iteration 1 2 3 4 5

T N [Day] 0.069767

2π/T N [°/Day] 5160

•

ω [°/Day]0 -2.9607 -2.9709 -2.9709 -2.9709

n-no [°/Day] 0 -3.1067866381 -3.1165189172 -3.1165507994 -3.1165509038

no [°/Day] 5160 5166.06752097 5166.08738547 5166.08745054 5166.08745076

a [km] 7.1587e+003 7.1531e+003 7.1531e+003 7.1531e+003 7.1531e+003

h [km] 7.8061e+002 7.75e+002 7.7499e+002 7.7499e+002 7.7499e+002

i [°] 98.5214161466 98.4979087210 98.4978319134 98.4978316618 98.4978316610

Table 1. The Iterations Number and the Satellite Parameters with K=3 and N=43

1 2 3 4 598.46

98.47

98.48

98.49

98.5

98.51

98.52

Figure 2. Inclination Angle in Degree (vertical axis) Versus Iteration Number

2 3 4 5

98.4978

98.4978

98.4978

98.4978

98.4979

98.4979

98.4979

98.4979

Figure 3. Inclination Angle in Degree (vertical axis), Versus Iterations Number (2, 3, 4, 5)

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0 5 10 15 20 25 30 35 40 45-200

-150

-100

-50

0

50

100

150

200

Figure 4. Greenwich Longitude of the Ascending Node (vertical axis) Versus the Orbit Number

500 1000 1500 2000 2500 3000 3500 4000-100

-80

-60

-40

-20

0

20

40

60

80

Figure 5. Elevation angles (Vertical axis) versus Minutes During 3 days

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200 400 600 800 1000 1200 1400

0

5

10

15

20

25

30

35

40

45

50

Figure 6. Elevation angles (Vertical axis) versus Minutes for one day in Minutes

910 915 920 925 930

0

5

10

15

20

25

30

35

40

45

50

Figure 7. Maximum Elevation angles (Vertical axis) versus Minutes for a small period during one day

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-100 -80 -60 -40 -20 0 20 40 60 800

200

400

600

800

1000

1200

Figure 8. Histogram of Elevation angles (Horizontal axis) versus Minutes during 3 days

0 1000 2000 3000 4000 50000

50

100

150

200

250

300

350

400

Figure 9. Azimuth angles (Vertical axis) versus Minutes for a small period during 3 days

0 1000 2000 3000 4000 50000

2000

4000

6000

8000

10000

12000

14000

Figure 10. Ranging in KM (Vertical axis) versus Minutes for a small period during 3 days

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