This
introduction
to
coordinates
on
a
sphere
explains
how
latitude
and
longitude
define
locations
on
Earth,
and
similarly,
how
declination
and
right
ascension
define
locations
on
the
celestial
sphere.
The
lesson
also
introduces
systems
of
timekeeping,
e.g.
local
solar
time,
time
zones,
universal
time
and
the
International
Date
Line.
The
objectives
are
for
the
student
to
know
how
any
location
on
Earth
...



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This
lesson
covers
basic
methods
for
finding
one's
position
on
Earth.
Latitude
can
be
deduced
from
the
height
above
the
horizon
of
the
pole
star
or
of
the
noontime
Sun,
while
longitude
requires
an
accurate
clock
giving
universal
time.
The
student
will
understand
how
finding
one's
local
longitude
requires
comparing
local
time
with
universal
time
(UT),
which
may
be
obtained
from
an
accurate
clock,
possibly
...



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This
introduction
to
the
labeling
of
points
on
a
plane
by
their
Cartesian
coordinates
can
optionally
be
extended
to
coordinates
in
3dimensional
space,
to
plane
polar
coordinates
and
to
3dimensional
polar
coordinates.
Students
should
learn
to
use
Cartesian
coordinates
(x,y)
for
defining
the
position
of
a
point
in
two
dimensions
and
to
use
Cartesian
coordinates
(x,y,z)
in
3dimensional
space
and
learn
...



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This
lesson
provides
an
overview
of
solar
and
lunar
calendars,
their
history
and
lore
and
also,
of
the
day
and
the
month,
and
their
relations
to
the
rotation
period
of
the
Earth
and
the
orbital
period
of
the
Moon.
Students
learn
the
differences
between
a
solar
day,
sidereal
day
and
mean
solar
day,
and
what
each
is
used
for
as
well
as
the
differences
between
the
solar
year
and
the
Julian
and
Gregorian
...



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This
lesson
includes
a
historical
review,
starting
with
the
existence
of
the
horizon
at
sea,
proceeding
to
various
studies
of
the
Earth's
size
and
shape,
and
leading
to
the
attempt
by
Columbus
to
reach
India
by
sailing
westward.
Students
will
understand
the
concept
of
the
horizon
at
sea
as
evidence
that
the
Earth
is
round,
calculate
the
size
of
the
Earth
using
Eratosthenes'
methods,
and
the
origin
...



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This
lesson
introduces
"pretrigonometry,"
the
estimate
of
the
distance
to
a
faraway
point.
Students
will
use
"pretrigonometry"
to
calcuate
distance
and
will
use
the
"thumb
method"
of
estimating
distances
in
the
field
and
understand
the
reason
it
works.
Finally,
they
will
understand
how
astronomers
used
the
diameter
of
the
Earth's
orbit
around
the
Sun
as
a
baseline
for
estimating
the
distance
of
...



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This
lesson
describes
the
calculation
by
which
Aristarchus
used
the
duration
of
a
total
lunar
eclipse
to
deduce
the
distance
of
the
Moon.
Students
will
learn
about
eclipses
of
the
Moon
and
a
simple
application
of
pretrigonometry
as
they
discover
how
Aristarchus,
a
Greek
astronomer
of
230
BC,
used
a
simple
observation
of
the
eclipse
of
the
Moon,
plus
clever
reasoning,
to
deduce
the
distance
of
the
...



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This
lesson
traces
the
beginning
of
the
heliocentric
theory
of
the
solar
system,
the
idea
that
the
solar
system
revolves
around
the
Sun,
to
an
observation
by
Greek
astronomer
Aristarchus,
which
convinced
him
that
the
Sun
was
much
bigger
than
the
Earth.
Students
will
learn
how
Aristarchus
used
the
position
of
the
halffull
Moon
to
estimate
the
distance
to
the
Sun,
and
the
results
he
obtained
by
employing
...



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In
this
lesson
the
ellipse
is
studied
in
polar
coordinates
(r,f),
with
the
function
cos(f).
This
places
the
origin
point
at
a
focus
(more
appropriate
for
planetary
motion)
and
introduces
the
eccentricity
e.
It
is
also
noted
that
planets
actually
orbit
the
center
of
gravity
of
the
solar
system
and
that
distant
planets
may
be
detected
by
motions
of
their
central
star
around
the
centers
of
gravity
of
...



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This
activity
has
students
use
simple
sine
waves
to
explore
constructive
and
destructive
interference
in
seismic
waves.
After
plotting
the
summative
points
of
two
sine
waves,
students
connect
the
points
to
create
the
resulting
complex
wave.
Once
they
have
successfully
drawn
their
complex
wave,
they
will
answer
the
questions
listed
on
the
student
handout.
Provided
are:
a
list
of
materials,
procedure,
...



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