Characterization of the spectra of rotating truncated gas planets and inertia-gravity modes

The gravitational acceleration of an object near the Earth's surface is called the acceleration due to gravity. It can be measured by conducting simple experiments on Earth. However, such an experiment is impossible to conduct on the surface of other planets.
Astronomical observations are thus used to measure the acceleration due to gravity on other planets. This can be determined by observing the effect of a planet's gravity on objects close to it. The crucial factor that helps in this...

The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.

The torque-free motion refers to the movement of a rigid body in space when no external torques are acting upon it. This type of motion can be observed in environments where there are no external forces or frictions, like in outer space. For example, a rotation of Mars in space is a torque-free motion. Mars is an axisymmetric object, meaning it has an axis of symmetry along which it rotates, designated as the z-axis. The rotating frame of reference is defined such that the center of mass of...

In the early 17th century, German astronomer and mathematician Johannes Kepler postulated three laws for the motion of planets in the solar system. His first law states that all planets orbit the Sun in an elliptical orbit, with the Sun at one of the ellipse's foci. Therefore, the distance of a planet from the Sun varies throughout its revolution around the Sun.
While in an elliptical orbit, the total energy of the planet is conserved. Therefore, the planet slows down when it is at apogee and...

Since all objects on the Earth's surface move through a circle every 24 hours, there must be a net centripetal force on each object, directed towards the center of that circle. The points of the north and south poles are the only exception to this rule.
For an object on the Earth's equator, the net centripetal force that accounts for its rotation is the Earth's pull towards its center, or the weight minus the normal force that prevents it from piercing into the Earth's surface....

The comparability between linear and angular velocities, linear and angular accelerations, and the kinematic equations of translational and rotational motion can be extended to the concept of inertia.
If a rigid body is rotating about an axis but is not in translational motion, its translational kinetic energy is zero. However, since each particle undergoes rotational motion, it possesses non-zero velocity and kinetic energy. Thus, the kinetic energy of the rigid body, which is the sum of the...