Projectile and Satellite Motion

This set covers the fundamental concepts of ballistics, the equations of projectile motion, and the physics governing circular and elliptical orbits.

Projectile Motion

The motion of an object moving in free-fall, where the only force acting on the object is gravity.

Free-fall

An ideal scenario that ignores dissipative forces such as friction and air drag.

Ballistics

The physics of projectile motion used to understand and quantify the motion of objects such as rockets, planets, and artificial satellites.

Inertia (Horizontal Projection)

The principle based on Newton’s first law that keeps a projectile moving at the same speed in the horizontal direction because no forces are acting on it.

Acceleration due to Gravity

The force acting in the vertical direction on a projectile, represented by the value $-9.8\,m/s^2$, where the negative sign indicates it points down.

Parabola

The shape of the motion of a projectile when it moves with both horizontal and vertical motion.

Launch Angle for Maximum Range

In the absence of air drag, an angle of $45$ degrees with respect to the horizon creates the best tradeoff between time in the air and horizontal motion.

Kinematics Equations Usage

Equations best used in projectile analysis when calculating timing, such as how long an object remains in the air.

Conservation of Energy Usage

An analysis method best used for calculating heights, specifically how high a projectile will be at any given speed.

Kinematic Velocity Equation

$$v_{final} = v_{initial} + a \times t$$

Kinematic Distance Equation

$$d = \frac{1}{2} \times a \times t^2 + v_{initial} \times t$$

Satellite

A projectile that falls around the Earth rather than falling back down to its surface.

Orbital Velocity Formula

$v = \sqrt{\frac{G \times M_{Earth}}{r}}$, where $r$ is the radius of motion (radius of Earth plus orbital height).

Orbital Velocity of the ISS

The speed of the International Space Station, which orbits approximately $400\,km$ high, is approximately $7,672\,m/s$.

Circular Orbit

A special case of an elliptical orbit where the satellite's height and speed remain constant throughout the motion.

Elliptical Orbit

An orbit where the satellite's distance from the planet changes, causing speed to increase when closest and decrease when farthest.