66

There are, I think, at least four parts to this argument: the first being the theoretical argument that ties it all together and the remainder being observational evidence for the Moon's orbit increasing in size. 1. The underlying theoretical argument. This, of course, is the idea that tidal braking causes the Earth to slow down in its rotation and the Moon ...


52

From the PyEphem Quick Reference Guide: Rising and setting are sensitive to atmospheric refraction at the horizon, and therefore to the observer’s temp and pressure; set the pressure to zero to turn off refraction. It seems likely that, if you're using the default settings, the result returned is including atmospheric refraction, giving the results you ...


26

@BMF's comment links to (Gold & Soter 1969) Icarus 11, (3), November 1969, pp 356-366 Atmospheric tides and the resonant rotation of Venus. Since it is paywalled I'll add a short summary: From the abstract: The observed spin-orbit resonance of Venus, whereby the same side of Venus faces the Earth at each inferior conjunction, cannot be explained ...


22

Correct me if I am wrong, but if we count sunsets by the center of the Sun apparently crossing the horizon then the Sun is supposed to set every day at latitudes under the arctic circle. That is not how PyEphem defines sunrise and sunset. It defines sunrise as the time the top of the Sun would nominally first appear above an unobscured horizon (no mountains)...


13

This is a fun little problem that's remarkably close and the math is pretty easy when you use the right periods. Venus' synodic period, relative to Earth, is 583.92 days on average. He uses 584, but lets strive for accuracy. Venus' solar day is 116.75 days, so 5 solar days is 583.75 days - Venus does 5 rotations in nearly the same amount of time that ...


9

Wikipedia's article on the Arctic Circle provides the explanation. Firstly, it says: because the sun appears as a disk and not a point, part of the midnight sun may be seen on the night of the northern summer solstice up to about 50 minutes (′) (90 km (56 mi)) south of the Arctic Circle. As the Arctic Circle is currently at roughly 66°34′N, this means a ...


8

The orbit of an astronomical body around another astronomical body is an ellipse, with the primary in one of the two focal points of the ellipse. Thus the orbiting body gets closer to the primary until it reaches its closest point, and then gets farther away from the primary until it reaches its farthest point, and then gets closer again. When an ...


8

The motion of the Sun in the direction perpendicular to the Galactic plane is perfectly well understood. The mass of the stellar component, which dominates over dark matter at the solar galactocentric radius, is strongly concentrated towards the plane - that's why it is called the Galactic plane. Very roughly, you can characterise the density as $\rho_0 \exp(...


7

This is directly related to another question: Why are asteroids with zero orbital inclination rare? If captured, irregular moons are randomly oriented in space then there is very little chance of them having either inclination angles near zero or near $180^\circ$. This is because, if they are uniformly distributed in space, the fraction of orbits within a ...


6

According to Wikipedia, the orbital relationship between Venus and the Earth is coincidental and not because they are locked in a true orbital resonance, but it may be due to a true resonance in the past, or the system may be evolving toward a resonance in the future. A number of near-integer-ratio relationships between the orbital frequencies of the ...


6

The solar system is chaotic, but it is also stable! The fixed and linkages between the bars of a double pendulum allow for very rapid energy transfer between the arms. This makes the chaotic motion develop rapidly. The interactions between planets are gravitational and much much weaker, moreover, the planets are heavier and it takes a lot more energy to ...


6

Nobody says that nothing exists "above" or "below" the galactic plane. The stars are thickest at the galactic plane and get scattered thinner and thinner with increasing distance from the galactic plane. It is often said that the disc of the galaxy is only 1,000 light years thick, but that is a round figure. The galactic halo is a ...


5

For those who don't have ready access to a copy of Astronomical Algorithms, Meeus's first approximation looks like: $$ \text{JDE} = 2541547.51 + 365.259636 ~k + 1.6 \times 10^{-8} ~k^2 $$ where k, the number of anomalistic years since the January 2000 perihelion, is half of some integer. This neglects the influence of the Moon and other planets, so he adds a ...


4

There's two parts to this question, the first part is relatively easy. The 2nd part, more tricky. How are shepherd moons such as Pan and Daphnis able to exist without being disintegrated by Saturn's tidal forces despite literally orbiting within the rings themselves? I'm going to focus on Pan because it's larger and closer. It's unusual, ravioli ...


4

why doesn't Earth's leading tidal bulge (encircled in the green circle 1) pull on the moon's tidal bulge It does.... leading to a force, and consequently a torque There's nothing here that will give an ongoing torque. Because of the Earth's high rotational speed and lag in response to forces, the earth's bulge stays displaced from the direction of net ...


4

Short Answer: The gravitation of Jupiter and all the other planets makes Kepler’s third law a bit less accurate than it would be if their gravity were zero. The gravitational interaction between the planets, however, doesn’t have much effect on either the period or semi-major axis of any of the planets, especially in the short term. Long Answer: You might ...


4

Do you need 1000 years? 50 years? 1-hour accuracy? 1-second accuracy? A simple linear interpolation for the perihelia from the year 2000 to 2050 gives a maximum error of about 1.3 days for the year 2009 and a mean absolute error of about 19.3 hours: et = 31558511.31638778 * year - 63116806104.00429 et is the so called ephemeris time (used by NAIF team in the ...


4

I post another answer because I think it should work better for you. Since I read in one your comment that you “only need a few years past and (mostly) future from 2021” and that you need “at least one-hour accuracy”, here’s my proposed method. I still don't know how many years you really need, but the following table shows the perihelia and aphelia with a 1-...


4

What Kepler (and others before and after him) wanted to do is predict where a planet would be. To do this we need some set up: First we want a coordinate system. This is a system of axes: x, y and z, at right angles to each other. And it should be an inertial coordinate system, so Newton's laws work. This means that the axes should not be rotating. And we ...


3

As Rob Jeffries says, no moons are in retrograde equatorial orbit in our solar system. One reason why prograde equatorial orbits are more likely than retrograde equatorial orbits has to do with tidal locking. Our Moon, for example, is tidal locked with the Earth. The Earth is actually also spinning down to tidal lock with the Moon. However, most ...


3

Is there a problem here though? For any given month won't the full Moon oscillate between low and high above the horizon at midnight on an 18.6 year cycle? No. The full moon is always opposite to the sun (within 5.2 degrees, the angle between the moon's orbit and the ecliptic). So, when in summer the sun is high in the sky, the full moon will be low, ...


3

The transit of a star when it reaches its highest point is called the upper culmination and when it reaches its lowest point is called the lower culmination. I think both are referred to as meridian transits.


3

The first question (how are the tables generated?) is easy to answer. The acknowledgement on the Astropixels page says: It is based on procedures described in Astronomical Algorithms by Jean Meeus (Willmann-Bell, Inc., Richmond, 1998). For the second question (how accurate are the calculations?), there are 3 sources of error that I can think of: The ...


3

Maps of the sky are being used to actually get to know the sky. Thus you take the map and hold it above your head (as opposed to a map of the Earth's surface where you look down on Earth). Thus East and West are switched between that two types of maps, so that directions match actual directions when viewing the map.


3

Although the Earth's rotation is slowing due to tidal interactions with the Moon, the timescale for the Earth to reach synchronous rotation with the Moon's orbit is quite long, even by astronomical standards, and certainly won't happen during the red giant phase. The current change in Earth's rotation is 1.7 ms/century over the past 100 years, and 2.3 ms/...


3

A lunar occultation of Venus happens when light from Venus can not reach the observer because the Moon blocks it. The simplest model for this would be to draw a line in 3D from Venus to the observer and detect when that line passes through some part of the Moon. However that doesn't take into account the time it takes for the light to travel from Venus to ...


3

It does. But it also transfers momentum to the moon which raises the orbit. The two effects mirror each other. One tends to slow the moon's rotational speed, the other tends to raise the orbit of the moon. The consequence is that the month gets slightly longer, but the same face of the moon continues to point towards Earth.


3

To describe the position of an orbiting body you need 6 numbers. There are different ways to do this: You can give the position $(x,y,z)$ and velocity $(\dot x, \dot y, \dot z)$. At a given time $t_0$, and then use Newtons laws to work out the position of the planet at any time in the future. You can give the orbital parameters: Eccentricity (the shape of ...


3

There is no easy formula for what you want. Astronomical Algorithms provides an algorithm for the times of perihelion and aphelion passages of the Earth-Moon barycenter. The times at which the Earth itself is closest to / furthest from the Sun is made much more complex by the fact that the Earth and Moon orbit one another as well as the Sun. Because ...


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