How can inhabitants of the far side of moon guess that the moon is revolving around the earth?
You ask an interesting question. To answer it I think is is necessary to assume some answers to some questions. Here are a few examples.
1. Are these inhabitants humans? If not what are they?
2. Assuming they are humans, how do they live on the moon? What kind of structure protects them from the near vacuum? What do they eat and drink?
3. What do they know about the moon? Do they know it's size, it's shape.
4. What kind of technology do they have? Do they have good telescopes? Have they made calculations about the motions of the planets they can see relative to the pattern of fixed starts?
5. What do they know about gravity? What do they know about the influence of gravity on orbits of massive bodies?
Given they have adequate physical knowledge, astronomical skills, and technology, here are a few things they should be able to figure out.
1. The Moon on which they live rotates about some axis connected to a point in the sky about which the "fixed" stars visibly rotate with a not-entirely uniform but close to uniform period of time.
2. The Moon is revolving about a planet (which we know to be called the Earth) which is revolving about the Sun.
3. The period of these two revolutions.
I am less sure about their ability to figure out with any accuracy the mass of the Earth and Moon, and their distance from the Sun, and the distance between the Moon and the Earth.
I hope this is helpful.
The moon still rotates once per day, but, a day on the moon lasts about 28 earth days. The sun still rises on the dark side of the moon, its just that the earth never rises very high on that side.
Buzz's reply is full of irrelevancies. Chronos is right - the moon obviously rotates, and the earth does not move very far in the sky. Those two facts are enough to conclude that the moon revolves around the earth.
I think we are not interpreting the OP the same way.
The reason I ask all those question is to help me figure out what AJ is really asking. My guess is that AJ is thinking about people living on the far side of the moon that never sees the Earth, and who have no direct knowledge about the Earth and its people. He is asking if such people could figure out that the moon is in orbit about a planet, and also figure out properties of such a planet. I get that you think the OP is asking something completely different, and I have no idea what that is.
Perhaps the OP will clarify his question.
But the earth is visible on almost 20% of the far side.
My interpretation of the the OP's intention is that the people live in an area of the Moon well inside the region which never sees the Earth.
Irrelevant, they still see they rotate wrt the sun and see other planets in the solar system doing the same thing. If they have any semblance of intelligence they surely realize another massive body must be nearby.
But they still don't know what they are rotating around. and as buzz did ... that is the way I also interpret the OP question
I do not disagree, save that their science must be pretty primitive to prevent them from realizing the existence of a nearby massive body.
What i mean is -: if there were humans living on far side of moon and unable to see earth, then can they make out that they are revolving around earth by making observations from their location? This is obviously a hypothetical situation. So, the question such as "how can humans survive on moon?" may be kept aside. Also, the purpose of question is to encourage discussion on how to draw inferences from limited scope of observation. So, any response based on modified assumptions is also welcome.
I'd measure 'daily' parallax of visible planets.
Providing the distances to those planets are known with some accuracy (found out e.g. by using yearly parallax measurements), it will also net the observers an estimate of the mass of the planet they're orbiting.
But you have to suspect that such a daily parallax existed first, and how likely is that? The distance the Sun-Moon system moves in one Lunar day far exceeds the width of the Moon's orbit, So the "daily" parallax caused by the Moon's orbit around the Sun is going to much much smaller than the parallax caused by the Sun-Moon orbit around the Sun in the time same period. Also, to measure the daily parallax, you would have to look at the planet when it was near the horizon in one direction, and compare it to its relative position to the stars when it was near the other horizon. Then your measurements would have to accurate enough to note the difference between this parallax and the one you get when the planet is at the zenith on consecutive days.
The two times of the year when the yearly parallax would not be a problem is when the orbital velocity of the Earth-Moon system is pointing directly at or away from the planet. But now you are having to take one of your measurements with the Sun in the sky. And while on the Moon, you aren't going to get blue sky to deal with, you still have to look near the horizon and would have glare from the surface to deal with.
The above problems are not insurmountable for someone dedicated to making them, its just that they are not the types of observations that would likely to be made if you weren't already looking for it.
I may be mistaken about this, but I have a vague memory of reading that it took astronomers a rather long time after knowing the relative distances (in terms of the AU with an unknown value) between the various objects (sun, planets, moons) to get a reasonably accurate distance scale for these measurements.
Early laboratory calculations of the speed of light helped the scale estimates by noticing the time it rook for Jupiter's moons to transit Jupiter. As I recollect, radar echos from the moon nailed it down.
I found some history:
The last major effort using these techniques was in the 1930's. Parallax observations of an asteroid, called Eros, passing close to Earth were used to fix the value of the astronomical unit at 150 million kilometers. [My note: The error of this value is about 0.4%]
With the invention of radar, the distance to Venus could be determined very precisely.In order achieve accuracy when using parallax you need a wide base. The diameter of Earth was the original best base. On the moon, the short term base using two points available to the Moon's residents on the Moon's surface would be much smaller, but using half a rotation period, the base would be the diameter of the moon's orbit. However, I am not sure how the Moon people would have determined a value for that, since they could not use the parallax of the Earth's motion.
You're right. This is assuming the observers do know what is the radius of their orbit around the Sun, so that they can use yearly parallax at all.
I took the question to mean that we are actively trying to find if there's a planet we're orbiting, so we'd set out to surmount just those kind of obstacles. I.e., make a working hypothesis that there isn't one, and try to disprove it by checking whether all parallactic measurements are consistent with no additional orbital motion.
One way they might encounter the Earth accidentally is in the tidal effects of the Earth's gravity. Earth's gravity would vary by about 1 part in 200, and it would be down from 9.8 m/s^2 by a factor of about 1 part in 3000 or so, so the variation would be about 1 part in 10,000 of the Moon's gravity. That could perhaps be observed, though I doubt it's very easy. But it would be something they might encounter accidentally once they start doing very sensitive experiments on motion.
They could monitor the apparent size of the Sun. Here's a YouTube I made showing how the size of the Sun changes over the course of a year on both the Earth and Moon. Fixed on the far side of the Moon, the Sun would be set while the Moon was farthest, but there's still enough variation in size while the Sun is visible that they should be able to notice.
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