APOLLO 17
MISSION
COMMENTARY
12/7/72
05:00 GET, SC
[Cernan?] Bob,
I know we're
not the first to
discover this,
but we'd like
to confirm
from the crew
of America
that the world
is round.
Apollo Moon mission flight path
composite
from the
VIIRS on
satellite
Suomi
NPP, Jan.
4, 2012
ANCIENT EGYPTIAN COSMOLOGY
Nut
Ra
Shu
air god
Geb
Ground is a flat disk that floats on Nun, the primordial ocean.
The Well of Eratosthenes
gnomon
As Hipparchus c. 190 – c. 120 BC first divided the circle
into 360 degrees, Eratosthenes could not give, nor for his
geometrical purposes need he have given, an angular
measure in degrees for the inclination of the sun at noon
mid-summer at Alexandria. We can:
tan AP^PB = AP/PB = 1/8,
so AP^PB = arctan 0.125 = 7.1250 degrees.
Inclination of the sun = 90 – 7.1250 = 82.875 degrees
= 82o 52' 30"
The common Attic stadion was about
185 m, which would imply a
circumference of 46,620 km, i.e. 16.3%
too large. However, if we assume that
Eratosthenes used the "Egyptian
stadion" of about 157.5 m, his
measurement turns out to be 39,690
km, an error of less than 1%!
Simplified map after Eratosthenes c. 220 BC of the
Oikoumene with an east-west length of 77,800 stadia and
a south-north breadth of 33,000 stadia
Eratosthenes‘ great discovery was that regardless of their location,
east or west, south or north, at all places where the ratio of shadowlength to gnomon-height was recorded for noon mid-summer and
noon mid-winter, the apex AP^PB of a constructed winter triangle was
exactly (as nearly could be measured) greater than that of a summer
triangle by what today we would call 47 degrees. This would not be
true if Earth is flat and the elevation of the sun is just 40,000 stadia
above Earth’s surface.
The difference between the apexes AP^PB of a constructed noon midwinter triangle and that of a noon mid-summer triangle would become
progressively greater the further north a place is. As this is not
observed, the hypothesis of a flat Earth is falsified.
gnomon
To find the direction of True North
1) you need to prepare a level place where the shadow of the stick's top
(gnomon) falls.
2) this level place must be extensive enough so that the shadow-end
will be within it for several hours before and after midday.
3) mark the end of the shadow where it first lies. Put a stone or scratch
a mark there. This is P1 in the Figure 6.1a
4) make a loop at one end of a piece of rope and drop the loop over the
vertical stick (gnomon) and stretch the rope taunt through P1.
5) with the rope stretched taunt and with a scribe (piece of chalk) held
to the rope draw a circle from P1 around the gnomon
6) Use the rope and scribe to construct the direction of true north.
7) Local noon is the moment when the shadow cast by the gnomon lies
along the north-south line that you have constructed. This is so for every
day of the year,
The change in the
position of the sun
at the same clock
time each day
occurs because:
1) Earth’s rotationaxis is tilted,
and
2) Earth’s orbit is
elliptical (Earth
moves faster at
its Perihelion
and slowest at
its Apehlion).
The tilt of Earth’s
axis is 23.5°
The eccentricity of Earth’s
orbit is 0.016
Analemma plotted as
seen at noon GMT (clock
time) from the Royal
Observatory, Greenwich,
England (lat. 51.48° N,
long. 0.0015° W).
Equation of Time is the difference between clock time
adjusted for longitude in a time zone and local solar time .
Initially nautical almanacs provided the data required for
the method of lunar distances, a technically demanding
and mathematically complex method of determining
longitude before the invention of accurate clocks for
shipboard use.
The common availability of precise chronometers on ships
beginning in the early 1800s, and the development of
methods of "sight reduction" by Sumner, St.-Hilaire and
others, provided an easier procedure for navigators to
determine their position at sea. The almanacs provided the
necessary data for these methods.
1980s UTC replaces GMT in Nautical and Air Almanacs
In 1879, the USGS began to map the Nation's topography.
The most current maps are available from The National Map
data base. The production and release of these US Topo
maps (UTM [Universal Transverse Mercator] projection and
including geographic coordinates) started in October 2009.
The first 3-year production cycle for the conterminous 48
states was completed in September 2012, and the second in
September 2015, and are currently in the third cycle. Hawaii,
Puerto Rico, and US Virgin Islands also have US Topo
coverage. Alaska has been started, and should be complete
by 2018.
Geosat for
three years
followed a 17
day exactly
repeating orbit
allowing
cyclical and
transient
variations of
sea height to be
averaged out to
a accuracy of 5
cm. (NASA)
GRACE twin satellites. (NASA)
The geoid undulations are primarily of long wavelength.
Short wavelength changes in the geoid undulation (gravity
anomaly variations in the wavelength band 15 to 200 km)
correlate well with seafloor topography and image
seamounts, trenches, ridges, and fault scarps in the oceans.