A. Gravity
1. Newton’s Laws of Motion
a. First Law: An object at rest, or in motion in a straight line at a constant speed, will
remain in that state
... [Show More] unless acted upon by a force
i. Aka. inertia
2. Second Law: The acceleration of a body due to a force will be in the same direction as
the force, with a magnitude inversely proportional to its mass.
a. OR the magnitude of force necessary to produce a certain acceleration on a body
will be directly proportional to its mass
b. A higher mass requires a greater force
c. F = ma or force = mass x acceleration
i. Example: if you apply the same amount of force to a soccer ball and a
car the ball will move faster
3. Third Law: for every action there is an equal and opposite reaction.
a. Example: The sun’s force of gravity keeps the planets in orbit around it
b. The planets exert and equally strong pull on the sun (causes it to move slightly)
4. Newton’s Law of Universal Gravitation
a. All objects with mass experience attraction towards each other as a result of the
gravitational force between them
b. Fg =
𝐺(𝑀1𝑀2)
𝑟
i. Fg: force of gravity
ii. G: universal constant of gravitation
iii. M1: mass of one object
iv. M2: mass of a second object
v. R: distance between the two objects
c. The gravitational force is directly proportional to the mass of each interacting
object and inversely proportional to the distance between them, squared
i. 𝑔 𝛼 𝑚
𝑟
d. the ratio of the gravitational of gravitational accelerations experienced by a person
or object on two different planets
i. gÆ
g𝐵
(
𝑚𝐴
)
= 𝑚𝐵
r𝐵
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e. when you take the ratio of the gravitational accelerations experienced by two
objects of different masses being influenced by a third body, their values of g
are the same
i. the strength of the gravitational force between higher-mass objects is
greater than for lower masses, it requires a greater force to be applied
to have the same overall acceleration
5. Gravity Game
a. strength of a gravitational field depends on the planet’s mass and radius.
b. As the mass of the planet increases, the jump height decreases by the same factor
as the mass
c. The mass of the planet and the jump height are inversely related
d. As the radius of the planet increases, the jump height increases as the square of
the radius.
e. Gravity is inversely proportional to the square of the radius
B. Seasons
1. Affected by the Earth’s tilt with respect to plane in which they orbit the Sun
a. No tilt = no seasons
b. Mars (25 degrees) and Earth (23 degrees) have almost the same tilt
c. Ex: when it is summer in the Northern hemisphere it is winter in the Southern
hemisphere
2. “1 AU” (astronomical unit) is the distance from the center of the Earth to the center of
the Sun.
a. about 150 million kilometers (93 million miles)
3. changes in the distance from the Sun during a year are not significant factors in
changing temperatures on planets because most planets’ orbits are nearly circular
4. perihelion: point in the orbit of an object that is closest to the sun
5. aphelion: point in the orbit of an object that is furthest from the sun
a. March 21st and September 21st are days of the year where both day and night are
exactly twelve hours everywhere on Earth
b. June 21st and December 21st are the longest and shortest days of the year
respectively
6. June 21st
= Summer Solstice
a. Northern hemisphere tilted toward Sun
7. December 21st
= Winter Solstice
a. Northern hemisphere tilted away from Sun
C. Phases of the Moon
1. Each day, the Moon does not move very far along its orbit
a. Its orbit is tilted with respect to the Earth
2. The Moon is tidally locked to the Earth, so the same side is always facing us
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3. Completes one set of phases over the course of about one month
a. About two phases a week
4. Just like the Sun, the Moon rises in the east and sets in the west
a. Due to the rotation of the Earth
5. The moon orbits the Earth, and this is the key for the moon’s phases
a. The rotation of the Earth= 1 day, the orbit of the Sun by the Earth= 1 year, the
time it takes the moon to orbit the Earth= 1 month (1 “month”) or 27-30 days
6. Phases result from changes in the relative positions of
a. the Moon
b. the Earth, or a viewer on the Earth’s surface
c. the Sun
7. phases are determined by the fraction of the illuminated portion of the Moon’s surface
visible from Earth
8. The Moon is always 50% illuminated
a. What we see on Earth is just a fraction of that half
i. Ex: we see all of the 50% when there is a full moon
ii. Ex: we see half of the 50% when the Moon is in its first or third quarter
phase
9. Full Moon: Earth is in a direct line between the Sun and Moon
a. The moon is fully lit up, therefore completely visible to us
b. Overhead at midnight
10. New Moon: Moon is between the Sun and Earth
a. Overhead during the day but it is obscured by the brightness of the sun so it is not
visible to us
b. Overhead at noon
11. First Quarter Phase: mid-way between a new moon and a full moon
a. One of the two “half moon” phases
b. Sees the right half of the moon lit up
c. Seen overhead at 6pm
12. Third (or Last) Quarter Phase: after the full moon, mid-way to the next new moon
a. One of the two “half moon” phases
b. Sees the left half of the moon lit up
c. Seen overhead at 6am
13. Waxing: Moon will be MORE illuminated in the coming days
a. Advancing toward Full Moon
14. Waning: Moon will be LESS illuminated in the coming days
a. Advancing toward New Moon
15. Gibbous: Phase of the Moon when all is illuminated EXCEPT for a crescent
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16. Transiting: when the Moon is at its highest point overhead
a. Six hours before this time the Moon is rising
b. Six hours after this time the Moon is setting
i. Ex: The Full Moon is rising at 6pm, transiting at midnight, and setting at
6am
D. Eclipses
1. Solar Eclipse: occur during the New Moon phase
a. The Moon is between the Sun and the Earth
b. A portion of the Earth’s surface falls under the Moon’s shadow
2. Lunar Eclipse: occur during the Full Moon phase
a. when the Moon is opposite the Sun from the Earth
b. the moon falls in the shadow of the planet Earth
3. not every New Moon causes a solar eclipse somewhere on the Earth’s surface and not
every full moon causes a a partial or full lunar eclipse.
a. Due to the plane in which Moon orbits the Earth is tilted with respect to the plane
in which the Earth orbits the Sun
b. The planes rarely line up at the same time as the Sun-Earth-Moon or the SunMoon-Earth
c. Partial or total lunar eclipse tend to occur more frequently than solar eclipse
because the shadow cast by the Earth is larger than that of the moon
E. Mars’ Moons
a. Mars has two natural satellites:
i. Phobos
1. Named after son of Ares (Mars)
a. Meaning of name: Fear
2. Discovered by American astronomer Asaph Hall in 1877
3. Possibly a captured asteroid
4. Has a low orbit above Mars which is decaying over time
a. Will eventually be tidally disrupted in around 50
million years
5. Fast orbit
a. Means circles Mars three times a day
b. Combined with small orbital inclination allows regular
occurrence of eclipses
ii. Deimos
1. Named after son of Ares (Mars)
a. Meaning of name: dread
2. Discovered by American astronomer Asaph Hall in 1877
3. Orbits much farther from Mars
4. slowly drifting away from the planet over time
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5. an oddly-shaped, heavily cratered body of rock
6. has no appreciable atmosphere
7. has a seeming smooth surface
a. due to low surface gravity as to not experience
secondary cratering from returning impact ejecta
F. Constellations
1. Constellations vs. Asterisms
a. Constellation: a region in the sky
i. The night sky is divided into 88 official constellations
ii. Contain asterisms, and many more stars, nebulae, galaxies, and other
objects too faint to see
1. Does not mean the constellation physically contains all those
objects, just means these objects are in the direction of
respective constellations
iii. Which constellations are visible on a given night depends on the time
of year and the viewer’s location
1. As the Earth/Mars travels around the Sun in its orbit, the Sun
blocks view of constellations in its direction
2. Constellations visible at midnight one night will be behind the
Sun at noon half a year later
i. Constellations previously obscured by daylight will be
prominent in the nighttime sky
b. Asterism: a shape traced out in the sky by imagining connecting lines between
stars
i. Big Dipper: an asterism made by a subset of the stars in the asterism
“Ursa Major” (“great bear”)
2. Ecliptic & the Zodiac
a. Ecliptic: as the Earth orbits the Sun, the Sun traces out an apparent path across the
celestial sphere
i. also applies to the plane in which the Earth orbits the Sun
b. Zodiac: subset of constellations which are crossed by the ecliptic line
i. The stars of these zodiac constellations do not move appreciably from
one year to the next
ii. Sun’s annual motion through them appears very regular
iii. Cyclical variations in Earth’s motion over thousands of years, causes
some drift in the timing of the Sun’s passage through the zodiac
constellations
1. this precession is responsible for change over time in which star
is best considered a “pole star”
i. currently, Polaris is Earth’s north star
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G. Light
i. names of the zodiac constellations: Aries, Taurus, Gemini, Cancer,
Leo, Virgo, Libra, Scorpio, Ophiuchus, Sagittarius, Capricorn,
Aquarius, and Pisces
1. Electromagnetic Radiation
a. Energy comes in many forms and can transform from one type to another
b. Light / electromagnetic radiation: energy transported by charged particles (eg.
Electrons and protons) that create electromagnetic fields when they move
c. Waves
i. Mechanical and electromagnetic waves are two important ways that
energy is transported
ii. Mechanical waves: caused by a disturbance or vibration in matter
1. Eg. waves in water and sound waves in air
2. Medium: matter that waves are traveling through
i. Eg. Water waves are formed by vibrations in a liquid,
while sound waves are formed by vibrations in a gas
ii. Classical waves transfer waves without transporting
matter through the medium
1. Eg. Waves in pond don’t carry water molecules,
the wave’s energy travels through the water
d. Electromagnetic Waves
i. Electricity and Magnetism can be static
1. Eg. Energy that makes your hair stand on end
2. Eg. A refrigerator magnet
ii. Changing magnetic field will induce a changing electric field, and viceversa
1. Changing fields form electromagnetic waves
2. Electromagnetic waves don’t require a medium to propagate
i. Can not only travel through air, solid materials, but
through vacuum of space
iii. Maxwell’s Equations: relationship between electricity and magnetism
iv. Hertz: unit of frequency of a radio wave, one cycle/second
v. Heinrich Hertz’s experiment demonstrated radio waves both
demonstrated that the velocity of radio waves was equal to the velocity
of light (radio waves are a form of light)
vi. Also determined how to make electric and magnetic fields detach
themselves from wires and go free as electromagnetic waves
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vii. Formed by the vibrations of electric and magnetic fields
1. Perpendicular to one another in the direction the wave is
traveling
2. Once the energy is formed, it travels at the speed of light
(~300000km/s) until further interaction with matter
e. Photons: discrete packets of energy that make up light
i. Carry momentum
ii. Have no mass
iii. Travel at speed of light
f. All light has both particle-like and wave-like properties
g. The design of an instrument can affect how the light is sensed and how it
influences properties
i. Eg. An instrument that diffracts light into a spectrum for analysis is used
to observe wave-like property of light
ii. Eg. Digital cameras detectors are used to observe the particle-like
nature of light
h. Polarization
i. Physical property of light, being able to be polarized
i. A measurement of the electromagnetic field’s alignment
i. Electromagnetic energy: described by energy, frequency, and wavelength
i. Described in terms of frequency (Hertz): radio and microwaves
ii. Described in terms of wavelength (meters): infrared and visible light
iii. Described in terms of energy: electron volts
j. Frequency: number of crests that pass a given point within one second
i. Hertz (Hz): one wave/cycle per second
1. A wave with 2 cycles that pass a point in one second has a
frequency of 2 Hz
k. Wavelength: the distance between crests
l. Energy units are in electron volts (eV)
i. eV: the amount of kinetic energy needed to move an electron through
one-volt potential
ii. energy and wavelength are indirectly proportional
1. energy increases as the wavelength shortens
iii. energy and frequency are directly proportional
1. energy increases as the frequency increases
2. Electromagnetic Spectrum
a. Tip to remember order of waves from longest to shortest wavelength: Rabbits
make interesting very unique eXpensive gifts
i. Radio, Microwave, Infrared, Visible, UV, X-ray, Gamma
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b. Wavelength of visible light
i. The portion of light that we can see
ii. When the full spectrum of visible light travels through a prism, the
wavelengths separate into colors of the rainbow
1. Each color is a different wavelength
i. Violet has the shortest wavelength (380nm)
ii. Red has the longest wavelength (700nm)
c. UV = Ultraviolet light
1. Ultra means above
2. A color “more violet than violet”
3. Causes sunburn
d. IR = Infrared light
1. Infra means below
2. “Below red”
3. Shows heat, like a person, as very bright
4. Shows cold things, like ice, as very dark
e. X-rays can go through skin and get to bone
i. More energy than visible light
ii. Shorter wavelength and higher frequency
f. Gamma rays have highest energy of them all
3. Blackbody Radiation
a. When an object grows hotter it radiates energy dominated by shorter wavelengths
and changes color before our eyes
i. an object emits radiation over a broad range of wavelengths depending
on its effective temperature
ii. Eg. A flame on a blow torch shifts from reddish to bluish in color as it
adjusted to burn hotter
b. Our sun produces more yellow and green light than other colors because the
surface temperature is around 5800 K
c. Cooler objects (around 20 degrees Celsius / 300 K) would emit in the infrared but
it will not produce visible light
i. Cooler objects have overall lower emission at all wavelengths than
hotter ones
d. Perfect blackbody: an ideal theoretical construct
i. an ideal object that is both a pure emitter and absorber
ii. approximation is generally good in many cases
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H. Spectroscopy
1. Types of Spectra
a. 3 main types:
a.Continuum
i. Produced by blackbody radiation, and recording broad-spectrum
emission
ii. Objects’ peak emission at around a certain color may be shown
as a brighter image in a particular region of the spectrum
1. Overall there’s a smooth transition between colors
2. Emission
i. Comes from the specific energies of electron level transitions in
the atoms of an object
ii. Electrons drop from an excited energy level to a lower one
releasing a photon that represents the energy difference
i. The photon’s energy is detected as a thin bright point in
a dark spectrum
iii. The several electron-level transitions going on together in a
group of atoms of a certain chemical element will result in an
emission spectrum with several bright lines at wavelengths
specific to the transitions
i. Emission spectrum is a “fingerprint” to the existing
elements
3. Absorption
i. Result of detecting a continuum source on the other side of a
cloud of unexcited gas
ii. Intervening material preferentially absorbs photons of energies
corresponding to its electron energy transitions
i. Effectively removes the colors from the continuum
spectrum
ii. The excited gas re-emits the photons eventually but not
in the same direction the photons were originally
traveling in
iii. Stars have cooler hydrogen and helium, and traces of other
elements in their outer atmospheres above the hotter regions,
which are responsible for their visible light output
I. Telescopes
1. Parts and Properties of Telescopes
a. A telescope: collects and concentrates light
i. The size of a telescope’s primary lens affects its light gathering power
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