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Old 2021-10-30, 22:54   #1
rudy235
 
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Default Thought experiment: Lunarians

Suppose that there exists a civilization on the far side of the Moon. It is a huge empire of roughly 8 million square kilometers (more or less the size of Australia)

This empire is centered at the selenographic coordinates 0º Latitude and 180º longitude.

For reasons that are not going to be discussed they are unable to travel more than 500 kilometers away from the center of the empire –0º Latitude 180º longitude–. Than means they can go about 15º North,South, East and West from their base.

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They are quite savvy in the mathematical sciences and they have standards of measuring length with very good precision.
They can measure time and mass and angles , also with very good precision.

Their astronomical abilities are comparable to the Mayans, the Sumerians and the Babylonians (and even a bit better) They have not discovered the telescope yet but they have incredibly good sight. They can see at 160 meters what a normal human can see at 20 .
The question is.

CAN THEY KNOW OF THE EXISTENCE OF THE EARTH?

If so How?

Last fiddled with by Dr Sardonicus on 2021-10-31 at 14:11 Reason: w
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Old 2021-10-31, 02:09   #2
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Change in the angular diameter (0.0014023°) of the Sun between Solar Noon and Sunrise/Sunset which would be about 7 days apart should give it away. If they could detect it.

Google says:

Quote:
what is the diameter of the Sun
1.3927 million km


what is the distance of Earth from the Sun
148.53 million km

what is the center-to-center distance of Earth from the Moon
The average distance from the center of Earth to the center of the moon is 238,897 miles (384467 kilometers).


what is the diameter of the Moon
3474.8 km

....

A marine sextant can measure angles with a precision of less than 0.5' better than 1/100th of a degree.
ETA That's assuming they know the diameter of the Moon. Aristotle Calculated the diameter of the Earth with 98% accuracy using shadows of sticks.
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Old 2021-10-31, 03:16   #3
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FTR the above model assumes that the moon rotates around the center of the earth for simplicity. In reality the Earth/Moon system rotate around their barycenter which is about 4671 km on average off earth’s center.

ETA One interesting realization of this thought experiment is that although moon is an actor of both Solar and Lunar Eclipses, there is no eclipses visible from/on the far side of the moon.

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Old 2021-10-31, 03:40   #4
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Quote:
Originally Posted by a1call View Post
Change in the angular diameter (0.0014023°) of the Sun between Solar Noon and Sunrise/Sunset which would be about 7 days apart should give it away. If they could detect it.

Google says:



ETA That's assuming they know the diameter of the Moon. Aristotle Calculated the diameter of the Earth with 98% accuracy using shadows of sticks.
Thanks for your reply.
You are referencing to the "wobble of the Earth" every 27.33 days. However, it took The genius of Newton and Pierre Laplace in the 17th and 18th Centuries to estimate its effect.

I have the feeling that Babylonian Astronomy (700 BCE) –great as it was– was not up to par with Newton or Laplace. (Even Aristoteles was a full 1000 years after Babylon). in Newton and Laplace times, (17th and 18th Centuries) telescopes were already present, and I have the feeling that although the elements are there there was not enough "cultural environment" as to discern.
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Old 2021-10-31, 03:48   #5
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So the trick is the recognise that the lunar orbit around the Sun is a wobbly* ellipse, and not a simple ellipse.

The main reference point is the Sun, as already mentioned so if there is a method to measure the distance to the Sun then you are done.

Otherwise closely observing the movements of Venus/Mercury/Mars would also provide some clues that the local orbit is not so simple.

* A technical term.
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Old 2021-10-31, 08:56   #6
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Quote:
Originally Posted by rudy235 View Post
Suppose that there exists a civilization on the far side of the Moon. It is a huge empire of roughly 8 million square kilometers (more or less the size of Australia)

This empire is centered around the selenographic coordinates 0º Latitude and 180º longitude.

For reasons that are not going to be discussed they are unable to travel more than 500 kilometers away from the center of the empire –0º Latitude 180º longitude–. Than means they can go about 15º North,South, East and West from their base.

Attachment 26039



They are quite savvy in the mathematical sciences and they have standards of measuring length with very good precision.
They can measure time and mass and angles , also with very good precision.

Their astronomical abilities are comparable to the Mayans, the Sumerians and the Babylonians (and even a bit better) They have not discovered the telescope yet but they have incredibly good sight. They can see at 160 meters what a normal human can see at 20 .
The question is.

CAN THEY KNOW OF THE EXISTENCE OF THE EARTH?

If so How?
Tides provide another possibility. The moon's orbit is elliptical with respect to the Earth and so the Earth raises tides in the body of the moon.

You didn't say that they hadn't invented the seismograph.

Another possibility is if a comet or NEO passes near enough to be both visible and perturbed by the Earth-Moon system. They should be able to see the Galilean satellites and perhaps Titan, which would give them a leg up to develop Newtonian gravitation.

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Old 2021-10-31, 09:24   #7
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These babylonian selenite have a 8 x zoom vison?
Look at Jupiter! Look at the gallilean moon!

if they can distinguish its rotation then they will certainly reach some conclusion.
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Old 2021-10-31, 10:17   #8
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Quote:
Originally Posted by firejuggler View Post
These babylonian selenite have a 8 x zoom vison?
Look at Jupiter! Look at the gallilean moon!

if they can distinguish its rotation then they will certainly reach some conclusion.
The Galilean moons are visible to some human naked eyes; the diameter of Jupiter varies between 30" and 45". Naked eye astrometers, such as Tycho Brahe, reached an accuracy of close to 60" in their star catalogues so we can reasonably assume the Selenites could manage 8" --- they can resolve the disk of Jupiter. Unfortunately the Great Red Spot is only around 4" across so they would not be able to use it to measure Jupiter's rotation period.

As noted above, they could have come up with a heliocentric cosmology and Newtonian universal gravitation theory, especially if they had observed multiple double stars and, in particular, the alpha Centauri AB relative motion in their 80-year orbit which varies between 2" and 22".

A human naked-eye limiting magnitude is around mag. 8 to 8.5. Very few people get much below 6.5 on the earth because the sky is so bright, something Selenites would not have to contend with. Titan is mag 8.4 and reaches 200" separation from Saturn, which is why I suggested that it may be visible to a keen sighted individual on the moon, equivalent to terrestrial observations of Galilean satellites. Anyway the original premise was 8-fold better vision. If that is in both resolution and light grasp, there is another 2-4 magnitudes for a start.

Further support for the heliocentric cosmology comes from the phases of Venus. Keen sighted humans can see the non-circular shape of that planet (SWMBO is one, I am not) but can't resolve the crescent. With 8-times better resolution it would be apparent.
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Old 2021-10-31, 11:15   #9
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With the stated travel restrictions, the lunatics might assume that the moon is flat and all these funny wobbles are just astrology and numerology.
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Old 2021-10-31, 13:10   #10
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Quote:
Originally Posted by Dobri View Post
With the stated travel restrictions, the lunatics might assume that the moon is flat and all these funny wobbles are just astrology and numerology.
Nope.

The distance between Syene and Alexandria is only 7.2 degrees. The lunar inhabitants are allowed to move 30 degrees; easily enough for them to measure the size and shape of the Moon.
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Old 2021-10-31, 13:39   #11
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Quote:
Originally Posted by xilman View Post
Very few people get much below 6.5 on the earth because the sky is so bright, something Selenites would not have to contend with.
You didn't mention seeing issues under the atmosphere of earth. Even keen eyed individuals can be limited by by local seeing.
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