Of Particular Significance

Tag: Higgs

(This is the fourth post in a series, though it can be read independently; here are post #1 , post #2 , and post #3.)

For many years, I thought that measuring the distance to the Sun was quite difficult for a non-astronomer. I had the impression that it requires precision measurements, often involving telescopes or information from satellites, and that it was only easy to obtain a minimum distance and a maximum distance that were still quite far apart, as I explained in my last post.

But it’s not true. As I’ll explain today, it turns out that anyone can estimate the distance to the Sun, at night, with nothing more than the naked eye, basic reasoning, and… meteors.

Just from the fact that a long meteor crosses the sky in a few seconds, you can infer that the Earth-Sun distance is something like 100 million miles (km). If the Sun were only 10 million miles (km) away, the meteors would lazily drift among the stars, only a bit faster than the motions of the space station and other satellites, which take minutes to cross the sky. Meanwhile, if the Sun were a billion miles (km) away, then meteors would flash across the sky in a fraction of a second.

With a little more work and knowledge, you can use meteors to make an estimate of the Sun’s distance that’s well within a factor of 2 of the truth. It’s not even that hard to get a precise measurement that’s good to 10% or so.

It may seem odd that one can use such little specks of dust in the Earth’s atmosphere to determine, without a telescope, how far it is to the Sun. But in fact the method is simple. It’s so simple that it must have been pointed out two centuries ago. Curiously, though, I’ve never seen it written down anywhere. It seems to be little-known, even to scientists.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 23, 2024

(This is the third post in a series, though it can be read independently; here are post #1 and post #2; and post #4 blows this one out of the water, so don’t miss it!)

Measuring the distance to the Sun is challenging, for reasons explained in my last post. Long ago, the Greek thinker Aristarchus proposed a geometric method, which involves estimating the Moon’s sunlit fraction on a certain date. Unfortunately, because the Sun is so far away, his approach isn’t powerful enough; Aristarchus himself underestimated the distance. [This last remained true for later astronomers before the 17th century, though they got closer to the truth, presumably by using more precise methods than you or I could easily apply. I doubt anyone truly found a maximum possible distance to the Sun just using geometry.] The best we can do, using Aristarchus’ method and our naked eyes, is determine a minimum possible distance to the Sun: a few million miles.

Figure 1: A simple application of Aristarchus’ method tells us that the minimum distance to the Sun is a few million miles (km), ruling out the red region. But the entire green region is still allowed.

Today we’ll see how to obtain a maximum distance to the Sun, using an approach suggested in the previous post: by measuring speeds. Specifically, we’ll make use of a speed that the ancient astronomers weren’t aware of: the speed of light, also known as the cosmic speed limit c. That’s 186,000 miles (300,000 km) per second, or 5.9 trillion miles (9.5 trillion km) per year. We’ll find the Sun’s distance is less than 12 billion miles… still much larger than its true distance, but a significant improvement on our starting point!

Figure 2: By the end of this post, we’ll know a maximum possible distance for the Sun, too.
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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 19, 2024

(This is the second post in a series; here’s post #1.)

It’s not too hard to measure the distance to the Moon; the Greeks did it over two thousand years ago. First you measure the size of the Moon, which can be done in various ways; for instance, you can use the occultation (i.e. blocking) by the Moon of a star or planet, or the outer edges of a solar eclipse, as viewed in different locations on the Earth. These measurements do require multiple people at different locations to accurately report what they have witnessed, but they don’t require any fancy equipment or highly precise observations. Then you can quickly determine the distance to the Moon using the angular diameter of the Moon on the sky.

However, measuring the distance to the Sun, or to any other planet, is much more difficult. Today I’ll explain why… and this will help us envision a way around the problem.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 17, 2024

A couple of years ago I wrote a series of posts (see below) showing how anyone, with a little work, can verify the main facts about the Earth, Moon, Sun and planets. This kind of “Check-It-Yourself” astronomy isn’t necessary, of course, if you trust the scientists who write science textbooks. But it’s good to know you don’t have to trust them, because you can check it on your own, without special equipment.

The ability to “do it yourself” is what makes science, as a belief system, most robust than most other belief systems, past and present. It also explains why there aren’t widely used but competing scientific doctrines that fundamentally disagree about the basics of, say, the Sun and its planets. Although science, like religion, is captured in texts and teachings that have been around for generations, one doesn’t need to have faith in those books, at least when it comes to facts about how the world works nowadays. The books may be from the past, but most of what they describe can be independently verified now. In many cases, this can be done by ordinary people without special training, as long as they have some guidance as to how to do it. The purpose of the “Check-It-Yourself-Astronomy” series is to provide that guidance.

As I showed, nothing more than pre-university geometry, trigonometry, and algebra, along with some star-gazing and a distant friend or two, is required to

However this list is missing something important. From these methods, one can only obtain the ratios of planetary sizes to each other and to the Sun’s size, and the ratios of distances between planets and the Sun. Yet I did not explain how to measure the distance from the Earth to the Sun, or the distance from the Sun to any of the other planets, or the sizes of the other planets. It’s difficult to learn these things without sophisticated equipment and extremely precise measurements; the easiest things to measure about the planets and the Sun — their locations, motions and sizes — aren’t sufficient. (I’ll explain why they’re not sufficient in my next post.)

But shouldn’t there be a way around this problem?

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 16, 2024

The Moon has a four-week cycle; it is full every four weeks (actually every 29.5 days). But ocean tides exhibit a two-week cycle; they are large one week and then smaller the next.

Specifically, as in Fig. 1 below, ocean tides are stronger (“spring tides”) around New Moon and Full Moon than they are at First Quarter Moon and Last Quarter Moon (“neap tides”). The pattern is seen, roughly at least, all around the world (though the details are not simple, as they depend on the shape of the coastline and other factors.)

Figure 1: Tides in Anchorage, Alaska, USA, during October 2023; the blue line shows how the water rises and falls about twice a day (note the vertical columns are each two days wide!) The pattern of strong and weak tides on alternate weeks is clearly visible. New Moon occurred on October 14 and Full Moon on October 28th, just before the peak tides.

What’s behind this pattern? And what does it tell us about the Sun and Moon that we wouldn’t otherwise easily know? Perhaps surprisingly, it tells us that the average mass density of the Sun — its mass divided by its volume — is only a little smaller than the average mass density of the Moon. Here’s why.

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Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON January 12, 2024

[Note added: the predicted storm has begun, as of about 1000 UTC, 5:00 AM NYC time; good for early birds on the west coast and those in Asia.] If you live in Canada, Europe or the northern half of the US, keep an eye to the north late tonight and possibly tomorrow night. A series of solar flares occurred on the Sun in the last couple of days, and when their repercussions reach Earth, they may cause quite a storm in the Earth’s magnetic field… resulting in Northern Lights (Aurora Borealis). [There will be Southern Lights too, though the nights are short right now down south.]

Something to watch: https://www.swpc.noaa.gov/products/ace-real-time-solar-wind , data from the ACE satellite, serves as an early-warning system; if its readings start suddenly going crazy, that typically means a CME (coronal mass emission, i.e. a swarm of particles blown out of the Sun’s outer atmosphere [its corona]) has hit the satellite. Usually that means the CME is an hour at most from hitting Earth, at which point auroras become more likely; the stronger the CME, the more southerly the northern lights will usually reach.

Here’s a picture of some of the ACE data as of 10:30 NYC (330 UTC) time, showing that something already happened a few hours ago, right at around 2300 UTC, enough to start a mild storm. The expectation is that something more dramatic may happen soon, and if it does, you should start making tea to keep you warm when you go out to look.

Readings from the ACE satellite as of 330 UTC Dec 1 (10:30 pm NYC Nov 30); note the sudden jump in the readings at 2300, typical of an arriving CME.

More generally, there’s a lot of data at https://www.swpc.noaa.gov/ , though it is not very user-friendly. A lot of its information is delayed by 3 hours, which is not so useful when you’re trying to catch a fleeting opportunity!

Good spotting! I myself am out of luck again, due to exhaustion tonight and bad weather tomorrow. But we are approaching solar maximum, so we should get multiple chances in 2024.

Picture of POSTED BY Matt Strassler

POSTED BY Matt Strassler

ON November 30, 2023

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