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Regularized luni-solar gravity dynamics on resident space objects

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A Correction to this article was published on 11 February 2022

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Abstract

Resident space object population in highly elliptical high perigee altitude (> 600 km) orbits is significantly affected by luni-solar gravity. Using regularization, an analytical orbit theory with luni-solar gravity effects as third-body perturbations in terms of Kustaanheimo-Stiefel regular elements is developed. Numerical tests with different cases resulted in good accuracy for both short- and long-term orbit propagations. It is observed that the luni-solar perturbations affect the accuracy of the analytical solution seasonally. The analytical theory is tested with the observed orbital parameters of the few objects in highly elliptical orbits. The analytical evolution of osculating perigee altitude is found to be concurrent with observed data. Solar perturbation, when compared with lunar perturbation, is established to be dominant over such orbits.

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Abbreviations

a :

semi-major axis (km)

E :

generalized eccentric anomaly (°)

E 0 :

initial generalized eccentric anomaly (°)

E f :

final generalized eccentric anomaly (°)

E K :

eccentric anomaly (°)

e :

eccentricity

L, H, D :

length, height, and diameter of the resident space object (m)

h :

altitude (km)

h p :

perigee altitude (km)

I :

inclination (°)

L(u):

Kustaanheimo—Stiefel matrix

M :

mean anomaly (°)

P n :

Legendre polynomial of degree n

r :

radial distance (km)

r :

position vector (km)

r K :

magnitude of the third-body position vector (km)

r K :

third-body position vector (km)

\({\rm{\dot r}}\), v :

velocity vector (km)

s :

fictitious time

t :

physical time (s)

u :

Kustaanheimo—Stiefel position vector

(u 1, u 2, u 3, u 4):

components of the Kustaanheimo—Stiefel position vector/Kustaanheimo—Stiefel variables

u* :

Kustaanheimo—Stiefel velocity vector

V :

perturbing potential

V K :

perturbing potential of the third-body

w :

angular frequency

ω K :

natural frequency

(x, y, z):

position vector components (km)

(x K, y K, z K):

position vector components of the third-body (km)

(x M, y M, z M):

position vector components of the Moon (km)

(x S, y S, z S):

position vector components of the Sun (km)

α 1, β :

Kustaanheimo—Stiefel regular elements

(α 1, α 2, α 3, α 4, β 1, β 2, β 3, β 4,):

Kustaanheimo—Stiefel regular elements

\({\cal B}\) :

bilinear relation

κ :

frequency ratio

ω :

argument of perigee (°)

Ω :

right ascension of the ascending node (°)

ϕ :

angle between the third-body and RSO vector in inertial geocentric equatorial coordinates (°)

σ :

intermediate angular variable (°)

τ :

time element

μ :

standard gravitational parameter of the Earth (km3 · s−2)

β S :

standard gravitational parameter of the Sun (km3 · s−2)

μ M :

standard gravitational parameter of the Moon (km3· s−2)

*:

derivative with respect to E

′:

derivative with respect to s

T:

matrix transpose

osc:

osculating element

LEO:

low Earth orbit

MEO:

medium Earth orbit

GEO:

geosynchronous orbit

TLE:

two line element

RSO:

resident space object

HEO:

highly elliptical orbit

KS:

Kustaanheimo—Stiefel

RK:

Runge—Kutta

SDP4:

simplified fourth-order deep space perturbations

GB:

giga bytes

RAM:

random access memory

FORTRAN:

formula translation

CPU:

central processing unit

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Acknowledgements

The authors gratefully acknowledge the support received by grant SR/S4/MS: 801/12 from Department of Science and Technology-Science and Engineering Research Board (DST-SERB), India.

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Authors and Affiliations

  1. Agnikul Cosmos Private Limited, Indian Institute of Technology Madras, Chennai, 600036, India

    Harishkumar Sellamuthu

  2. Department of Aerospace Engineering, Karunya Institute of Technology and Sciences, Coimbatore, 641114, India

    Ram Krishan Sharma

Authors
  1. Harishkumar Sellamuthu
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Corresponding author

Correspondence to Harishkumar Sellamuthu.

Additional information

Harishkumar Sellamuthu received his Ph.D. degree in 2019 from Karunya Institute of Technology and Sciences. As of March 2020, he is employed with Agnikul Cosmos as an astrodynamics researcher. He was a visiting researcher at Technion, Israel and The University of Texas at Austin, USA during 2015 and 2018, respectively. His research interests include astrodynamics and trajectory design, regularization, and space debris predictions. E-mail: hari251086@gmail.com.

Ram Krishan Sharma is a professor in aerospace engineering at Karunya Institute of Technology and Sciences since 2011. He received his B.S. (Honors) and M.S. degrees in mathematics, Ph.D. degree in space dynamics from University of Delhi, India in 1968, 1970, and 1977, respectively. He has worked in Indian Space Research Organization (ISRO) for 38 years. His research interests include celestial mechanics, astrodynamics, space debris, and interplanetary trajectories, and has over 100 research publications. E-mail: ramkrishansharma@gmail.com.

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Sellamuthu, H., Sharma, R.K. Regularized luni-solar gravity dynamics on resident space objects. Astrodyn 5, 91–108 (2021). https://doi.org/10.1007/s42064-020-0085-6

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