Angular Momentum, Kepler’s Laws, and Gravity
Angular Momentum of a Particle
The angular momentum of a particle about a point O is the vector product of the position vector r, with respect to that point, and its momentum p: L = r x p, where p = mv, where m is the mass and v the velocity of the particle can be rewritten as L = mr x v.
The angular momentum is measured in kg⋅m²/s. L is a vector quantity, its magnitude is L = mrvsinθ, where θ is the angle between r and v; if they are parallel, then L = 0.
Angular momentum characterizes the rotation
Understanding Anamorphosis, UTM Projection, and Topographic Representation
Anamorphosis: Linear, Angle, and Surface
Linear Anamorphosis: The linear anamorphosis factor is the ratio between a linear element dl on a plane and its corresponding element on the Earth dL. When both elements are equal, the linear anamorphosis modulus will drive the value. Lines with a linear modulus equal to unity are called Automeca.
Angle Anamorphosis: The difference between the angle between two directions on the Earth and the same directions on the plane is the magnitude of shear strain. Projections
Read MoreExtraterrestrial Life: From Ancient Times to Today
The Possibility of Extraterrestrial Life
The possibility of extraterrestrial life was first considered during ancient times.
Key Concepts in Science and Astronomy
In science, conceptual representations of observed phenomena are referred to as models.
- The circular shape of the Earth’s shadow on the Moon during a lunar eclipse suggested to the Greeks that the Earth was spherical in shape.
- The Ptolemaic model has planets moving in small circles.
- The first person to suggest that the Earth moved around the
Understanding Hydrostatic Pressure, Hydraulics, and Buoyancy
Hydrostatic Pressure
Hydrostatic pressure is the pressure within a liquid caused by the weight of the liquid itself.
Features of Hydrostatic Pressure:
- The pressure inside a liquid acts in all directions.
- The pressure is higher at greater depths.
- The pressure increases with the density of the liquid.
- The pressure is not dependent on the shape or width of the container.
The pressure at any point inside a liquid of density d is due to the weight of the liquid above it.
Fundamental Principle of Hydrostatics
The
Read MoreQuantum Mechanics: Concepts and Applications
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles.[1] It is the foundation of all quantum physics, including quantum chemistry, quantum field theory, quantum technology, and quantum information science.
Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale,
Read MoreUniverse: From Big Bang to Planets and Life
The Universe
- It’s a huge vacuum in which billions of galaxies float. For each galaxy, there are thousands of stars, planets, and nebulae.
- Some of them can be seen with the naked eye, and others can be seen with telescopes.
- Formation of the observable cosmos: 75% hydrogen, 20% helium, and 5% the rest of the elements.
Dark Matter
- 90% of the total matter in the universe is dark matter, whose composition and position are unknown because it cannot be seen or emit radiation.
- Proof of existence: A few galaxies