Celestial Sky

Celestial Sphere and Local Sky

The celestial sphere is an imaginary sphere surrounding Earth onto which all celestial objects are projected. The local sky refers to the sky as seen from a specific location on Earth.

• Celestial Sphere: Useful for mapping positions of stars and planets.

• Local Sky: Defined by the observer's horizon, zenith (point directly overhead), and cardinal directions.

• Application: Used in celestial navigation and astronomy.

Coordinates

Celestial coordinates are systems used to specify the positions of objects in the sky.

• Right Ascension (RA): Analogous to longitude, measured in hours, minutes, and seconds.

• Declination (Dec): Analogous to latitude, measured in degrees north or south of the celestial equator.

• Example: The star Sirius has RA ≈ 6h 45m, Dec ≈ -16°.

Constellations vs Asterism

Constellations are officially recognized patterns of stars, while asterisms are informal groupings.

• Constellation: Orion, Ursa Major.

• Asterism: The Big Dipper (part of Ursa Major).

Celestial Equator vs Ecliptic

The celestial equator is the projection of Earth's equator onto the sky. The ecliptic is the apparent path of the Sun across the sky over the year.

• Celestial Equator: Divides the sky into northern and southern hemispheres.

• Ecliptic: Tilted by about 23.5° to the celestial equator due to Earth's axial tilt.

Zodiac

The zodiac is a band of the sky along the ecliptic containing twelve constellations through which the Sun, Moon, and planets appear to move.

• Application: Used in astrology and for tracking planetary positions.

Circumpolar Stars / Motion of the Stars

Circumpolar stars never set below the horizon and are visible all year from certain latitudes.

• Motion: Stars appear to move in circular paths due to Earth's rotation.

• Example: Polaris is circumpolar for most northern hemisphere observers.

Circumpolar Constellations

These are constellations that never dip below the horizon at a given latitude.

• Examples: Ursa Major, Cassiopeia (Northern Hemisphere).

Motion of the Stars Depending on Latitude and Direction

The apparent motion of stars varies with observer's latitude and the direction they are facing.

• At the equator: Stars rise and set vertically.

• At the poles: Stars move parallel to the horizon.

Precession: Tilt of the Axis

Precession is the slow wobble of Earth's rotational axis, causing the celestial poles and equator to shift over time.

• Period: About 26,000 years.

• Effect: Changes the position of the North Star over millennia.

Local Time

Local time is determined by the position of the Sun in the sky relative to a specific location.

• Noon: When the Sun is highest in the sky.

• Time zones: Established to standardize local time across regions.

Seasons

Seasons are caused by the tilt of Earth's axis and its orbit around the Sun.

• Altitude of Sun: Changes throughout the year, affecting daylight duration.

• Earth's Orbit: If the orbit were different, seasons would change.

• Planetary Tilt: Essential for seasons; no tilt means no significant seasonal change.

Topics of Cancer and Capricorn

The Tropic of Cancer (23.5°N) and Tropic of Capricorn (23.5°S) mark the furthest points north and south where the Sun can be directly overhead.

• Application: Used in geography and understanding solar position.

Solstices and Equinoxes

Solstices are the points in the year when the Sun is at its greatest distance from the celestial equator. Equinoxes are when the Sun crosses the celestial equator.

• Summer Solstice: Longest day of the year.

• Winter Solstice: Shortest day of the year.

• Vernal/Autumnal Equinox: Day and night are approximately equal.

Moon and Its Phases

The Moon goes through a cycle of phases due to its position relative to Earth and the Sun.

• Phases: New Moon, First Quarter, Full Moon, Last Quarter.

• Cycle: Approximately 29.5 days.

Tidal Lock

Tidal lock occurs when an object's orbital period matches its rotational period, causing one side to always face its partner.

• Example: The Moon is tidally locked to Earth.

Shadow of the Earth and the Moon: Umbra / Penumbra

During eclipses, shadows are cast with two main parts: umbra (full shadow) and penumbra (partial shadow).

• Lunar Eclipse: Earth’s shadow falls on the Moon.

• Solar Eclipse: Moon’s shadow falls on Earth.

Eclipses: Every Full and New Moon?

Eclipses do not occur every full or new moon due to the tilt of the Moon’s orbit.

• Nodes: Eclipses only occur when the Moon is near the nodes of its orbit.

Types of Eclipses, Durations

There are several types of eclipses, each with different durations.

• Solar Eclipse: Total, partial, annular.

• Lunar Eclipse: Total, partial, penumbral.

• Duration: Solar eclipses last a few minutes; lunar eclipses can last several hours.

Planets in the Sky

Planets are visible in the night sky and can be distinguished from stars by their steady light and motion.

• Visible Planets: Mercury, Venus, Mars, Jupiter, Saturn.

• Application: Used for navigation and observation.

Wave Properties

Period, Amplitude, Wavelength, and Frequency

Waves are characterized by several key properties:

• Period (T): The time for one complete cycle of the wave.

• Amplitude (A): The maximum displacement from equilibrium.

• Wavelength (λ): The distance between successive crests or troughs.

• Frequency (f): The number of cycles per second (measured in Hz).

Relationship Between Wave Properties

• Wave Speed (v): Related to wavelength and frequency by the equation:

• Period and Frequency: Related by:

Example Calculation

• How many vibrations per second are represented in a wave of 101.7 MHz? Frequency Hz, so there are vibrations per second.

Natural Frequencies, Resonance, Examples

Every system has natural frequencies at which it tends to oscillate. Resonance occurs when a system is driven at its natural frequency, resulting in large amplitude oscillations.

• Example: A swing, musical instruments, bridges.

Does the Medium Move with the Wave?

In most cases, the medium does not travel with the wave; only the energy and disturbance move.

• Example: Water waves: water molecules move in circles but do not travel with the wave.

Types of Waves

Waves can be classified based on their nature and the direction of particle motion.

• Transverse Waves: Particles move perpendicular to wave direction (e.g., light, water waves).

• Longitudinal Waves: Particles move parallel to wave direction (e.g., sound waves).

Summary Table: Wave Properties

Additional info: Some context and definitions have been expanded for clarity and completeness, as the original notes were brief and listed only keywords.