Astronomy

test prep

Moon Phase / position and time of day

The Moon Phase refers to the appearance of the illuminated portion of the Moon as observed from Earth, which changes cyclically due to its position relative to the Earth and Sun. This phenomenon is tied to specific times of the day and the Moon's orbital position.

The path of the sun in the sky

is known as the ecliptic. It represents the apparent motion of the sun through the celestial sphere over the course of the year.

Newton’s law of universal gravitation

is a fundamental principle describing the attractive force between two bodies, proportional to their masses and inversely proportional to the square of the distance between them.

Tycho’s Work

significantly advanced astronomical observations. He meticulously recorded the positions of celestial bodies, paving the way for modern astronomy and Kepler's laws.

Altitude of NCP = Observer’s latitude

is the angle between the observer's local horizon and the North Celestial Pole, indicating the observer's latitude.

Kepler’s Third law Calculation

describes the relationship between the time a planet takes to orbit the Sun and its average distance from the Sun, stating that the square of the orbital period is proportional to the cube of the semi-major axis of its orbit.

Galileo’s Discoveries

revolutionized the understanding of motion and astronomy, including the observation of Jupiter's moons and the phases of Venus.

Kepler’s first law

states that planets move in elliptical orbits with the Sun at one focus, describing the shape of planetary orbits.

Kepler’s second law

states that a line drawn from a planet to the Sun sweeps out equal areas in equal times, illustrating the speed of a planet's orbit varies with its distance from the Sun.

Parallax as proof of the Earth’s revolution

is the apparent shift in position of nearby stars against more distant background stars as observed from different positions in Earth’s orbit, providing evidence for Earth’s movement around the Sun.

Importance of sunspots and lunar craters

Sunspots are temporary phenomena on the Sun's photosphere that appear as dark spots due to lower temperatures caused by intense magnetic activity. Their study is crucial for understanding solar activity, its influence on Earth's climate, and space weather. Lunar craters are impact formations on the Moon's surface, providing insights into the history of the solar system, the frequency of asteroid and comet impacts, and the geological processes that have shaped celestial bodies.

Foucault pendulum as proof of Earth’s rotation

A Foucault pendulum is a device that provides experimental proof of Earth's rotation. It consists of a heavy bob suspended from a long wire, allowing its plane of oscillation to remain fixed in space while the Earth rotates underneath it, causing the pendulum's apparent plane of swing to precess over time.

The importance of Jupiter’s Moon’s orbital motion

Galileo's observation of Jupiter's moons directly challenged the geocentric model, offering strong evidence for the heliocentric view by showing objects orbiting another planet. This discovery was pivotal for Copernicus's model and laid the groundwork for Kepler's and Newton's laws.

Retrograde motion

Retrograde motion refers to the apparent temporary backward (westward) movement of a planet in the night sky relative to the background stars, as observed from Earth. This phenomenon is an optical illusion, not an actual reversal of the planet's orbit. It occurs due to the difference in orbital speeds between Earth and other planets. For outer planets (like Mars), it happens when Earth, moving faster in its inner orbit, overtakes the slower-moving outer planet. For inner planets (like Venus), it occurs when they pass between Earth and the Sun, moving faster than Earth.

Ptolemy and the geocentric model-epicycles

• Ptolemy was an ancient Greek astronomer.

• He proposed the geocentric model, with Earth at the center of the universe.

• The Sun, Moon, planets, and stars were thought to orbit Earth.

• To explain strange planetary motions, he added epicycles (small circles on larger orbits).

• This system explained retrograde motion but was later replaced by the heliocentric model.

Cause of phases of the moon

• The Moon does not produce its own light; it reflects sunlight.

• As the Moon orbits Earth, we see different portions of its sunlit half.

• This changing view creates the phases (new, crescent, quarter, gibbous, full).

• The cycle of phases takes about 29.5 days (a lunar month).

• Phases are caused by the Moon’s position relative to Earth and the Sun.

Definition of the AU

• A unit of distance used in astronomy.

• Defined as the average distance between Earth and the Sun.

• Equal to about 150 million kilometers (93 million miles).

• Helps compare distances within our solar system.

• Example: Earth = 1 AU, Jupiter ≈ 5.2 AU from the Sun.

Relative sizes of Earth and Moon

• Earth is about 4 times wider than the Moon.

• Earth’s diameter ≈ 12,742 km; Moon’s diameter ≈ 3,474 km.

• Earth’s volume is about 50 times larger than the Moon’s.

• Earth is roughly 80 times more massive than the Moon.

• The Moon is still large compared to most moons in the solar system.

Newton’s first law

• An object will stay at rest unless acted on by a force.

• An object in motion keeps moving in a straight line at constant speed.

• This tendency to resist change is called inertia.

• Forces (like friction or gravity) are needed to change motion.

• Explains why planets keep orbiting and objects in space keep drifting.

Rising time of a superior planet at opposition

• A superior planet orbits farther from the Sun than Earth (e.g., Mars, Jupiter).

• At opposition, Earth is directly between the Sun and the planet.

• The planet appears opposite the Sun in the sky.

• It rises at sunset and sets at sunrise.

• This makes it visible all night, at its brightest and closest to Earth

Solar eclipse geometry- what blocks what?

• A solar eclipse happens when the Moon passes between Earth and the Sun.

• The Moon blocks the Sun’s light, casting a shadow on Earth.

• From Earth, the Sun looks partially or fully covered.

• A total eclipse occurs when the Moon completely blocks the Sun.

• A partial or annular eclipse happens when only part of the Sun is covered.

Number of constellations visible at the equator

• The equator allows viewing of both northern and southern skies.

• Nearly all 88 modern constellations can be seen over the year.

• Visibility depends on the time of year and night sky conditions.

• Some constellations are only visible seasonally.

• Equatorial observers get the widest range of constellations on Earth.

Number of constellations visible at the poles

• At the poles, you can only see the half of the sky facing your pole (north or south).

• About half of the 88 modern constellations are ever visible.

• Some constellations circle the pole all year and never set (circumpolar).

• Others are never visible, hidden below the horizon.

• Visibility is constant throughout the year due to Earth’s rotation around its axis.

Phases of the moon and position on orbit

• The Moon’s phases depend on its position around Earth in its orbit.

• New Moon: Moon is between Earth and Sun; the sunlit side faces away.

• First Quarter: Moon is 90° from Sun; half of the near side is lit.

• Full Moon: Earth is between Moon and Sun; the near side is fully lit.

• Last Quarter: Moon is 270° from Sun; the other half of the near side is lit.

Lunar eclipses geometry- what blocks what?

• A lunar eclipse happens when Earth passes between the Sun and the Moon.

• Earth blocks sunlight from directly reaching the Moon.

• The Moon moves into Earth’s shadow (umbra or penumbra).

• During a total lunar eclipse, the entire Moon enters the umbra and can appear reddish.

• During a partial lunar eclipse, only part of the Moon enters Earth’s shadow.

Eclipse seasons

• Eclipse seasons are periods when the Sun is near the Moon’s orbital nodes.

• During these times, solar and lunar eclipses can occur.

• They happen roughly every 6 months.

• Each season lasts about 34–37 days, allowing for one or two eclipses.

• The timing depends on the alignment of the Sun, Earth, and Moon.

The length of the sidereal day (~23:56) and objects rising/transiting/setting 4 minutes earlier each day

• A sidereal day is the time Earth takes to rotate once relative to the stars.

• It is about 23 hours 56 minutes, slightly shorter than a solar day.

• Because of this, stars rise, transit, and set about 4 minutes earlier each solar day.

• This difference accumulates, making the night sky shift over the year.

• Sidereal time is used in astronomy for tracking stars and celestial objects.

Copernicus’ model of the solar system

• Proposed the heliocentric model, with the Sun at the center.

• Earth and other planets orbit the Sun in circular paths.

• Earth rotates on its axis, explaining day and night.

• This model replaced the geocentric model of Ptolemy.

• It laid the foundation for modern astronomy and planetary motion.

Physics demo: fire extinguisher and Newton’s third law

• Newton’s third law: For every action, there is an equal and opposite reaction.

• When a fire extinguisher sprays gas, the gas is pushed outward (action).

• The extinguisher (and person holding it) is pushed backward (reaction).

• This demonstrates conservation of momentum in everyday life.

• Shows how forces always come in equal and opposite pairs.

Physics demo: spinning on a stool with dumbbells and Kepler’s second law (conservation of momentum)

• Kepler’s Second Law: a line from a planet to the Sun sweeps equal areas in equal times.

• Demonstrates conservation of angular momentum in physics.

• When spinning with arms extended (holding dumbbells), rotation is slower.

• Pulling arms inwards makes rotation faster, keeping angular momentum constant.

• Shows how orbital speed changes depending on distance from the rotation axis, like planets in elliptical orbits.

Cause of the Earth’s seasons

• Seasons are caused by the tilt of Earth’s axis (≈23.5°) relative to its orbit.

• When a hemisphere tilts toward the Sun, it experiences summer.

• When it tilts away from the Sun, it experiences winter.

• Spring and autumn occur when the tilt is sideways relative to the Sun.

• The tilt changes the angle and intensity of sunlight, creating seasonal temperature differences.

Rayleigh’s scattering causing red lunar eclipses and the blue sky

• Rayleigh scattering occurs when sunlight interacts with small particles in Earth’s atmosphere.

• Shorter wavelengths (blue light) scatter more, making the sky appear blue.

• Longer wavelengths (red light) scatter less and pass through more easily.

• During a lunar eclipse, Earth’s atmosphere bends red light into its shadow, giving the Moon a reddish color.

• Explains why sky color and eclipse appearance are linked to light

Path of sun on sky, against background stars, from Oct 2025 to Dec 2025

• October 2025: The Sun continues its journey southward along the ecliptic, gradually decreasing in altitude as the days progress. By the end of the month, the Sun rises later and sets earlier, reducing daylight hours.

• November 2025: The Sun's path remains low in the sky, with shorter days and longer nights. The Sun's altitude at noon decreases further, and the Sun rises later and sets earlier each day.

• December 2025: The Sun reaches its lowest maximum altitude at noon for the year during the winter solstice on December 21, marking the shortest day and longest night in the Northern Hemisphere. After the solstice, the Sun's altitude begins to increase gradually, leading to longer days.

Number of constellations in the sky

• Modern astronomy officially recognizes 88 constellations.

• These cover the entire celestial sphere, both northern and southern hemispheres.

• Constellations help locate stars and celestial objects in the sky.

• Some constellations are circumpolar (never set), depending on your latitude.

• The boundaries of constellations were standardized by the International Astronomical Union (IAU) in 1922–1930.

The Meridian

• The meridian is an imaginary line in the sky running from north to south through the zenith (point directly overhead).

• It divides the sky into eastern and western halves.

• When a celestial object crosses the meridian, it is at its highest point in the sky.

• This moment is called culmination or transit.

• Observing objects on the meridian helps accurately measure time and position in astronomy.

Kepler’s third law calculation for an asteroid

• Kepler’s Third Law: P2∝a3P^2 \propto a^3P2∝a3 (orbital period squared is proportional to semi-major axis cubed).

• PPP = orbital period (in years), aaa = average distance from Sun (in AU).

• Example: If an asteroid’s orbit has a=4 AUa = 4 \, \text{AU}a=4AU, then P2=43=64P^2 = 4^3 = 64P2=43=64.

• Solve for PPP: P=64=8P = \sqrt{64} = 8P=64​=8 years.

• This law predicts orbital periods of planets, asteroids, and other solar system bodies.

Law of universal gravitation calculation for a new planet in solar system

• Newton’s law: F=Gm1m2r2F = G \frac{m_1 m_2}{r^2}F=Gr2m1​m2​​, where FFF = gravitational force.

• GGG = gravitational constant, m1m_1m1​ and m2m_2m2​ = masses of two objects, rrr = distance between them.

• Example: Calculate the force between the Sun and a new planet at distance rrr with mass mmm.

• Plug values into the formula to get FFF, showing how strongly the planet is pulled toward the Sun.

• This law explains orbital motion of planets, moons, and satellites in the solar system.

Coriolis force as a proof of Earth’s rotation

• The Coriolis force is an apparent deflection of moving objects on a rotating Earth.

• In the Northern Hemisphere, objects deflect to the right; in the Southern Hemisphere, to the left.

• It affects winds, ocean currents, and projectiles, showing rotation effects on motion.

• The deflection increases with speed and latitude, zero at the equator.

• Observing the Coriolis effect provides evidence that Earth rotates on its axis.