Author Capstone Axis

Earth Satellites at a Glance Earth satellites—natural (the Moon) or artificial—revolve around the planet in circular or elliptical paths, just like planets around the Sun. Because of that, the same three Kepler laws apply :contentReference[oaicite:0]{index=0}. Since 1957, artificial satellites have become key tools for telecommunication, geophysics, and weather monitoring :contentReference[oaicite:1]{index=1}. Circular-Orbit Mechanics Balancing forces. For a satellite […]

Gravitational Potential Energy Gravitational potential energy tells you how much energy a mass stores because of where it sits in Earth’s gravity field. Move the mass, and you change that energy. The sections below show you how to calculate the change in three everyday situations. 1. How g changes when you go below the surface

Acceleration Due to Gravity: Quick, Friendly Notes Gravity pulls every object toward Earth’s center. The pull per unit mass is called the acceleration due to gravity, g. 1  – At Earth’s Surface The familiar value of g comes from Newton’s law of gravitation and Newton’s second law: \( g \;=\; \dfrac{G\,M_E}{R_E^{\,2}} \) :contentReference[oaicite:0]{index=0} \(G\) –

The Gravitational Constant \(G\) 1 · Why we care about \(G\) \(G\) links two masses through Newton’s universal gravitation law: \(F = \dfrac{G\,M\,m}{d^{2}}\)  :contentReference[oaicite:0]{index=0} Here \(M\) and \(m\) are the masses, \(d\) is the distance between their centres, and \(F\) is the attractive force. 2 · Shell ideas you can trust Outside a hollow shell: A point mass outside acts

Acceleration Due to Gravity (g) — Key Ideas & Friendly Notes 1. Getting started — the big picture Imagine Earth as a perfectly uniform sphere. Outside that sphere, the pull you feel is exactly the same as if Earth’s whole mass ME sat at its centre. The gravitational pull on a small mass m at

Universal Law of Gravitation — Friendly Notes 1 · How Newton Reached the Law Newton compared the Moon’s centripetal acceleration \[ a_m = \frac{4\pi^{2}R_m}{T^{2}} \tag{} \] with the familiar surface value \(g\). Because \(R_m \approx 3.84\times10^{8}\,\text{m}\) and \(T\approx27.3\) days, the ratio \(g/a_m\) comes out close to 3600. That is exactly the square of the factor by

Kepler’s Laws — friendly notes for quick revision Around 1600, Johannes Kepler studied Tycho Brahe’s superb observations and spotted three clear patterns in planetary motion. These patterns—now called Kepler’s laws—explain how every planet goes around the Sun and set the stage for Newton’s law of gravitation. :contentReference[oaicite:0]{index=0} 1 · Understanding an ellipse An ellipse is a

Angular Momentum in Rotation About a Fixed Axis 1. One Particle Inside the Rotating Body The angular momentum of a particle at point P is $$\mathbf{l}=\mathbf{r}\times\mathbf{p}$$ with $$\mathbf{r}=\mathbf{OC}+\mathbf{CP}$$. Here CP is perpendicular to the axis and has length r⊥, so the speed is $$v=\omega r_{⊥}$$. The part of l along the axis (chosen as the z-axis)

Gravitation – Smart, Student-Friendly Notes 1. Why We Care We notice gravity every time a ball drops or we puff while climbing uphill. Galileo showed that, near Earth, every freely falling object speeds up at the same rate. Later, careful sky-watching by Tycho Brahe and the brilliant pattern-spotting of Johannes Kepler linked that everyday pull

Dynamics of Rotational Motion about a Fixed Axis When an object spins around an axle, every point in it shares the same angular displacement \(\theta\), angular speed \(\omega\), and angular acceleration \(\alpha\). That makes life easy: we can treat the whole rigid body as if it were “one big particle” located at its axle and use neat rotational versions