Astronomy Exam 1

G

universal gravitational constant (6.67 × 10^-11m³/(kg x s²)

Fundamental Principles of Gravity

universal attraction, mass dependence, distance dependence, inverse-square relationship

Universal Attraction

Every mass attracts every other mass through gravity

Mass dependence

gravitational force increases directly as mass increases

distance dependence

gravitational force decreases as distance increases

inverse-square relationship

force is inversely proportional to the square of the distance between centers F_G is proportional to 1/r²

inverse-square scaling rules

double distance, triple distance, half distance

double distance (r → 2r)

the gravitational force decreases to ¼ of its original value

triple distance (r → 3r)

the gravitational force decreases to 1/9 of its original value

half distance (r → ½ r)

The gravitational force increases to 4 times its original value

Gravitational interaction between earth and moon

earth and moon are gravitationally bound to each other

according to newton’s third law of motion: the gravitational force earth exerts on the moon has equal magnitude to the force the moon exerts on earth

the forces point in exact opposite direction along the line connecting their centers

Mechanism of synchronous rotation

the same side of the moon is always visible from earth because:

the moon’s rotation period = moon’s orbital period

the moon completes exactly on full rotation around its internal axis in the exact time it takes to complete one orbit around earth

rotation

an object spinning around its own internal axis

orbit/revolution

an object moving in a pathway around another external body

primary cause of seasons

the tilt of earth’s rotation axis relative to the plans of its orbit around the Sun

key seasonal phenomena

opposite season, sunlight angle, daylight duration

opposite seasons

summer occurs in one hemisphere while winter occurs simultaneously in the opposite hemisphere

sunlight angle

the angle at which sunlight strikes Earth’s surface changes continuously throughout the year

daylight duration

the amount of daylight received at a given location changes systematically over the course of the year

solar eclipse required moon phase

new moon

solar eclipse celestial alignment

moon is positioned directly between earth and the sun

lunar eclipse required moon phase

full moon

lunar eclipse celestial alignment

earth is positioned directly between the sun and the moon

reasons eclipses do not occur monthly

orbital inclination, elliptical orbit and angular size

orbital inclination

the moon’s orbital plane is tilted relative to earth’s orbital plane (the ecliptic). as a result, most new moons and full moons do not achieve the precise linear alignment needed for an eclipse

elliptical orbit and angular size

the moon’s orbit is elliptical. when the moon is near apogee (farthest from earth), its apparent angular size is too small to completely obscure the Sun and create a total solar eclipse

Kepler’s first law

planets travel around the sun in elliptical orbits with the sun situated at one focus of the ellipse

kepler’s second law

a line joining a planet and the sun sweeps out equal areas in equal time intervals; consequently, a planet moves faster when closer to the sun (perihelion) and slower when farther from the sun (aphelion)

kepler’s third law

for objects orbiting the sun, the square of the orbital period (P) in earth years is proportional to the cube of the semi-major axis (a) in astronomical units (AU): P² = a³

apparent retrograde motion

the periodic visual phenomenon where a planet appears to temporarily reverse direction and move backward against the background of fixed stars

why retrograde happens

planetary motion does not physically reverse direction; occurs when earth passes the outer planet in its orbit since earth has a faster orbital speed as it’s closer to the sun

our cosmic address from small to large

earth → solar system → milky way galaxy → local group → larger scale structure → universe

earth

terrestrial planet home

solar system

the sun and gravitationally bound orbiting bodies

milky way galaxy

spiral galaxy containing the solar system and billions of stars

local group

galaxy cluster containing the milky way, andromeda, and neighboring galaxies

local group

galaxy cluster containing the milky way, andromeda, and neighboring galaxies

local supercluster

broader collection of galaxy groups and clusters

universe

the totality of all space, time, matter, and energy

constellations

a designated region of the celestial sky containing an asterism as in (an apparent visible pattern formed by stars)

spatial misconceptions

stars forming a constellation do not constitute a physical, gravitationally bound cluster

stars in a constellation can be separated by immense distances in 3D space

stars in the same constellation do NOT necessarily share spatial proximity, similar physical dimensions or size, equivalent age or evolutionary stage,

one light year

9.46 × 10¹⁵m

principle of geometric measurement

ancient greek astronomers used geometric reasoning and angular observations to calculate celestial distances indirectly

earth’s radius

eratosthenes measured the angular difference of shadows cast at two different geographic locations on earth at noon

used the known physical distance between locations and proportional geometry to calculate earth’s circumference and radius

earth moon distance

using the measured radius of the earth, ancient astronomers could use the duration of a lunar eclipse and the duration of a month to setup another ratio to calculate the distance between the earth and moon

measuring earth sun distance

using the earth and moon distance astronomers used the angular distance between the moon and the sun during a particular phase of the moon and some trigonometry to calculate the distance between the earth and sun

escape velocity (v_escape)

the minimum initial speed required for an unpropelled object to break free from the gravitational pull of a massive celestial body under idealized conditions

escape velocity formula

v_escape= square root of 2GM/R

G= gravitational constant

M = mass of the astronomical body

R = radius of the body

kinematics equation (displacement under uniform linear acceleration is calculated using):

delta x = v_it + ½ at²

^{delta x = displacement}

v_i= initial velocity

a = acceleration

t = time elapsed

7 days in a week

tied to seven naked-eye celestial objects observed in antiquity (7 wanderers): sun, moon, mars, mercury, jupiter, venus, and saturn

30 days in a month

connected directly to the lunar phase cycle requiring approximately 30 days for the moon to cycle through all phases

365.25 days in a year

represents earth’s complete orbital period around the sun

fractional day necessitates calendar adjustments such as leap years every four years

determined by tracking the annual repetition of the sun’s position relative to background constellations

position, displacement, distance measured in

meters

velocity and speed measured in

meters per second

acceleration measured in

meters per second squared

mass measured in

kg

momentum (p) measured in

kgm

newton’s first law

an object at rest will stay at rest or an object in motion will stay in motion unless acted on by an outside force

newton’s second law

a force acting on an object results in a change in momentum for that object

weight and force measured in

newtons

angular momentum (L) measured in

kg m²/s