In the frame work of the perturbed restricted three-body problem, the solutions of halo orbits are developed up to fifth order approximation by using Lindstedt–Poincaré technique. The effect of oblateness of the more massive primary on the size, location and period of halo orbits around $L_1$ and $L_2$ are studied by considering the Earth–Moon system. Due to oblateness of the Earth, halo orbits around $L_1$ and $L_2$ enlarge and move towards the Moon. Also, the period of halo orbits around $L_1$ and $L_2$ decreases. Numerical solution for halo orbits around $L_1$ and $L_2$ in the Sun–Earth system is obtained by using the differential correction method for different values of radiation pressure and oblateness. The separation between the orbits obtained using fourth and fifth order Lindstedt–Poincaré method as well as differential correction method is found to be less than the separation between the orbits obtained using third and fourth order Lindstedt–Paincaré as well as differential correction method. This indicates that as the order of the solution increases the separation between consecutive solution decreases leading to more accurate solution.

在摄动受限三体问题的框架中，使用Lindstedt–Poincaré技术将光晕轨道的解扩展到五阶近似。更大质量的原边扁圆对周围光晕轨道的大小，位置和周期的影响${\mathrm{大号}}_{\mathrm{1个}}$ 和 ${\mathrm{大号}}_{\mathrm{2个}}$通过考虑地月系统来研究。由于地球的扁率，光晕绕轨道旋转${\mathrm{大号}}_{\mathrm{1个}}$ 和 ${\mathrm{大号}}_{\mathrm{2个}}$扩大并移向月球。另外，晕圈的周期大约是${\mathrm{大号}}_{\mathrm{1个}}$ 和 ${\mathrm{大号}}_{\mathrm{2个}}$减少。绕晕轨道的数值解${\mathrm{大号}}_{\mathrm{1个}}$ 和 ${\mathrm{大号}}_{\mathrm{2个}}$通过对辐射压强和扁率的不同值使用微分校正方法获得太阳-地球系统中的辐射。发现使用四阶和五阶Lindstedt–Poincaré方法以及微分校正方法获得的轨道之间的间距小于使用三阶和四阶Lindstedt–Paincaré以及微分校正方法获得的轨道之间的间距。这表明，随着溶液顺序的增加，连续溶液之间的间隔减小，从而导致更精确的溶液。