**Zeinath is a point above you**
The Sun’s Daily Cycle
1. Due to Earth’s 24-hour east-ward spin around its polar axis, the sun moves westward
across the sky ; it rises in the east, reaches its highest point at noon. then sets in the
2. N-Hemisphere: Sun is mostly seen on the south side of the sky, reaching due south
3. S-Hemisphere sun is mostly seen on north side of sky reaching due north at noon.
Local noon: when ur location is facing the sun.
Local midnight: When your location is facing the opposite side of the sky from the sun
local sunrise sunset: when the suns direction is perpendicular to your location
Suns annual cycle
1. fall and spring equinnox (Sep23-mar 21): Sun rises due E. and sets due W, speeding
equal time above and below the horizon(equal day and night0. (equinx: Latin for
Winter solstice: Sun rises and sets at its southernmost position, traversing a short, low
are in the sky(shortest day of the year and lowest noon sun)
- The seasonal changes in the suns daily are due to Earth’s 23.5degree tilt from its orbit
around the sun.
- Winter: When a hemisphere is tilted away from the sun, sunlight hits indirectly causing
low arcs and less light per area
- Summer: when a hemisphere is tilted toward the sun sunlight hits more directly
causing high areas and more light per area.
- December 22 winter solstice March 21 vernail equinx june 22 summer solstice
- when one hemisphere is tilted towards the sun, the other is tilted away, there fore the
seasons are longer during one side then the other
- at 23.5 N degres the sun can be seen directly overhead
- at 23.5N the noon sun is in the cancer constellation( looks like a crab)
- 23.5S The noon sun is in the Capricorn constellation when it is directly overhead
- the lower your latitude the higher the suns daily path
- Suns daily path is steeper at low latitudes the sun rise and sets faster
- Low latitudes are warmer because they recieve more light thro out the year.
- within 23.5 degrees summer solstice doesn’t set and winter solstice doesn’t rise
- the higher the latitude the more consecutive polar days/night
Positional Astronomy and the Cycle of the Stars
-The Celestial Sphere: our view of the sky projected on to the surface of an imaginary
sphere, a visual tool for describing the positions of celestial bodies, North celestial pole
is a line from the north pole going straight to the North celestial sphere same goes for
south and equator **Zeinath is a point above you**
- Mayan sites and records reveal: the Maya tracked celestial cycles in order to worship
the mayan gods associated with celestial bodies
1). Pyramid of Kukulcane
- 365 steps (shows mayan we aware of the sun’s annual cycle)
- annual serpent-pattern of light and shade tracks the time of year ( full serpent ends at
2). El caracole: openings in the observatory doen are aligned to the N-most & S-most
setting positions of planet Venus (allowed the maya to measure the duration of venus
full path in the sky)
3). Mayan bark books: durable boooks contained listings of historical events, including
celestial events(Dersend codex contains mayan dates of the full eclipse cycle & the
4). 2012: Mayan Calendar notation ends on december 21,2012. This is not based on
any astronomical cycle. Mayan records describe this date as the last date of one
calendar cycle, as opposed to the last date of all time
5). Mayan number symbols: visually represent their quantity, making them effiecent for
addition and subtraction of large numbers. This allowed the Mayan to easily record the
# of days between celestial events and to recognize their long-term patterns.
-Believed by many civilizations to be hearlds of bad times, due to the “damaged”
apperance of the sun or mon.
-Their long-term, complex cycle led may to believe that eclipse are random. The maya,
however, found their pattern.
The Moons Phases
1). Lunation: one complete cycle of moon phase (~29.53 days).
2. As the moon orbits Earth once a month, earth sees different portions of its sunlit side,
causing the moons appearance to cycle from completely dark (New) to completely
3. When the moon is waning(from full to new), it’s lit on the left; when the moon is
waxing(from new to full), it’s lit on the right.
4. The larger the visible portion of the moons lit side, the more night hours the moon is
visible(Full moon is only seen at night).
1). A solar eclipse occurs when the moon (New) passes between Earth andSun and
casts its shadow on Earth:
-A total eclipse is seen from the parts of Earth in the Moon’s primary shadow(umbra)
-a partial eclipse is seen from the parts of earth in the moon’s secondary
shadow(penumbra) **Zeinath is a point above you**
2).A Lunar eclipse occurs when the moon (Full) passes through Earths Shadow:
-Penumbra eclipse: when moon passes through Earth’s penumbra
-partial eclipse: when a part of the moon passes through Earths umbra
-total eclipse: when entire moon passes through Earth’s Umbra
3). The total eclipse moon appears red because its light has been so dimmed that only
its red light makes it through our atmosphere.
4). The appearance of the eclipsed sun is location-dependent, while the eclipsed moon
appears the same for all observers.
5). Eclipses do not occur every New and Full moon:
-Due to the 5th tilt of the moon’s orbit, Earth moon and sun are usually not in the same
-Eclipse seasons (when Moon, Earth and Sun are coplanar) only occur 2-3 times per
year and last 31-38 days
6). Since an eclipse season>1 lunation, there are 1-2 lunar & 1-2 solar eclipse each
season, though only 1 lunar/yr & 1 solar/1.5yrs are seen(solar seen less since observer
must be in Moon’s shadow).
7). The Mayan eclipse records:
- 8 pages of the Dresden Codex contain symbolic illustrations of eclipses.
- Bottom of each page contains a series of 177s and 148s (#days between eclipse
- Above each 177(or 148) are the range of Mayan dates expected for that season’s
- The table spans 1 complete eclipse cycle of Mayan dates, so eclipse warnings could
be predicted for eternity.
1. Next to the Sun and Moon, Venus is the brightest object in the sky.
2. In a given night, Venus moves with the stars due to Earth’s spin. But from night to
night, Venus changes it position relative to the stars, revealing itself as a
planet(Greek for “Wander”)
3. Every 584 days, Venus traverses a half-loop around the rising sun, then disappears.
When it reappers, it makes a half-loop around the setting sun, then disappears again.
4. The Mayan Venus records:
- 6 pages of the Dredon codex contains illustrations of the Mayan war hero KUKUclan,
who was deified and linked with the Planet Venus.
- On each page, bottom 4 numbers are the # of days between the 2 apperances and 2
disappearances of Venus.
- Each row gives the 4 Mayan dates of the apperances and disapperances in each 584-
day Venus cycle.
- The table spans 1 complete cycle of Mayan dates for these events, so they can be
predicted for eternity.
Annual Cycle of star:
-Due to Earth;s annual orbit around the sun, our visible window of stars changes each
night, so the stars we see can tell us the time of year **Zeinath is a point above you**
-When a star returns to the same position in the sky, Earth has completed 1
orbit(exactly 365.25 days have elapsed)
3. Within the latitudes of Egypt, the heliacal rise of Sirius(the brightest star in the sky)
coincides with the Nile’s annual flood. Sirius’ helical rise was therefore used to mark
each new year.
4. Origin of the 24-hour day:
- The Egyptians tracked time at night using a set of constellations which rise at
approximately equal intervals.
- On average, 12 of these constellations rise each night, so the Egyptians divided night
& day into 12 hours each.
5. The Orgin of the Leap Year:
- The Alexandrian government of Egypt established a calender containing 12 30-day
months (360 days) with 5 “leaps” days to stay synchronized with the 365-day seasonal
- Since the solar year=365.242 days, the civic calendar gradually fell behind the
- 239 BC: Ptolemy III aded Another leap day every 4 years: 4yrs x 365.24days/yr= 4
365-day civic yrs+1day-11.5 mins
- 46 BC: On the advice of the Egyptian astronomer Sosigenes, Julius Ceaser
incorporated the 4-year leap-day into the Julian Calendar (a 365-day calendar with 12
months of 28-31 days).
- 16th C: Pope Gregory XIII fixed the 11.5-minute error by decreeing: years divisible by
100 (but not 400) are not leap years (our modern Gregorian Calendar)
Babylonian Astronomy(2000-331 BC)
1. The Babylonians tracked the celestial cycles because they believed that the sky
foretold the future. This was the origin of western astrology.
2. Each night, a record of the sky entered a tablet. The daily records, combined with a
book of interpretations, were used to predict the celestial events (and their omens) for
the next year.
3. Babylonians numbers:
- A base-60 system (consisting of symbols for 1-60 multiplied by a power of 60),
because 60 has many factors (a convenient base for division).
- they therefore used units that are multiplies of 60:
e.g 60 min=1hour , 60sec=1min, 360degrees=1 circle, 60 arcminutes=1degress, 60
4. The Zodiac:
- The babylonians divided the stars into groups (constellations) and passed on their
descriptions to the Ancient Greeks, From whom today’s constellation names originated
- The constellations on the ecliptic (the zodiac constellations; Greek for”circle of
animals”) held a special importance, as the Sun, Moon & planets move along this strip
- Your Zodiac sign is the Sun’s constellation in the month you were born. **Zeinath is a point above you**
- Due to the precession of the equinoxes, the Sun’s constellations Have changed since
the zodiac signs were assigned~2000years ago
5. The babylonians named the 5 visible planets after the gods they best described. The
ancient Greeks adopted this practice, which led to the Greek, then Latin planet
names we use today.
- Mercury: (speedy scribe/messenger god): named for its fast motion across the sky
- Venus:(goddess of love/beauty): named for its brightness
- Mars(god of war/bloodshed): named for its red color
- Jupiter(father of the gods):named for its brightness and “majestic” motion)
- Saturn(god of old age):named for its faintness and slow motion
The “Star” of Bethlehem
1. The possibilities:
- supernova: the explosive death of a massive star (can appear as a temporary star;
nova stella=Latin for “new star”).
- Nova: the re-ignition of a dead star which has yanked fresh gas(star fuel) from a
companion star(can appear as a sudden, temporary star).
- comet: a rocky snowball in orbit around the sin (can appear as a temporary star)
2. A super, nova or comet is unlikely, as no other civilization recorded a sighting around
3. The only other scientific possibility:
- a planetary conjunction: when multiple planets line up in the same region of sky (not
star-like, but a rare and predictable event with astrological importance).
- In Dec of 7 BC, a jupiter-saturn conjunction occurred in the Pisces constellation (the
ancient sign of Jews), which occurs every ~800 years.
Astronomy in Ancient Greece
1. The fragmented geography and decentralized rule of Ancient Greece allowed for an
intellectual freedom that led to a revolution in scientific thought.
2. The popularity of Plato and Aristotle led to nearly 200 years of widespread belief in
the geocentric model, even though the heliocentric model was also taught in their
3. Thales (c 624-546 BC):
- Considered the “Father of Science” for attempting to find explanations for natural
phenomena that didn't involve the gods.
- His philosophy gained support when he demonstrated that some acts of nature (e.g.
eclipse) are predictable.
4. Anaximander (C. 610-546 BC):
- Set the earth “afloat” in Air.
- Developed the 1st moving model of the Universe, in which the motion of the celestial
bodies is explained by placing them on spinning wheels around Earth.
5. Pythagoras (c. 570-495 BC): **Zeinath is a point above you**
- According to legend, when he discovered that musical pitch is determined by the
length of the instrument, he realized: the Universe is a cosmos (a harmonious system
that obeys knowable laws).
- He taught that all celestial motion is perfectly circular, and that Earth is a sphere.
6. Evidence that Earth is a Sphere:
- Ships gradually disappear on the horizon bottom-first
- Earth’s Shadow on the eclipsed moon is always round
- When you travel North or South, the constellations rise and set more rapidly than they
would if Earth was flat.
7. Philolaus (c. 470-385 BC): Set the Earth in motion; by allowing Earth to rotate once
per day around a “central fire” the daily motion of the celestial bodies was explained .
8. Herakledes (c. 375-310 BC):
- With no reports from travelers of the “central fire”, he removed it, and set earth
spinning daily around its own axis.
- He placed Mercury & Venus in orbit around the Sun to explain the Sun-centered
appearance of their motion and their brightness changes.
9. Aristarchus: (c. 310-230 BC):
- Used Earth’s shadow on the eclipsed moon to measure the moon’s size relative to
- Used the angle in the sky between the Sun & quarter Moon to measure the Sun’s
distance & size relative to the moon’s.
- His measurements weren’t accurate, but he correctly deduced: the Sun is much larger
than Earth, and Earth is larger than the moon.
- This led him to propose a heliocentric model of the Universe, with only the Moon in
orbit around Earth(owing to the Moon’s straight night-to-night path around the sky).
10. Features of apparent planetary motion (i.e. the motion of planets we see across the
- Planets display both direct(forward) motion (W to E) and retrograde (backward) motion
(E to W).
- A planet’s apparent Speed is not constant (planets appear to slow down and speed up
across the sky).
- A planet appears to brighten & dim as it moves across the sky.
11. Plato (c. 428-348 BC)
- Began an intellectual tradition in which theories of nature were accepted o faith as
opposed to proven by observations
- Taught that all celestial bodies are perfect spheres with constant circular motion
- The goal of the philosophers after plato was to explain how the planets paths in the
sky can be explained by CCM.
12. Eudoxus (c. 410-355 BC): Attempted to explain planetary motion by placing the
planets on systems of invisible nested spheres (“crystal orbs”), each spinning with
CCM around Earth.
13. Aristotle (384-322 BC):
- Unlike Plato, he taught that theories must match observation, but his neglect of
quantitative analysis led him to the wrong conclusions.
14. The Aristotelian model: **Zeinath is a point above you**
- Earth is fixed at the centre of the Universe(geocentric).
- The Universe is divided into the terrestrial realm (Earth) and the celestial realm (the
heavens), where different laws of nature apply.
- All matter in the terrestrial realm is composed of four elements: Earth, water, air and
- All bodies in the celestial realm are perfect spheres and composed of a pure and
imperishable substance, called “Quintessences” (5th element) or “ether” (pure air).
- Planetary motion follows the Eudoxan model: planets are carried around Earth by
invisible spherical orbs with CCM (the daily motion of which is driven by a single outer
- “Whatever is moved must be moved by another”: the motion of the orbs is supplied by
the motionless Prime Mover (a spiritual, godlike entity residing in the outermost orb).
15. Aristotle taught: comets must be atmospheric phenomena because they don’t
appear eternal, therefore they can’t be celestial bodies.
16. Apollonius (c. 250-220BC): Upgraded the Eudoxan planetary model to the
Epicycle model, accepted for over 1500 years.
17. The epicycle model has CCM while explaining:
-non-constant apparent speeds
18. Eratosthenes(c. 276-195BC): Estimated Earth’s circumference by measuring the
angle spanned by the shadow cast by a stick.
19. Hipparchus (c. 190-120 BC):
- Complied the 1st Comprehensive star catalogue (~1000 stars) in the western world.
- Perfected the geocentric epicycle model for the sun and moon’s motion
20. Precession of the equinoxes:
-Hipparchus discovered that the sun’s coordinates on a given date are shifting
backwards ~1/100thDegree per year.
-Precession causes all star coordinates to shift 1/100thDegree east per year. As a
result, by 2200, polaris will no longer mark the North Celestial Pole.
21. Hipparchus‘ lost star catalogue:
- In 2005, a prictorial record of a star catalouge was found on the Farnese Atlas, a 7-foot
statue in Naples, Italy
- The star coordinates on the stane are preccesed ~2100 years from today. This date
Claudius Ptolemy (c. 150 AD)
1. Author of “Mathematical Treatise”, a.k.a “The Almagest” (arabic: “The Great
Treatise”), the definitive astronomy textbook for nearly 1500 years.
2. Created the Ptolemaic model (a modified version of the geocentric epicycle model
which matched the observed motion of the planets with greater accuracy).
3. Features of the Ptolemaic model:
- the addition of the equant, which allows non-constant motion
- the connection of the planets’ motion to the sun’s position
4. Ptolemy placed the planets in order of their decreasing apparent speed, The order of
the planets was correct, but the Sun and Earth were incorrectly switched. **Zeinath is a point above you**
5. By assuming no space between adjacent orbits, Ptolemy estimated the “Universe’s”
size to be ~20,000 Earth radii (actual: 260,000). Despite the error, this proved the
enormous distance to the stars.
Astronomy in the Middle Ages (~5th-15th C AD)
1. The Dark Ages (5th-7th C): As the Church became more involved in State affairs,
knowledge of Astronomy declined due to:
- Study of the sky not emphasized in the Bible
- Rejection of Ancient Greek ideas as contrary to Scripture
- Loss of Ancient Greek texts (Latin became the official language of Scholarship)
2. 9-12th C: Islamic scholars continued from where the Ancient Greeks left off, as the
Qur’an encourages knowledge of the sky for time-keeping
3. Interactions between Islamic scholars & Greek refugees led to translations of Greek
texts into Arabic (e.g. The Almagest).
4. Islamic Scholars created star catalogues in which the stars were renamed with Arabic
descriptions. When these catalogues made their way into Europe, the Arabic star
5. Contact between Christian & Islamic Scholars in Muslim Spain led to latin translations
of the Arabic versions of the Greek texts.
6. Regiomontanus (15th C): His Latin translation of The Almagest led Christians
scholars to adopt the Aristotelian-Ptolemaic cosmology owing to its consistency with
7. Buridan (14th C):
- Theorized that thrown/projected objects have impetus (in addition to their natural
motion towards Earth)
- Therefore, if Earth moves, projected objects inherit Earth’s impetus; this explains why
an object thrown upwards will land on the thrower’s head whether earth is moving or
1. Used Tycho’s planetary data to discover our modern laws of planatery
2. Kepler believed: the spacing of the planets is defined by a series of geometric shapes
around the sun.
3. There are only five 3D shapes that can be constructed with equal faces (the”Perfect
4. Kepler proposed: the 5 perfect solids define the spacing between the 6 known
planets around the Sun.
5. Planetary distances arising from kepler’s “Perfect Solids” model are nearly consistent
with Copernican distances. This strengthened Kepler’s belief in heliocentrism.
6. As a result of the Catholic Reformation, Kepler (a protestant) moved to Prague,
where he met Tycho
7. To prove his heliocentric model, Kepler agreed to work with Tycho to gain access to
Tycho’s data. **Zeinath is a point above you**
8. In 1600, William Gilbert(English physicist) showed: the behavior of magnetic compass
needles can be explained if the Earth has a magnetic field like a bar magnet.
9. Kepler Proposed:
- Since Earth is a magnet, the other celestial bodies may also be magnets, the Sun
being the largest.
- The Sun’s invisible magnetic force may therefore drive the planets in their heliocentric
10. Kepler placed the Sun off-centre (closer to Earth’s winter solstice position) to
explain the Sun’s faster apperent speed in winter.
11. Kepler realized: If the sun drives planetary motion, then an off-centre Sun must
induce non-constant planetary speeds.
12. Since Mars’ Orbit is eccentric (non-circular), Kepler was unable to fit Mars’
coordinates to a circular orbit.
13. Having rejected the traditional notions of CCM, Kepler was led to his 1st and 2nd
Laws of planetary motion.
14. Kepler’s 1st Law:
- The orbits of planets are ellipses with the Sun at one focus.
- The more elongated the ellipse, the greater its eccentricity.
- A circle is a special case of an ellipse with zero eccentricity
15. Keplers 2nd Law: A planets speed varies as it moves around its orbit; it moves
fastest when nearest the Sun (perihelion) and slowest when furthest form the Sun
16. 1627: Kepler published the “Rudolphine Tables”, calculated from his 1st and 2nd
laws and the most accurate planetary tables to date.
17. In Kepler’s “Harmony of the World’s (1619), he showed: the spacing between the
planets corresponds to harmonious music intervals. This led to his 3rd law of
18. Kepler’s 3rd Law: The square of a planet’s orbital period is equal to the cube of
the size of it’s orbit (i.e., the more distant the planet is from the Sun,the slower its
Galileo Galilei (1564-1642)
1. He observed the sky with a telescope and widely circulated his detailed observations.
2. his discoveries contradicted Aristotelian beliefs and supported heliocentrism.
3. The Refracting Telescope:
- Invented in Holland in 1609, the first telescope used the principle of refraction (the
bending of light rays as they pass from one medium to another; e.g. from air to glass).
- In a Galilean refractor, the primary lens sends more light to the eye than eye would
receive on its own, while the eyepiece re-focuses the rays for the eye.
- In a Keplerin refractor, the eyepiece is convex, which sends (inverted) light from a
larger region of sky to the eye.
- Most modern refractors are Keplerian (produce larger and brighter images)
4. In Galileo’s early work, he revealed fallacies in Aristotle’s theories about motion; e.g.,
he proved: all objects, regardless of mass, fall at the same rate. **Zeinath is a point above you**
5. Prior to the telescope, Galileo admitted his heliocentrism in letters to Kepler, but he
would not support it publicly.
6. in 1600, Giordano Bruno, a Copernican, was burned at the sake for heresy, sending a
strong message about the ruthlessness of the Roman Catholic Church in Defending
7. Galileo’s observations:
- His sketches of the moon’s surface revealed that celestial bodies are not perfect
- He saw that the Milky Way is not atmospheric 9as Aristotle taught), but the combined
light from millions of stars.
- He saw that planets have a disk-like appearance, while the stars remained point-like.
This showed: stars may be much more distant than planets, as suggested by the lack
of detectable stellar parallax
- He discovered Jupiter’s four brightest moons. This showed: If Jupiter can move with its
moons, so can earth
- he saw that Venus exhibits size and phase changes (all phases except full). This is
only possible if venus orbits the Sun (as in the Copernican & Tychonic models).
(This made the Ptolematic model obsolete, since gibbouses aren’t possible if Venus
never reaches the Sun’s opposite side).
- he couldn’t distingush phases in the outer planets, since only full and gibbous phases
are possible (outer planets are never between Earth and Sun).
- he saw appendages on either side of Saturn. He could not resolve them into rings, but
he still showed: not all celestial bodies are perfect spheres.
(A decade later, it was realized: the periodic disappearance of Saturn’s rings is due to
our changing view of their tilt.)
- His observation of the Sun suggested that sunspots are blemishes on the Sun’s
rotating surface (more evidence of imperfections in celestial bodies).
8. Galileo’s vocal support of Copernicanism invoked opposition from the Catholic
Church, which held to the geocentric statements in Scripture
9. Galileo retaliated by publishing a letter which argued that Bible stories are parables
and not meant to teach astronomy
10. This led to the banning of Copernicus’ book and Galileo’s papal ban (in 1616)
not to “hold or defend” heliocentrism.
11. when his friend became Pope, Galileo published “Dialogue on the Two Great
World Systems” (1632), a fictional debate between an Aristotelian, a Copernican, and
12. The Aristotelian (“Simpilico”) was portrayed as a fool who spoke the Pope’s
words, while the Copernican was wise and witty.
13. The book included Galileo’s (incorrect) argument that Earth’s ocean tides are
proof of Earth’s motion, a theory that the Pope had previously rejected.
14. The Inquisition sentenced Galileo to house arrest for life and to publicly recant
heliocentrism as heresy. His books were banned.
15. Despite this, his telescope observations were widely circulated, and helicentrism
gradually **Zeinath is a point above you**
Astronomy in 17th and 18th Century England
1. The Power of the Roman Catholic Church over scientific discovery did not extend to
England, where the church of England encoraged scientific innovation.
Rene Descrates (1596-1650)
1. His theories were taught in the 17th C universities in place of Aristotle’s .
2. He taught:
a) Empty space does not exist. Therefore, the space betwen celestial bodies is filled
with an invincible fluid (ether)
b) The spinning celestial bodies have turned the fluid into a system of whirling vortices
which carry the bodies in their orbits (eg, the planets whirl eternally around the Sun’s
1. As curator of Experiments for the Royal Society, e tested theories in many branches
2. He argued, contrary to Descartes, that planetary motion is due to an invisible
attractive force that acts across empty space (“gravitational attraction”).
3. Hooke’s supposition’s on gravity:
- Gravitational attraction is universal; it’s the cause of motion both on Earth and in
space. Eg. Earths gravity not only holds earth together and causes free-fall, but also
holds the Moon in orbit.
- Gravitational attraction increases with proximity to its source. Eg. the closer a body is
to Earth, the stronger Earth pull on it.
1.A polymath and introvert who, at 25 invented Calculus (the math that describes how
quantities change, and the only way to precisely describe motion)
2. Prior to Newton, it was believed: when sunlight passes through glass, the sunlight is
permanently changed into correct colors
3. Using 2 glass prisms, Newton proved: sunlight is composed of the colors of the
4. Dispersion: the splitting of light into its component colors when it passes through a
medium, due to the different refraction angles of each color.
5. Chromatic aberration: the failure of a lens to focus all colors in a light ray at the same
6. ~1670: Newton entered the scientific stage after his development of the reflecting
telescope, which eliminates the chromatic aberration of glass lenses.
7. Today, all large telescopes are reflectors,due to the difficulty in constructing a large
8. The debate of the royal society: does gravity waken with distance ( an “inverse law”)
or the square of distance (an “inverse-square law”)? **Zeinath is a point above you**
1. An independently-wealthy scientist who joined the Royal Society after charting the
2. In 1684, Halley and the Royal Society offered a prize to anone who could prove that
gravity is defined by the universe-square law.
3. To prove this, the inverse-square law must lead to Kepler’s Law’s of planetary
4. A few years earlier, Hooke had revealed his theory of gravity to Newton and
requested his help with the mathematical proof. Newton completed the proof in
5. When no one claimed the Royal Society’s prize, halley took the challenge to