scholarly journals On merging of resonant periodic orbits 4:3; 3:2 and 2:1 in Sun-Jupiter photo gravitational restricted three-body problem

2019 ◽  
Vol 7 (1) ◽  
pp. 17
Author(s):  
Prashant Kumar ◽  
Ram Krishan Sharma
Keyword(s):  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Solar Radiation Pressure ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Surface Of Section ◽  
Poincaré Surface Of Section ◽  
Frame Work ◽  
Three Body

We explore the merging of resonant periodic orbits in the frame work of planar circular restricted three body problem with the help of Poincaré surface of section. We have studied the effect of solar radiation pressure on 4:3, 3:2 and 2:1 periodic orbits. It is found that radiation pressure helps in merging these orbits (4:3 and 3.2 into 1:1 resonance and 2:1 into 1:1 resonance). At the time of merging these orbits become near-circular. The period and size of these orbits reduce with the increase in radiation pressure.  

scholarly journals Progression of bifurcated family f type periodic orbits in the circular restricted three-body problem

2017 ◽  
Vol 5 (2) ◽  
pp. 69
Author(s):  
Nishanth Pushparaj ◽  
Ram Krishan Sharma
Keyword(s):  
Solar Radiation ◽  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Solar Radiation Pressure ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Three Body

Progression of f-type family of periodic orbits, their nature, stability and location nearer the smaller primary for different mass ratios in the framework of circular restricted three-body problem is studied using Poincaré surfaces of section. The orbits around the smaller primary are found to decrease in size with increase in Jacobian Constant C, and move very close towards the smaller primary. The orbit bifurcates into two orbits with the increase in C to 4.2. The two orbits that appear for this value of C belong to two adjacent separate families: one as direct orbit belonging to family g of periodic orbits and other one as retrograde orbit belonging to family f of periodic orbits. This bifurcation is interesting. These orbits increase in size with increase in mass ratio. The elliptic orbits found within the mass ratio 0 < µ ≤ 0.1 have eccentricity less than 0.2 and the orbits found above the mass ratio µ > 0.1 are elliptical orbits with eccentricity above 0.2. Deviations in the parameters: eccentricity, semi-major axis and time period of these orbits with solar radiation pressure q are computed in the frame work of photogravitational restricted Three-body problem in addition to the restricted three-body problem. These parameters are found to decrease with increase in the solar radiation pressure.

scholarly journals Investigation of the effect of albedo and oblateness on the circular restricted four variable bodies problem

2017 ◽  
Vol 2 (2) ◽  
pp. 529-542 ◽  
Author(s):  
Abdullah A. Ansari
Keyword(s):  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Solar Radiation Pressure ◽  
Basins Of Attraction ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

AbstractThe present paper investigates the motion of the variable infinitesimal body in circular restricted four variable bodies problem. We have constructed the equations of motion of the infinitesimal variable mass under the effect of source of radiation pressure due to which albedo effects are produced by another two primaries and one primary is considered as an oblate body which is placed at the triangular equilibrium point of the classical restricted three-body problem and also the variation of Jacobi Integral constant has been determined. We have studied numerically the equilibrium points, Poincaré surface of sections and basins of attraction in five cases (i. Third primary is placed at one of the triangular equilibrium points of the classical restricted three-body problem, ii. Variation of masses, iii. Solar radiation pressure, iv. Albedo effect, v. Oblateness effect.) by using Mathematica software. Finally, we have examined the stability of the equilibrium points and found that all the equilibrium points are unstable.

scholarly journals Dynamics in the circular restricted three body problem with perturbations

2017 ◽  
Vol 5 (1) ◽  
pp. 19 ◽  
Author(s):  
Abdullah Abduljabar Ansari ◽  
Mehtab Alam
Keyword(s):  
Solar Radiation ◽  
Radiation Pressure ◽  
Body Problem ◽  
Equations Of Motion ◽  
Solar Radiation Pressure ◽  
Libration Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity Curves ◽  
Three Body

This paper presents the dynamics in the restricted problem with perturbations i.e. the circular restricted three body problem by considering one of the primaries as oblate and other one having the solar radiation pressure and all the masses are variable (primaries and infinitesimal body). For finding the autonomized equations of motion, we have used the Meshcherskii transformation. We have drawn the libration points, the time series, the zero velocity curves and Poincare surface of sections for the different values of the oblateness and solar radiation pressure. Finally, we have examined the stability and found that all the libration points are unstable.

scholarly journals Locations of Lagrangian points and periodic orbits around triangular points in the photo gravitational elliptic restricted three-body problem with oblateness

2019 ◽  
Vol 7 (2) ◽  
pp. 25
Author(s):  
Ancy Johnson ◽  
Ram Krishan Sharma
Keyword(s):  
Periodic Orbits ◽  
Radiation Pressure ◽  
Body Problem ◽  
Critical Mass ◽  
Stable Region ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Lagrangian Points ◽  
Triangular Points ◽  
Three Body

Locations of the Lagrangian points are computed and periodic orbits are studied around the triangular points in the photogravitational elliptic restricted three-body problem (ER3BP) by considering the more massive primary as the source of radiation and smaller primary as an oblate spheroid. A new mean motion taken from Sharma et al. [13] is used to study the effect of radiation pressure and oblateness of the primaries. The critical mass parameter  that bifurcates periodic orbits from non-periodic orbits tends to reduce with radiation pressure and oblateness. The transition curves defining stable region of orbits are drawn for different values of radiation pressure and oblateness using the analytical method of Bennet [14]. Tadpole orbits with long- and short- periodic oscillations are obtained for Sun-Jupiter and Sun-Saturn systems.  

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