arXiv subjects

M. N. Tarabishy

Publications and source records attributed to M. N. Tarabishy.

4 recordsLinked to original sources

arXiv2024

The Law of Closest Approach

In this work, we introduce the Law of Closest Approach which is derived from the properties of conic orbits and can be considered an addendum to the laws of Kepler. It states that on the closest approach, the distance between the objects is minimal and the velocity vector is perpendicular to the position vector with maximum speed. The ratio of twice the kinetic energy to the negative potential energy is equal to the eccentricity plus one. The advantage of this law is that both speed and position are at extremum making the calculation of the eccentricity more robust.

physics.class-ph↗

arXiv2022

Simplified Gyroscopic Treatment

Gyroscopic motion explanation in texts is relatively long and requires reasonable level of comfort with the mathematical tools used. On the other hand, popular explanation outside academic courses does not explain the phenomenon and only describes it leaving many to think that it is so weird that it defies physics. In this paper we offer a simplified and mathematically sound explanation that can be used in either setting.

physics.ed-ph↗

arXiv2021

A New Theorem Relating the Tangent Secant Theorem to the Golden Ratio

The golden ratio is usually shrouded in mystique and mystery, however, showing its emergence from a familiar geometric setting makes it a more natural phenomenon. In this work, we present a new theorem connecting the Tangent Secant theorem to the golden ratio. Such a connection enhances the learning process of the theorem, and it demystifies the golden ratio in physics and other disciplines.

math.GM↗

arXiv2021

Comparison Between International Space Station and Airplane Flying

Inertial forces are not intuitive; therefore, interesting examples are great help for learners. In this paper, we examine simple models for International Space Station (ISS) and airplane flying and identify the inertial forces involved and their effect. In both cases there are centrifugal forces but in the case of the ISS, the centrifugal force is the only major force opposing the gravitational attraction that is pulling it towards the Earth at 0.885 the gravity at the surface of the Earth. While in the case of an airplane, it is a minor component amounting to less than 1% in the best case of flying along the equator west to east. Other inertial forces including the Coriolis force affect the airplane. Another thing we see is that flying with the Earth direction west to east gives a markedly higher forces than flying in the opposite direction. The maintenance of the ISS orientation with respect to Earth requires rotation of ISS around its center of gravity (cg) at the same rate as it revolves around the Earth (4 degrees per minute) while for an airplane, maintaining level flight at a constant speed and height does not require direct intervention because the amount of adjustment is so small and gradual that it is handled by the pilot system as a part of the disturbances that affects the airplane.

physics.ed-ph↗