#### Black Hole

##### May contain traces of nut

I don't understand the fascination the media has with the so-called Super-Moon. Last night's Full Moon was supposed to be the closest/largest/brightest since 1948 or until 2034.

For those who don't know, the Moon (and all other astronomical bodies in stable orbits) orbits a central body (in this case the Earth) in an ellipse, but not with the Earth at the centre of the ellipse - it is to one side of the long (major) axis of the ellipse at what is known as the focus (actually: there are two foci, symmetrically placed either side of the centre - but only one is occupied). The consequence is that, as the Moon progresses around its orbit, when it crosses the major axis nearest the focus it is closest to the Earth, and when it crosses the major axis at the other end it is furthest from the Earth.

The orientation of the orbit is reasonably constant in space. Meanwhile, the Earth is orbiting the Sun. Full Moon occurs when the Moon is opposite the Sun in the sky (as seen from Earth), so the circumstances for a Super-Moon occur every time the Earth is at a point in its orbit around the Sun such that the major axis of the Moon's orbit is in line with the Sun and the point where the Moon is nearest the Earth (the perigee) is away from the Sun. This happens once a year.

However, it is then a matter of luck (not really pure chance - it is predictable) whether the Moon is at that point in its orbit at the same time as the alignment with the Sun occurs. In the worst case, the Moon could be at New instead of Full, so it was Full 15 days previously and won't be Full again for another 15 days. This moves the point of the Full Moon away from the perigee, by a maximum of approximately 15 degrees.

I've been talking about elliptical orbits, and I guess most people will be imagining a school geometry textbook ellipse (squashed circle) with the minor axis about half the length of the major axis. In fact, the difference between the major axis and minor axis of the Moon's orbit around the Earth is only 0.15%. That's right - less than one six-hundredth. Try to draw a scale diagram on a piece of A4, and the difference between the ellipse of the Moon's orbit and a perfect circle would be less than the thickness of the pencil line. The only thing you might notice is that the location of the Earth is offset from the centre of the circle by 5.5% of the radius. (Do the same thing for the Earth's orbit around the Sun and you are onto a hiding to nothing: the ellipse diverges from a circle by a rediculous 0.014%, with the Sun displaced from the centre by 1.7%.)

The consequence of all this is that, actually, there is incredibly little difference between the distance to the Moon when it is at perigee and the distance when it is 15 degrees in its orbit away from perigee. I've calculated it from the NASA figures and here are the stats:

That's right: 642 km difference. That may sound a lot, but it's 0.18% of the perigee distance. Bear in mind that the distance of the observer on Earth to the Moon can be as much as 4,000 km different according to where you are - six times as great as the difference between the best possible Super Moon and the most sub-optimal Super Moon 15 days off prime.

So what's all the fuss about? Well, at least it gets people looking at the night sky. The real spectacle is that the Super-Moon differs from the Micro-Moon (when the Full Moon occurs at apogee) by about 11%, and the brightness by about 23%. But the actual difference between successive full moons is far less than that, and the difference between sucessive Super-Moons practically indiscernible, so it's all rather a damp squib.

The exact dimensions and orientation of the Moon's orbit wobble a little, due to a variety of factors including the fact that the Earth and Moon are not "on their own" - the Sun and other bodies in the Solar System have perturbing effects. Another perturbing influence is that the Earth is not spherical, and finally the Moon's overall distance from the Earth is gradually increasing due to the accelerating effect of the tides (energy is being transferred from the rotation of the Earth, slowing it down, to the orbit of the Moon, moving it away), so, actually, the Moon is gradually (very, very slowly) getting smaller in the sky, and eventually there will be a "peak" Super-Moon that is never beaten.

For those who don't know, the Moon (and all other astronomical bodies in stable orbits) orbits a central body (in this case the Earth) in an ellipse, but not with the Earth at the centre of the ellipse - it is to one side of the long (major) axis of the ellipse at what is known as the focus (actually: there are two foci, symmetrically placed either side of the centre - but only one is occupied). The consequence is that, as the Moon progresses around its orbit, when it crosses the major axis nearest the focus it is closest to the Earth, and when it crosses the major axis at the other end it is furthest from the Earth.

The orientation of the orbit is reasonably constant in space. Meanwhile, the Earth is orbiting the Sun. Full Moon occurs when the Moon is opposite the Sun in the sky (as seen from Earth), so the circumstances for a Super-Moon occur every time the Earth is at a point in its orbit around the Sun such that the major axis of the Moon's orbit is in line with the Sun and the point where the Moon is nearest the Earth (the perigee) is away from the Sun. This happens once a year.

However, it is then a matter of luck (not really pure chance - it is predictable) whether the Moon is at that point in its orbit at the same time as the alignment with the Sun occurs. In the worst case, the Moon could be at New instead of Full, so it was Full 15 days previously and won't be Full again for another 15 days. This moves the point of the Full Moon away from the perigee, by a maximum of approximately 15 degrees.

I've been talking about elliptical orbits, and I guess most people will be imagining a school geometry textbook ellipse (squashed circle) with the minor axis about half the length of the major axis. In fact, the difference between the major axis and minor axis of the Moon's orbit around the Earth is only 0.15%. That's right - less than one six-hundredth. Try to draw a scale diagram on a piece of A4, and the difference between the ellipse of the Moon's orbit and a perfect circle would be less than the thickness of the pencil line. The only thing you might notice is that the location of the Earth is offset from the centre of the circle by 5.5% of the radius. (Do the same thing for the Earth's orbit around the Sun and you are onto a hiding to nothing: the ellipse diverges from a circle by a rediculous 0.014%, with the Sun displaced from the centre by 1.7%.)

The consequence of all this is that, actually, there is incredibly little difference between the distance to the Moon when it is at perigee and the distance when it is 15 degrees in its orbit away from perigee. I've calculated it from the NASA figures and here are the stats:

Semi-major axis (NASA): 384,400 km

Eccentricity (NASA): 0.0549

Semi-minor axis (BH): 383,755 km

Apogee (NASA): 405,500 km

Perigee (NASA): 363,300 km

Distance to orbit 15 degrees from perigee (BH): 363,942 km

Eccentricity (NASA): 0.0549

Semi-minor axis (BH): 383,755 km

Apogee (NASA): 405,500 km

Perigee (NASA): 363,300 km

Distance to orbit 15 degrees from perigee (BH): 363,942 km

*NB: The NASA figures are only given to four significant digits, meaning my derived figures are also only accurate to four digits. However, as I am interested in differences and ratios, the argument remains valid.*That's right: 642 km difference. That may sound a lot, but it's 0.18% of the perigee distance. Bear in mind that the distance of the observer on Earth to the Moon can be as much as 4,000 km different according to where you are - six times as great as the difference between the best possible Super Moon and the most sub-optimal Super Moon 15 days off prime.

So what's all the fuss about? Well, at least it gets people looking at the night sky. The real spectacle is that the Super-Moon differs from the Micro-Moon (when the Full Moon occurs at apogee) by about 11%, and the brightness by about 23%. But the actual difference between successive full moons is far less than that, and the difference between sucessive Super-Moons practically indiscernible, so it's all rather a damp squib.

The exact dimensions and orientation of the Moon's orbit wobble a little, due to a variety of factors including the fact that the Earth and Moon are not "on their own" - the Sun and other bodies in the Solar System have perturbing effects. Another perturbing influence is that the Earth is not spherical, and finally the Moon's overall distance from the Earth is gradually increasing due to the accelerating effect of the tides (energy is being transferred from the rotation of the Earth, slowing it down, to the orbit of the Moon, moving it away), so, actually, the Moon is gradually (very, very slowly) getting smaller in the sky, and eventually there will be a "peak" Super-Moon that is never beaten.

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