physics 2

. General Relativity

Equivalence Principle

It states that free fall is indistinguishable from weightlessness, meaning there is no observable difference between floating in zero gravity and falling freely in a gravitational field.

Curved Spacetime

Massive objects distort the fabric of spacetime, and this curvature affects the motion of other objects, replacing Newton’s concept of a force of gravity.

Gravitational Lensing

It’s the bending of light by gravity, causing background objects to appear distorted or duplicated, as seen in Einstein rings or arcs.

Schwarzschild Radius

t’s the radius of a sphere such that if all the mass of an object is compressed within that sphere, not even light can escape — defining the event horizon of a black hole.

Event Horizon

It’s the boundary around a black hole from which nothing, not even light, can escape. Inside it, all paths curve inward.

Spaghettification

It’s the stretching of objects into long, thin shapes due to intense tidal forces near a black hole’s event horizon.

Gravitational Time Dilation

Light escaping a strong gravitational field loses energy, resulting in a shift to longer (redder) wavelengths — unrelated to motion.

Tests of General Relativity

1) Precession of Mercury’s orbit, (2) Deflection of starlight during solar eclipses, and (3) Gravitational time dilation (used in GPS systems).

Black Hole

A region of space where gravity is so strong that the escape velocity exceeds the speed of light, forming when a mass collapses beyond the neutron star limit (>3 solar masses).

Misconceptions About Black Holes

That they suck everything in like vacuum cleaners — in reality, they behave like normal massive objects unless you're very close.

Evidence for Stellar-Mass Black Holes

Observations of X-ray binaries like Cygnus X-1, where a visible star orbits an unseen, massive companion with an X-ray-emitting accretion disk.

Supermassive Black Hole

A black hole with millions to billions of solar masses, typically found at the centers of galaxies, such as Sagittarius A* in the Milky Way.

Gravitational Waves

• Ripples in spacetime caused by accelerating masses, such as black hole or neutron star mergers; confirmed by LIGO in 2015.

Milky Way Galaxy

It’s a barred spiral galaxy containing billions of stars, dust, gas, and a supermassive black hole at its center.

Galactic Components

The thin disk, thick disk, bulge, and halo — each containing stars of different ages and compositions.

Orion Arm

In the Orion Spur, a minor arm of the galaxy between the Sagittarius and Perseus arms.

Thin Disk

A flat region containing young stars, gas, and dust, with high rotation speed and active star formation.

Thick Disk

It contains older stars, less gas, and rotates more slowly than the thin disk.

Stellar Halo

A spherical region surrounding the disk containing old, metal-poor stars and globular clusters.

Population I & II Stars

Population I are young, metal-rich stars in the disk (like the Sun); Population II are old, metal-poor stars in the halo and bulge.

Harlow Shapley’s Discovery

He mapped globular clusters to show the galactic center is near Sagittarius, not Earth — revolutionizing our view of our position in the galaxy.

Galactic Rotation Curve

Stars at different distances orbit at roughly the same speed, indicating the presence of dark matter.

Dark Matter

An invisible substance that doesn’t emit or absorb light, but exerts gravitational influence — explaining flat rotation curves and unseen mass.

Galactic Bar

A central, elongated structure of stars connecting the bulge to spiral arms; confirmed via infrared observations.

Sagittarius A*

A supermassive black hole (~4.6 million solar masses) at the Milky Way’s center, observed via infrared and X-ray emissions and stellar orbits.

Infrared and Radio Observations

Because dust obscures visible light, while infrared and radio waves can penetrate it and reveal star motions and black hole activity.

Galaxy Formation Theories

A theory that the galaxy formed from a rotating gas cloud, where halo stars formed first, followed by the collapse into a disk.

Galaxy Mergers

Mergers (e.g., with the Sagittarius Dwarf Galaxy) add stars, alter orbits, and contribute to the halo and bulge, with the Andromeda collision predicted in the distant future.

Edwin Hubble

He used Cepheid variables to measure the distance to Andromeda, proving it lies outside the Milky Way — confirming the existence of other galaxies.

Cepheid Variable

heir period-luminosity relationship makes them “standard candles”, letting astronomers calculate distances to nearby galaxies.

Great Debate

• A scientific dispute between Shapley and Curtis over whether “spiral nebulae” were inside the Milky Way — Curtis was correct; they are external galaxies.

Spiral Galaxies

Galaxies with a central bulge, disk, and spiral arms of stars and gas, often showing active star formation (e.g., Milky Way, Andromeda).

Elliptical Galaxies

Spheroidal galaxies made mostly of old stars, with little dust or gas, and no arms or disk structure.

Irregular Galaxies

Galaxies lacking a regular shape, often rich in gas and dust, and containing both young and old stars (e.g., Magellanic Clouds).

Hubble Sequence (Tuning Fork)

A system classifying galaxies into ellipticals, spirals, and irregulars, with spirals further split into normal and barred types.

Lenticular Galaxies

Galaxies with a disk and bulge but no spiral arms, containing little gas and dust — intermediate between spirals and ellipticals.

Mass-to-Light Ratio

A measure of total mass (including dark matter) compared to visible light output. High M/L ratios suggest the presence of dark matter.

Dark Matter in Galaxies

Flat rotation curves at large radii indicate more mass than we can see — requiring dark matter halos to explain the gravitational effects.

Type Ia Supernova

They have a standard luminosity (~4.5 billion L☉), so their brightness tells us their distance — great for measuring distances to far galaxies.

Tully-Fisher Relation

A relationship between a spiral galaxy’s rotation speed and its luminosity, used to estimate distances based on 21-cm hydrogen line width.

Redshift

A shift of light to longer wavelengths (redder) due to recession from Earth, revealing the expansion of the universe.

Hubble-Lemaître Law

The velocity of galaxy recession (v) is proportional to its distance (d): v = H × d. This shows that the universe is expanding.

Standard Candle

An object with a known luminosity (e.g., Cepheids or Type Ia supernovae) used to measure astronomical distances by comparing apparent brightness.

Expanding Universe

Galaxies aren’t flying apart through space — rather, space itself is stretching, increasing the distances between galaxies over time.

Accelerating Expansion

• Observations of distant supernovae showed that the universe’s expansion is accelerating, likely due to dark energy.

Quasar (Quasi-Stellar Object)

A very luminous, distant object powered by matter falling into a supermassive black hole at the center of a galaxy. Quasars are among the brightest objects in the universe.

Active Galactic Nucleus (AGN)

The central region of a galaxy with a supermassive black hole that is actively accreting matter, producing huge energy output — quasars are a type of AGN.

Accretion Disk

Matter spirals into a black hole through an accretion disk, heating up and emitting radiation due to intense friction and gravitational energy conversion.

Early Universe Quasars

Quasars were more common in the early universe, suggesting that active black hole accretion played a major role in early galaxy growth.

Normal vs. Active Galaxies

Normal galaxies emit light from stars. Active galaxies emit additional radiation from an AGN, especially in X-rays, UV, and radio.

Homogeneous Universe

On large scales, the same types and amounts of matter are distributed throughout — it’s uniform in composition everywhere.

Isotropic Universe

The universe looks the same in every direction — no preferred direction exists in space.

Galaxy Group

A small collection of galaxies bound by gravity (e.g., the Local Group, which includes the Milky Way and Andromeda).

Galaxy Cluster

A larger structure containing hundreds to thousands of galaxies bound by gravity (e.g., the Virgo Cluster).

Supercluster

A giant collection of galaxy clusters, forming part of the largest known structures in the universe (e.g., the Laniakea Supercluster).

Cosmic Web

he large-scale structure of the universe where galaxies and clusters form filaments and walls, separated by vast voids.

Gravitational Lensing

Evidence for Dark Matter

Galaxy rotation curves, gravitational lensing, and structure formation models all require more mass than visible matter explains — leading to the concept of dark matter.

Large-Scale Structure

Galaxies form clusters, which form superclusters, connected in vast filaments — like a foam-like web stretching across the cosmos.

Big Bang Theory

It’s the leading explanation for the origin of the universe, stating that the universe began as a hot, dense point ~13.8 billion years ago and has been expanding ever since.

Hubble Time

The estimated age of the universe based on the inverse of the Hubble constant: about 13.8 billion years.

osmic Microwave Background

Faint radiation left over from the Big Bang, now cooled to about 2.73 K, observed as a blackbody spectrum — key evidence for the Big Bang.

CMB Fluctuations

Tiny variations (~1 in 100,000) in temperature across the CMB, representing density differences in the early universe that led to galaxy formation.

Nucleosynthesis

It predicts the correct abundance of light elements (hydrogen, helium, lithium), which stars alone could not have produced.

Inflation

A brief period of extremely rapid expansion just after the Big Bang that explains the uniformity, flatness, and isotropy of the universe.

Horizon Problem

The question of how regions of the universe now separated by vast distances have the same temperature — resolved by inflation.

Flatness Problem

The universe appears geometrically flat, which requires fine-tuned conditions in the early universe — again explained by inflation.

Redshift

The stretching of light to longer wavelengths due to the expansion of space, not just motion — used to determine galaxy velocities and distances.

Accelerating Expansion

Observations of distant supernovae showed that the expansion of the universe is accelerating, suggesting the presence of dark energy.

Dark Energy

A mysterious force causing the accelerating expansion of the universe; it dominates the universe’s energy content but is poorly understood.

Standard Candles

As standard candles with known brightness, they allow astronomers to measure distances to galaxies and track cosmic expansion.

Distance Modulus

A calculation that relates an object’s apparent brightness and intrinsic luminosity to determine its distance — affected by redshift and expansion.

Kepler’s First Law

Planets move in elliptical orbits with the Sun at one focus, not the center.

Kepler’s Second Law

A line connecting a planet to the Sun sweeps out equal areas in equal times — planets move faster when closer to the Sun.

Kepler’s Third Law

The square of a planet’s orbital period (P²) is proportional to the cube of its semimajor axis (a³): P² ∝ a³

Inverse-Square Law

Brightness decreases with the square of the distance:
B=Lr2B = \frac{L}{r^2}B=r2L​

Wien’s Law

The peak wavelength of a star’s light is inversely proportional to temperature:
λpeak=2.9×106T\lambda_{\text{peak}} = \frac{2.9 \times 10^6}{T}λpeak​=T2.9×106​

Spectral Classes

O, B, A, F, G, K, M — "Oh Be A Fine Girl/Guy, Kiss Me"

HR Diagram

A plot of luminosity vs. temperature (or spectral class). Most stars lie on the main sequence; others are white dwarfs, giants, or supergiants.

Main Sequence

A star fusing hydrogen in its core, in gravitational and thermal equilibrium — ~90% of stars are in this phase.

Stellar Parallax

By observing a nearby star’s apparent shift against distant stars as Earth orbits the Sun.
1 parsec = 3.26 light-years

Variable Stars (Cepheids)

Their pulsation period correlates with intrinsic luminosity, making them reliable standard candles.

Proton-Proton Chain

The primary fusion process in the Sun:
1H+1H→2H+e++ν1H + 1H \rightarrow 2H + e^+ + \nu1H+1H→2H+e++ν
→ then forms helium, releasing energy.

CNO Cycle

A hydrogen fusion process in hot, massive stars involving carbon, nitrogen, and oxygen as catalysts.

Stellar Lifetimes

More massive stars burn fuel faster and have shorter lifetimes.

• O-type: ~1 million years

• M-type: ~200 billion years

White Dwarf

The hot, dense core left after a low-mass star sheds its outer layers. Supported by electron degeneracy pressure.

Chandrasekhar Limit

he maximum mass (~1.4 M☉) a white dwarf can have before collapsing into a neutron star or black hole.

Supernova

The core collapse of a massive star after iron builds up, or a white dwarf exceeding the Chandrasekhar limit (Type Ia).

Pulsar

A rotating neutron star emitting beams of radio waves. If the beam points at Earth, we detect a pulse.

Lighthouse Model

The idea that a pulsar’s magnetic poles emit beams that sweep across the sky, like a rotating lighthouse.