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Nonperturbative treatments of the UV limit of pure gravity suggest that it admits a stable fixed point with positive Newton's constant and cosmological constant. We prove that this result is stable under the addition of a scalar field with…
Parker Solar Probe (PSP) observations have revealed that most of the solar wind acceleration occurs very close to the Sun. This acceleration is partly due to the global electric potential originating from the mass disparity between…
We use a large, statistical set of measurements from the Wind spacecraft at 1 AU, and supporting synthetic spacecraft data based on kinetic plasma theory, to show that the compressible component of inertial range solar wind turbulence is…
We look for particular solutions to the restricted three-body problem where the bodies are allowed to either lose or gain mass to or from a static atmosphere. In the case that all the masses are proportional to the same function of time,we…
We determine the general form of the potential of the problem of motion of a rigid body about a fixed point, which allows the angular velocity to remain permanently in a principal plane of inertia of the body. Explicit solution of the…
In this article, I discuss the motion of $N$ point masses in non-relativistic mechanics, when the interaction between them is purely the Newtonian gravitational interaction, with $N$ greater than or equal to 2. The dynamical equations of…
Following Smale, we study simple symmetric mechanical systems of $n$ point particles in the plane. In particular, we address the question of the linear and spectral stability properties of relative equilibria, which are special solutions of…
The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is…
A solvable many-body problem in the plane is exhibited. It is characterized by rotation-invariant Newtonian (``acceleration equal force'') equations of motion, featuring one-body (``external'') and pair (``interparticle'') forces. The…
We resolve the paradox that although magnetic collimation of an isotropic solar wind results in an enhancement of its proton flux along the polar directions, several observations indicate a wind proton flux peaked at the equator. To that…
The equations governing motion of the satellite under the effect of oblateness of Earth and atmospheric drag have been simulated, for a fixed initial position and three different initial velocities, till satellite collapses on Earth.…
The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of the two other bodies, the primaries, which evolve in Keplerian ellipses. A trajectory is called oscillatory if…
We establish the existence of saddle points for a free boundary problem describing the two-dimensional free surface of a ferrofluid which undergoes normal field instability (also known as Rosensweig instability). The starting point consists…
The solar corona is a complex system, with nonisothermal plasma and being in the self-gravitating field of the Sun. So the corona plasma is not only a nonequilibrium system but also a nonextensive one. We estimate the parameter of…
A simple collinearity argument implies that the massless particle three-point function of helicities $h_1, h_2, h_3$ with corresponding real-valued four-momenta $k_1, k_2, k_3$ taken as all incoming or all outgoing (i.e., $k_1 +k_2…
In this paper, we consider the linear stability of the elliptic relative equilibria of the restricted 4-body problems where the three primaries form a Lagrangian triangle. By reduction, the linearized Poincar\'e map is decomposed to the…
We study the motion of a compressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free…
The restricted three-body problem describes the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$ that circle each other with period equal to $2\pi$. For small $\mu$, a resonant periodic motion…
The equations of the restricted three-body problem describe the motion of a massless particle under the influence of two primaries of masses $1-\mu$ and $\mu$, $0\leq \mu \leq 1/2$, that circle each other with period equal to $2\pi$. When…
We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influence due to three bodies following the figure-eight…