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3

That argument seems correct. A calculation by timeanddate.com would suggest that the day is about 9 seconds longer in Kazan than in Moscow on the 23rd of September, consistent with your prediction

6

Note that the Sun here is point-like and there is no refraction. What have I done wrong? Your supposition that the altitude of the Sun is directly related to the length of the day is wrong. Proof with counterexample: observe the altitude of the Sun on the equator and in the Moscow on the equinox; but still, the lengths are the same. And what is the correct ...

2

For a very restricted set of conditions, yes. If $v_{c,1}$ is the First Cosmic Velocity, also known as the Circular Orbit Velocity, then what you have written is the definition of the angular velocity of an object in a circular orbit of altitude $h$ over Earth. In general, no. For objects in elliptical orbits, there will only be two points on their orbits ...

1

Kepler's laws and the associated orbit only hold for a two-body problem, so the 'barycenter' in the question can only be understood as the center of mass of the sun and a particular planet (ignoring the other ones), not as the solar system barycenter. And in this sense the convention is to take the sun at the focus, which means the semi-major axis is the (...

5

Yes, "future perihelic oppositions will bring Earth and Mars even closer." No, in the long term (after about 25000 years), Mars's eccentricity will start to decrease, and then perihelic opposition will not be as close. By frankuitaalst from the Gravity Simulator message board. - Data generated with Gravity Simulator written by Tony Dunn.Source JPG ...

2

I agree with your thinking as far as it goes; it is probably not possible to learn about chaos theory nor celestial mechanics by observing these moons, because: We (believe we) know the underlying laws and mathematics that govern motion (in general at least) We won't be able to study such objects long enough and careful enough to make any tests that haven't ...

8

In the most general case, there are three (spatial) degrees of freedom for each body, for a total of 9 degrees of freedom. The circular restricted three-body problem forces the two larger masses to be in perfectly circular orbits defined by their masses and the chosen orbital radii (with the third body having negligible mass and thus no influence on their ...

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