MATT STRASSLER
Of Particular Significance

Alert — Aurora (Northern Lights) Possible Tonight

There was a big solar flare on Monday, which as often happens created a flash of X-rays (travel time to Earth 8.5 minutes), a blast of high speed protons and electrons (travel time minutes to hours), and a “Coronal Mass Ejection” (CME) of slower subatomic particles (travel time 1 to 3 days.) It’s the CME that is one of the main triggers for auroras borealis (north) and australis (south).

Update 23:00 Eastern Time (0300 UT): the CME has arrived in the past hour. There are northern lights going on, but so far they are still quite far north compared to predictions. This could change, but it will soon be too late for me to report on it, and it’s pretty cloudy here so I’m unlikely to stay up late hoping. Checking “northern lights” or “aurora” on Twitter is a good way to get real-time information, and there are some webcams on https://aurora.live/camera/ .

Aurora forecasts are not very reliable yet, because of a lack of data about the CMEs themselves and the ever-changing environment between the Sun and the Earth through which they are moving. So neither timing of arrival nor strength of impact can be predicted with great confidence. With that caveat, it seems likely that the flare will arrive late tonight or early in the morning in Europe, late afternoon to evening in the United States. Its effects could be as strong as any we’ve seen in a number of years; auroras may well be visible well into central Europe and the northern third of the United States, or even further south than that, on and off over a period of many hours. Fingers crossed.

We will have mostly cloudy skies here, so I probably won’t see this one. But I hope many of you are lucky enough to see a spectacle tonight!

Update: Also today, an even stronger flare occurred. If this one also created a CME that’s aimed toward Earth, we may have another round of strong auroras within a couple of days. See the data below showing X-rays detected from today’s flare, and from Monday’s earlier flare.

Measurements by two of our geostationary weather satellites of X-rays coming from the Sun; large peaks are caused by solar flares which produce X-rays in great abundance. The more X-rays, the stronger the flare.

Oh, and by the way, sometime soon I’ll show you how to use solar flares and CMEs to solve one of the hardest problems in do-it-yourself astronomy. If only the Greeks had known!

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON March 30, 2022

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How to Estimate the Distance to the Outer Planets Yourself

Now, the last step in mapping out the other planets, before heading for more intriguing territory.

In a previous post I showed you how you can measure the distance between Venus and the Sun, RVS, relative to the distance between Earth and the Sun, RES. Under the assumption that Venus’s orbit around the Sun is circular (or nearly so), you can use the fact that when the angle between Venus and the Sun reaches its maximum (the moment of greatest elongation, and also approximately the moment when Venus appears half lit by the Sun), there’s a simple right-angle triangle in play. High school trigonometry then gives you the answer: RVS/RES ≈ 0.72 ≈ 1/√2. The same trick works for Mercury, which, like Venus, is a near Sun-orbiting planet, closer to the Sun than Earth.

But there’s no maximum angle for Mars, Jupiter, or the other far planets. These planets are further out than Earth and can even appear overhead at midnight, when they are 180 degrees away from the Sun. Fortunately there’s another right triangle we can use, again under the assumption of a (almost-)circular orbit, and that can give us a decent estimate.

The Triangle for the Far Sun-Orbiting Planets

Let’s focus on Mars first, although the same technique will work on the outer planets. Mars has a cycle in which it disappears behind the Sun, from Earth’s perspective, on average every 780 days. (That start of the cycle is called “solar conjunction,” or just “conjunction” when the context is clear.) About half a cycle later, after on average 390 days, it is at “opposition”: closest to Earth, largest in a telescope, appearing overhead at midnight, and at its brightest. But if we wait only a quarter cycle, on average 195 days after conjunction, then the Mars-Sun line is at a 90 degree angle to the Earth-Sun line. That means that Mars, Earth and the Sun form a right-angle triangle with the right angle at the location of the Sun.

So on the day of first quarter we should measure the angle on the sky between Mars and the Sun. That’s the angle A on the figure below. Then the Mars-Sun distance RMS and the Earth-Sun distance RES are the two sides of a right-angle triangle. That means they are related by the tangent function:

  • RMS/RES = tan A.
For a planet whose distance RPS from the Sun is greater than Earth’s, an estimate of its distance compared to the Earth-Sun distance RES can be made using the fact that (were its orbit perfectly circular) it would make a right-angle triangle after the first or third quarter of its cycle, with the right angle located at the Sun. Sizes of Earth, Sun and planet not shown to scale.
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POSTED BY Matt Strassler

ON March 28, 2022

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A Prediction from String Theory

(An advanced particle physics topic today…)

There have been various intellectual wars over string theory since before I was a graduate student. (Many people in my generation got caught in the crossfire.) But I’ve always taken the point of view that string theory is first and foremost a tool for understanding the universe, and it should be applied just like any other tool: as best as one can, to the widest variety of situations in which it is applicable. 

And it is a powerful tool, one that most certainly makes experimental predictions… even ones for the Large Hadron Collider (LHC).

These predictions have nothing to do with whether string theory will someday turn out to be the “theory of everything.” (That’s a grandiose term that means something far less grand, namely a “complete set of equations that captures the behavior of spacetime and all its types of particles and fields,” or something like that; it’s certainly not a theory of biology or economics, or even of semiconductors or proteins.)  Such a theory would, presumably, resolve the conceptual divide between quantum physics and general relativity, Einstein’s theory of gravity, and explain a number of other features of the world. But to focus only on this possible application of string theory is to take an unjustifiably narrow view of its value and role.

The issue for today involves the behavior of particles in an unfamiliar context, one which might someday show up (or may already have shown up and been missed) at the LHC or elsewhere. It’s a context that, until 1998 or so, no one had ever thought to ask about, and even if someone had, they’d have been stymied because traditional methods are useless. But then string theory drew our attention to this regime, and showed us that it has unusual features. There are entirely unexpected phenomena that occur there, ones that we can look for in experiments.

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POSTED BY Matt Strassler

ON March 20, 2022

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This Weekend, Measure the Distance to Venus Yourself

This Sunday, Venus reaches a special position from which it is easy to estimate roughly how large the average Venus-Sun distance (RVS) is relative to the average Earth-Sun distance (RES).  (I say “on average” because the Venus-Sun distance isn’t quite constant.  Venus’s orbit, like that of all the planets, isn’t quite circular.  But this is a small effect that we can ignore for the purpose of rough estimates.)

If you are a true diehard astronomy-geek, by all means get up at 5 or 5:30 in the morning on Sunday (or really any of the next few days) to check this directly.  I can assure you (since I have been up at that time recently, due to chronic insomnia more than astronomy-geekhood) that Venus looks absolutely gorgeous against the deep blue of the pre-dawn sky.  But if you have no intention on getting up that early, or clouds intervene, there’s a shortcut — on your phone.

Greatest Elongation, Near-Circular Orbits, Half-Lighting and Right Angles

On Sunday, Venus moves to a position where, from Earth’s perspective, the angle between Venus and the Sun on the sky reaches its maximum.  This position is called “greatest elongation“, and it is reached twice per cycle, once in the evening sky and once in the morning.  If Venus’s orbit were perfectly circular, this would also be the moment when Venus appears half-lit; as we’ve been seeing in two recent posts (1,2), that’s an effect of simple geometry:

  • if Venus’s orbit were circular, then at greatest elongation, the triangle formed by Earth, Venus and the Sun would be a right angle where Venus is located, and Venus would be half-lit.

This holds for Mercury too, as it would for any near Sun-orbiting planet.

Since Venus’s orbit isn’t quite circular, this isn’t precisely true; half lit and the right angle come together, but greatest elongation is off just a few days. This is a minor detail unless you’re an astronomy-geek, and won’t keep us from getting a good estimate of the Venus-Sun distance.

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POSTED BY Matt Strassler

ON March 18, 2022

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Who Orbits Who, and Where? Check it Yourself

So far the arguments given in recent posts give us a clear idea of how the Earth-Moon system works: Earth’s a spinning sphere of diameter about 8000 miles (13000 km), and the size of the Moon and its distance are known too (diameter about 1/4 Earth’s, and distance about 30 times Earth’s diameter). We also know that the Sun is much further than the Moon and larger than the Earth, though we don’t know more details yet.

What else can we learn just with simple observations? Since the stars’ daily motion is an illusion from the Earth’s spin, and since the stars do not visibly move relative to one another, our attention is drawn next to the motion of the objects that move dramatically relative to the stars: the Sun and the planets.  Exactly once each year, the Sun appears to go around the Earth, such that the stars that are overhead at midnight, and thus opposite the Sun, change slightly each day.  The question of whether the Earth goes round the Sun or vice versa is one we’ll return to.   

Let’s focus today on the planets (other than Earth) — the wanderers, as the classical Greeks called them.  Do some of them go round the Earth?  Others around the Sun?  Which ones have small orbits, and which ones have big orbits? In answering these questions, we’ll start to build up a clearer picture of the “Solar System” (in which we include the Sun, the planets and their moons, as well as asteroids and comets, but not the stars of the night sky.)

The Basic Patterns

If we make the assumption (whose validity we will check later) that the planets are moving in near-circles around whatever they orbit, then it’s not hard to figure out who orbits who. For each possible type of orbit, a planet will exhibit a different pattern of sizes and phases across its “cycle“ when seen through binoculars or a small telescope. Even with the naked eye, a planet’s locations in the sky and changes in brightness during its cycle give us strong clues. Simply by looking at these patterns, we can figure out who orbits who.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON March 13, 2022

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Which is Bigger, the Sun or the Earth?  Check it Yourself!

Once you’ve convinced yourself the Earth’s a spinning sphere of diameter about 8000 miles (13000 km), and you’ve estimated the Moon’s size and distance (diameter about 1/4 Earth’s, and distance about 30 times Earth’s diameter), it’s easy to convince yourself the Sun’s bigger than the Earth, and much further than the Moon.  It just takes a couple of triangles, and a bit of Moon-gazing.

Since that’s all there is to it, you can guess that the ancient Greek astronomers, masters of geometry, already knew the Sun’s the larger of the two.  That said, they never did quite figure out how big and far the Sun actually is; we need modern methods for that.

It’s Just a Phase

The Moon goes through a monthly cycle of phases, lasting about 291/2 Earth days, in which the part that glows brightly with reflected sunlight grows and shrinks, from crescent to full and back again.  The phases arise because there are two simple ways of dividing the Moon in half:

  • At any moment, the half of the Moon that faces Earth — let’s call it the near half of the Moon — is the only half that we can potentially see. (We’d only be able to see the far half, facing away from Earth, if the Moon were transparent, or a big mirror was sitting beyond the Moon.)
  • At any moment, the half of the Moon that faces the Sun is brightly lit — let’s call it the lit half.  The other half is dark, and its presence can only be detected by the fact that it can block stars that it moves in front of, and through a very dim glow in which it reflects sunlight that first reflected from the Earth (called “Earthshine.”)  

The phases arise because the lit half and the near half aren’t the same, and the relationship between them changes from night to night.   See the diagram below. When the Moon is more or less between the Sun and the Earth (it rarely passes exactly between, because its orbit is tilted by a few degrees out of the plane of the drawing below) then the Moon’s lit half is its far half, and the near half is unlit. We call this dark view of the Moon the “New Moon” because it is traditionally viewed as the start of the Moon’s monthly cycle. 

Figure 1: The Moon’s phases, assuming the Sun’s much further than the Moon. When the Moon is roughly between the Earth and Sun, its near half coincides with the unlit half, making it invisible (New Moon). As the cycle proceeds, more of the near half intersects with the lit half; after 1/4 or the cycle, the Moon’s near half is half lit and half unlit, giving us a “half Moon.” At the cycle’s midpoint, the near side coincides with the lit half and the Moon appears full. The cycle then reverses, with the other half Moon occurring after 3/4 of the cycle.

When the Moon is on the opposite side of the Earth from the Sun (but again, rarely eclipsed by Earth’s shadow because of its tilted orbit), then its near side is its lit side, and that creates the “Full Moon”, a complete white disk in the sky. 

At any other time, the near side of the Moon is partly lit and partly unlit. When the line between the Moon and Earth is perpendicular to the Earth-Sun line, then the lit side and unlit side slice the near side in half, and the Moon appears as a half-disk cut down the middle.

When I was a child, I wondered why half this half-lit phase of the Moon, midway between New Moon (invisible) and Full Moon (the bright full disk), was called “First Quarter”, when in fact the Moon at that time is half lit.  Why not “First Half?”  Two weeks later, the other half of the near-side of the Moon is lit, and why is that called “Third Quarter” and not, say, “Other Half”?

This turns out to have been an excellent question. The fact that a Half Moon is also a First Quarter Moon tells us that the Sun is large and far away!

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POSTED BY Matt Strassler

ON March 9, 2022

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