# The motion near L{sub 4} equilibrium point under non-point mass primaries

## Abstract

The Circular Restricted Three-Body Problem (CRTBP) possesses five equilibrium points, that comprise three collinear (L{sub 1}, L{sub 2}, and L{sub 3}) and two triangular points (L{sub 4} and L{sub 5}). The classical study (with the primaries are point mass) suggests that the equilibrium points may cause the velocity of infinitesimal object relatively becomes zero and reveals the zero velocity curve. We study the motion of infinitesimal object near triangular equilibrium point (L{sub 4}) and determine its zero velocity curve. We extend the study by taking into account the effects of radiation of the bigger primary (q{sub 1} ≠ 1, q{sub 2} = 1) and oblateness of the smaller primary (A{sub 1} = 0, A{sub 2} ≠ 0). The location of L{sub 4} is analytically derived then the stability of L{sub 4} and its zero velocity curves are studied numerically. Our study suggests that the oblateness and the radiation of primaries may affect the stability and zero velocity curve around L{sub 4}.

- Authors:

- Department of Astronomy, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132 (Indonesia)
- Astronomy Research Division, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132 (Indonesia)
- Department of Computational Science, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Jalan Ganesha 10, Bandung 40132 (Indonesia)

- Publication Date:

- OSTI Identifier:
- 22488916

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1677; Journal Issue: 1; Conference: 5. international conference on mathematics and natural sciences, Bandung (Indonesia), 2-3 Nov 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIAGRAMS; EQUILIBRIUM; MASS; STABILITY; THREE-BODY PROBLEM; VELOCITY

### Citation Formats

```
Huda, I. N., E-mail: ibnu.nurul@students.itb.ac.id, Utama, J. A., Madley, D., Tampubolon, I., Dermawan, B., Hidayat, T., and Wibowo, R. W.
```*The motion near L{sub 4} equilibrium point under non-point mass primaries*. United States: N. p., 2015.
Web. doi:10.1063/1.4930676.

```
Huda, I. N., E-mail: ibnu.nurul@students.itb.ac.id, Utama, J. A., Madley, D., Tampubolon, I., Dermawan, B., Hidayat, T., & Wibowo, R. W.
```*The motion near L{sub 4} equilibrium point under non-point mass primaries*. United States. doi:10.1063/1.4930676.

```
Huda, I. N., E-mail: ibnu.nurul@students.itb.ac.id, Utama, J. A., Madley, D., Tampubolon, I., Dermawan, B., Hidayat, T., and Wibowo, R. W. Wed .
"The motion near L{sub 4} equilibrium point under non-point mass primaries". United States. doi:10.1063/1.4930676.
```

```
@article{osti_22488916,
```

title = {The motion near L{sub 4} equilibrium point under non-point mass primaries},

author = {Huda, I. N., E-mail: ibnu.nurul@students.itb.ac.id and Utama, J. A. and Madley, D. and Tampubolon, I. and Dermawan, B. and Hidayat, T. and Wibowo, R. W.},

abstractNote = {The Circular Restricted Three-Body Problem (CRTBP) possesses five equilibrium points, that comprise three collinear (L{sub 1}, L{sub 2}, and L{sub 3}) and two triangular points (L{sub 4} and L{sub 5}). The classical study (with the primaries are point mass) suggests that the equilibrium points may cause the velocity of infinitesimal object relatively becomes zero and reveals the zero velocity curve. We study the motion of infinitesimal object near triangular equilibrium point (L{sub 4}) and determine its zero velocity curve. We extend the study by taking into account the effects of radiation of the bigger primary (q{sub 1} ≠ 1, q{sub 2} = 1) and oblateness of the smaller primary (A{sub 1} = 0, A{sub 2} ≠ 0). The location of L{sub 4} is analytically derived then the stability of L{sub 4} and its zero velocity curves are studied numerically. Our study suggests that the oblateness and the radiation of primaries may affect the stability and zero velocity curve around L{sub 4}.},

doi = {10.1063/1.4930676},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1677,

place = {United States},

year = {2015},

month = {9}

}