Fourth-order gravity gradient torque of spacecraft orbiting asteroids

The dynamical behavior of spacecraft around asteroids is a key element in design of such missions. An asteroids irregular shape, non-spherical mass distribution and its rotational sate make the dynamics of spacecraft quite complex. This paper focuses on the gravity gradient torque of spacecraft around non-spherical asteroids. The gravity field of the asteroid is approximated as a 2nd degree and order-gravity field with harmonic coefficients C20 and C22. By introducing the spacecrafts higher-order inertia integrals, a full fourth-order gravity gradient torque model of the spacecraft is established through the gravitational potential derivatives. Our full fourth-order model is more precise than previous fourth-order model due to the consideration of higher-order inertia integrals of the spacecraft. Some interesting conclusions about the gravity gradient torque model are reached. Then a numerical simulation is carried out to verify our model. In the numerical simulation, a special spacecraft consisted of 36 point masses connected by rigid massless rods is considered. We assume that the asteroid is in a uniform rotation around its maximum-moment principal axis, and the spacecraft is on the stationary orbit in the equatorial plane. Simulation results show that the motion of previous fourth-order model is quite different from the exact motion, while our full fourth-order model fits the exact motion very well. And our model is precise enough for practical applications.

Y Chromosomes of 40% Chinese Are Descendants of Three Neolithic Super-grandfathers

Demographic change of human populations is one of the central questions for delving into the past of human beings. To identify major population expansions related to male lineages, we sequenced 78 East Asian Y chromosomes at 3.9 Mbp of the non-recombining region (NRY), discovered >4,000 new SNPs, and identified many new clades. The relative divergence dates can be estimated much more precisely using molecular clock. We found that all the Paleolithic divergences were binary; however, three strong star-like Neolithic expansions at ~6 kya (thousand years ago) (assuming a constant substitution rate of 1e-9/bp/year) indicates that ~40% of modern Chinese are patrilineal descendants of only three super-grandfathers at that time. This observation suggests that the main patrilineal expansion in China occurred in the Neolithic Era and might be related to the development of agriculture.