Higher Physics: Our Dynamic Universe

Comprehensive vocabulary flashcards covering the Higher Physics Our Dynamic Universe unit: The Expanding Universe, Special Relativity, and Gravitation.

Doppler Effect

The observed change in the frequency of a wave when the source of the wave is moving relative to a stationary observer.

Observed Frequency Formula (Doppler Effect)

The equation $f_o = f_s \left(\frac{v}{v \pm v_s}\right)$, where the negative sign is used when the source moves towards the observer, and the positive sign is used when the source moves away.

Redshift ($z$)

The shift of spectral lines from receding astronomical bodies toward longer wavelengths, defined by the ratio $z = \frac{\lambda_o - \lambda_r}{\lambda_r}$.

Blueshift

The shift of spectral lines from astronomical bodies approaching an observer toward shorter wavelengths at the blue end of the visible spectrum.

Hubble-Lemaître Law

The relationship stating that the recessional velocity of a distant galaxy is directly proportional to its distance from Earth: $v = H_0 d$.

Hubble's Constant ($H_0$)

The constant of proportionality in the Hubble-Lemaître Law, having an accepted value of $2.3 \times 10^{-18}\,\text{s}^{-1}$.

Age of the Universe

The estimated duration of the Universe's expansion calculated as $t = \frac{1}{H_0}$, giving approximately $4.35 \times 10^{17}\,\text{s}$ or $13.8\,\text{billion years}$.

Dark Matter

Unaccounted-for matter inferred from the unexpectedly high orbital speeds of stars within galaxies, providing more gravitational mass than can be accounted for by observable stars.

Dark Energy

A hypothetical form of energy that opposes gravitational attraction, causing the expansion rate of the Universe to accelerate; it is thought to account for approximately $74\%$ of the Universe.

Cosmic Microwave Background Radiation (CMBR)

Residual electromagnetic radiation corresponding to a temperature of approximately $2.7\,\text{K}$ detected in every direction in the sky, providing key evidence supporting the Big Bang theory.

Olbers' Paradox

The apparent contradiction that if the universe were infinitely old and static with infinite stars, the night sky would be completely bright; resolved because the expanding universe has a finite age.

Stellar Radiation Distribution

The spread of radiation emitted across wavelengths showing that hotter stars have a shorter peak wavelength and emit more radiation per unit surface area per unit time than cooler stars.

Inertial Reference Frame

A frame of reference in which an observer moves at a constant velocity (constant speed in a straight line) relative to another frame.

Absolute Reference Frame

A hypothetical unique, universal frame of reference against which all motion in the universe could be measured, which Einstein's theory proved does not exist.

Einstein's First Postulate of Special Relativity

The postulate stating that all observers moving at constant speeds relative to one another (in inertial reference frames) will observe the same laws of physics.

Einstein's Second Postulate of Special Relativity

The postulate stating that the speed of light in a vacuum ($3 \times 10^8\,\text{m/s}$) is the same for all observers, regardless of their motion relative to the source.

Proper Time ($t$)

The time interval measured by a clock situated in the reference frame in which the event being timed is at rest.

Dilated Time ($t'$)

The time interval measured by an observer moving relative to the frame of the event, calculated as $t' = \frac{t}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}$, which is longer than proper time.

Muon Decay Evidence

Experimental proof of time dilation: short-lived muons created $10\,\text{km}$ high with a half-life of $1.56 \times 10^{-6}\,\text{s}$ survive to reach Earth in large numbers (~$50\,000$ per million) because their internal clocks run slow relative to Earth.

Proper Length ($l$)

The length of an object measured by an observer who is at rest relative to the object.

Length Contraction

The decrease in length measured by an observer moving at speed $v$ parallel to the dimension of travel, given by $l' = l \sqrt{1 - \left(\frac{v}{c}\right)^2}$.

Lorentz Factor ($\gamma$)

The relativistic factor $\gamma = \frac{1}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}$, which is approximately equal to $1$ for speeds below $0.1c$ and causes noticeable relativistic changes at speeds above $0.8c$.

Projectile

Any object that accelerates freely downwards due to gravity while simultaneously moving with constant forward velocity.

Horizontal Velocity Component ($u_{\text{hor}}$) of an Angled Projectile

The constant component of an angled projectile's initial velocity, resolved using the formula $u_{\text{hor}} = u \cos(\theta)$.

Vertical Velocity Component ($u_{\text{ver}}$) of an Angled Projectile

The component of a projectile's launch velocity resolved by $u_{\text{ver}} = u \sin(\theta)$, which experiences a constant downward acceleration due to gravity of $a = -9.8\,\text{m/s}^2$.

Satellite Orbit

A continuous free-fall trajectory where an object projected horizontally at high speed falls around Earth's curved surface without ever reaching the ground.

Newton's Law of Universal Gravitation

The law stating that the gravitational force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of their separation: $F = G \frac{m_1 m_2}{r^2}$.

Universal Constant of Gravitation ($G$)

The physical constant in Newton's gravitational equation with a value of $6.67 \times 10^{-11}\,\text{N}\,\text{m}^2\,\text{kg}^{-2}$.

Light Gate Falling Object Experiment

An experimental arrangement that measures acceleration due to gravity by recording transit times of a known mask length $l$ through two light gates to find $u$, $v$, and transit time $t_2$, using $v = u + a t_2$.