Glossary
Angular Momentum
A measure of an object's rotational inertia and rotational velocity, conserved in orbital systems where no external torques act.
Example:
A figure skater pulls their arms in to increase their spin rate, demonstrating the angular momentum conservation principle.
Angular Momentum
A measure of an object's rotational inertia, which is conserved for a satellite orbiting a central object in the absence of external torques.
Example:
As a satellite moves from periapsis to apoapsis in an elliptical orbit, its speed changes, but its angular momentum about the central object remains constant.
Apoapsis
The point in an elliptical orbit where the orbiting object is farthest from the central body, resulting in its lowest speed and highest potential energy.
Example:
At its apoapsis, a spacecraft might slow down enough to be captured by another planet's gravity.
Apoapsis
The point in an elliptical orbit where the satellite is farthest from the central object, characterized by the lowest kinetic energy and least negative gravitational potential energy.
Example:
At its apoapsis, a satellite moves slowest in its elliptical path, as its kinetic energy is at a minimum.
Central Object
The massive body around which a smaller object (satellite) orbits, often considered stationary due to its significantly larger mass.
Example:
In our solar system, the Sun is the central object for Earth's orbit.
Central Object Motion
In a satellite-central object system, the central object is considered stationary due to its significantly larger mass compared to the orbiting satellite.
Example:
When analyzing the motion of the International Space Station around Earth, we treat Earth's central object motion as negligible.
Circular Orbits
An orbit where a satellite maintains a constant distance and speed around a central object, resulting in constant kinetic and gravitational potential energy.
Example:
Many communication satellites are placed in circular orbits around Earth to ensure consistent signal coverage.
Circular Orbits
Orbits where a satellite maintains a constant distance from the central object, resulting in constant total mechanical energy, gravitational potential energy, kinetic energy, and angular momentum.
Example:
A geostationary satellite maintains a circular orbit around Earth, appearing to hover over a fixed point on the equator.
Conservation Laws
Fundamental principles stating that certain physical quantities remain constant in an isolated system over time.
Example:
The conservation laws of energy and momentum are crucial for understanding collisions.
Conservation Laws
Fundamental principles, such as conservation of energy and angular momentum, that dictate the behavior and motion of satellites in gravitational systems.
Example:
Understanding conservation laws allows us to predict a satellite's speed at different points in its elliptical orbit without knowing the exact forces at every moment.
Elliptical Orbits
An orbit shaped like an ellipse where the satellite's distance and speed around the central object vary, though total mechanical energy and angular momentum remain constant.
Example:
Planets in our solar system, like Mars, follow elliptical orbits around the Sun, not perfect circles.
Elliptical Orbits
Orbits where a satellite's distance from the central object varies, leading to constant total mechanical energy and angular momentum, but varying gravitational potential and kinetic energies.
Example:
Comets often follow highly elliptical orbits around the Sun, speeding up as they get closer and slowing down as they move farther away.
Escape Velocity
The minimum speed an object needs to completely break free from the gravitational pull of a massive body and never fall back.
Example:
To launch a probe to another star, it must achieve Earth's escape velocity to leave our planet's gravitational influence.
Escape Velocity
The minimum speed an object needs to completely break free from the gravitational pull of a central object, where its total mechanical energy becomes zero.
Example:
To launch a probe to Mars, it must achieve escape velocity from Earth's gravitational field.
Gravitational Constant (G)
The universal constant of proportionality in Newton's Law of Universal Gravitation, representing the strength of the gravitational force.
Example:
The value of the gravitational constant (G) is tiny, which is why gravity is only noticeable with very massive objects.
Gravitational Constant (G)
A fundamental physical constant that quantifies the strength of the gravitational force between two objects.
Example:
The value of the gravitational constant (G) is essential for calculating the force of attraction between any two masses in the universe.
Gravitational Potential Energy
The energy an object possesses due to its position within a gravitational field, defined as zero at infinite separation and negative closer to the mass.
Example:
As a rocket launches, its gravitational potential energy increases (becomes less negative) as it moves away from Earth.
Gravitational Potential Energy
The energy stored in a system due to the gravitational interaction between two masses, defined as zero at infinite separation and becoming increasingly negative as masses get closer.
Example:
As a rocket ascends from Earth, its gravitational potential energy becomes less negative, indicating an increase in its potential to move away from the planet.
Kinetic Energy
The energy an object possesses due to its motion, directly proportional to its mass and the square of its speed.
Example:
A fast-moving asteroid has significant kinetic energy, which could cause a large impact if it hits a planet.
Kinetic Energy
The energy an object possesses due to its motion, which in a circular orbit is always half the magnitude of the gravitational potential energy.
Example:
At its closest approach to the Sun, a planet's kinetic energy is at its maximum due to its increased speed.
Periapsis
The point in an elliptical orbit where the orbiting object is closest to the central body, resulting in its highest speed and lowest potential energy.
Example:
When a satellite reaches its periapsis, it experiences its fastest orbital speed.
Periapsis
The point in an elliptical orbit where the satellite is closest to the central object, characterized by the highest kinetic energy and most negative gravitational potential energy.
Example:
When a spacecraft performs a gravity assist maneuver, it often passes through the periapsis of a planet's orbit to gain speed.
Total Mechanical Energy
The sum of an object's kinetic energy and gravitational potential energy within a system. In orbital mechanics, it is always conserved if only gravity acts.
Example:
Even as a comet speeds up near the Sun and slows down far away, its total mechanical energy remains constant.
Total Mechanical Energy
The sum of an object's kinetic energy and gravitational potential energy, which remains constant in the absence of non-conservative forces.
Example:
For a satellite in a stable orbit, its total mechanical energy is always negative, indicating it is bound to the central object.