2015IOAA理论短问题第1题-共振轨道

英文题目

Several exoplanets have been observed in the Gliese 876 system $$\left(M_{G} = 0.33\pm 0.03 M_{\odot}\right)$$ as given in the following table,

Gliese System	Mass	Semi Major Axis (AU)
Gliese 876 b	$$2.276M_{J}$$	0.2083
Gliese 876 c	$$0.714M_{J}$$	0.1296
Gliese 876 d	$$6.8M_{\oplus}$$	0.0208
Gliese 876 e	$$15M_{\oplus}$$	0.334

where $$M_{\odot}$$ is mass of Sun, $$M_{J}$$ is mass of Jupiter, $$\left(M_{J}=1.89813 \times 10^{27} \mathrm{~kg}\right)$$, and $$M_{\oplus}$$ is mass of Earth. Assume that all these planets revolve around Gliese 876 in the same direction. Two planets are said to be in resonant orbits if the synodic period of one planet with respect to the other planet is an integer multiple of the orbital period of the second planet.

Find if any of the exoplanets of Gliese 876 system may have resonant orbits.