July 20 Yet again, I've slipped in sending out my columns here. Three, in this mailing.
The Hubble Constant has always intrigued me - both for the way it was "discovered" and for what it tells us about our universe. So any mention of it I run across, I invariably stop to read more. One of those, some months ago, was about a more accurate calculation of the Constant. And that, using a phenomenon we all experience every time we close one eye and then the other: parallax. Things we owe to the parallax effect, July 9: https://www.livemint.com/opinion/columns/things-we-owe-to-the-parallax-effect-11625771615330.html There's a followup, next. yours, dilip --- The things we owe to the parallax effect ----------------- Dilip D'Souza Try this experiment. Face a window from across the room. Close your right eye. Hold your left index finger upright in front of your nose, so that its right edge matches the right edge of the window. Got that? Keeping your finger steady, close your left eye and open your right. The finger seems to jump to the left. Estimate how much it jumped. For me, it was about six times the width of the window. Now straighten your arm so your upright index finger is an arm's length away. Repeat. Your finger appears to jump left again, but a much smaller distance. In my case, about the width of the window. You just had an up close and personal encounter with parallax: the way an object you're looking at seems to shift in relation to more distant objects as you change where you're looking from, and how much it shifts depends on how far it is from you. In effect, you have a way to measure the distance to your finger. It's more complicated than just this much, but a good way to understand what's happening is that there's a mathematical relationship at work: the further your index finger, the less it seems to move in relation to the window - the smaller the parallax shift. In fact, you can use parallax to estimate the distance to the window - after all, you likely have a good idea of how far away your finger is, but you may not know how far the window is. The idea of parallax is at the core of a recent flood of estimates of distances to stars. Observe a star against a background of other, much further, stars. Repeat your observation six months later, when the Earth has moved to a point in its orbit diametrically opposite the first point. The shift in the Earth's position, of course, is analogous to looking out of first your left and then your right eye. And of course, you expect to see the effect of parallax: that the star you're observing seems have moved in relation to more distant ones. If you can measure how much it seems to have moved and if you have a reasonable idea how far it is, you can calculate how far the distant stars are. There are complications, of course. For one thing, all stars move, all the time. So if you do notice that the star seems to have moved against the background, is that due to parallax? Or to its own intrinsic movement? Or both? For another thing, even the nearest star is so far away that an apparent change in its position due to parallax will be tiny indeed and extremely hard to detect. To put this in perspective: the distance between the Earth's positions six months apart - the diameter of its orbit - is about 300 million km, or about 1000 light seconds (i.e. light takes 1000 seconds to travel that distance). Compare to the distance to Proxima Centauri, the star that's closest to us - which is about 4.2 light years, or about 130,000 times the diameter of Earth's orbit. How much of a parallax shift do you think you might notice in a finger that's held upright 10km from you? That's a measure of the challenge astronomers face in observing and measuring parallax. Still, we have some powerful telescopes indeed stationed in space. One, the European Space Agency's Gaia space observatory, is in an orbit that that varies between 250,000 km and 700,000 km above the Earth's surface. From there, Gaia measures the position, movement and distance of millions of cosmic objects, stars included. In particular, a team of astronomers has used Gaia to detect parallax shifts in many stars. Their work has given us new degrees of precision in our calculation of how far they are from us. In turn, that has refined our estimate of a number that's fundamental to our understanding of our universe: the Hubble Constant. A quick introduction to the Hubble Constant might be in order. You've heard of the Doppler shift, which explains why a car's horn sounds higher-pitched as it approaches you, and lower as it speeds away from you. That is, if you hear a horn getting steadily lower-pitched, you know the car is moving, and moving away from you. If you are able to measure the sound's frequency, you might even calculate the speed of the motion. Over a century ago, astronomers began to notice that the light from distant celestial objects was Doppler shifted as well. The natural inference came as a surprise: most of these objects are moving away from us. But it's not just that they are moving away. The astronomers found that the further an object is from us, the more its light is Doppler shifted. What that implied was even more of a surprise: the further the object, the faster it is moving away. That is, there is a relationship between speed and distance. That relationship is captured in the Hubble Constant, named for the great astronomer Edwin Hubble who first made these observations. He estimated that for every million light years further an object is from us, the speed at which it recedes from us increases by 150 km/s. The Hubble Constant, then, was 150km/s/mly. "Was", because more accurate modern measurements suggest it is about 23km/s/mly. These days, it is usually expressed using parsecs (pc) rather than light years. Since one parsec is just over three light years, the Hubble Constant is about 70km/s/Mpc (megaparsec, or million parsecs). Why is this one number so fundamental? If a galaxy, say, is accelerating as time passes, as it travels ever further from us - well, think about running the clock backward. The galaxy slows down as it gets closer to us, it gets even closer and slows down still more, and this is simultaneously happening to all galaxies, all approaching each other, until we reach that mysterious moment when all the matter in the universe was once smooshed together. We've reached that instant before the cataclysmic Big Bang. From the Hubble Constant, we can actually calculate how long ago that was: about 14 billion years. 14 billion years: that's how old the universe is. See why the Hubble Constant is fundamental to our understanding, our idea, of our universe? That the new measurements of distance using parallax are much more accurate means we can more precisely calculate the Hubble Constant. In a paper they submitted to the Astrophysical Journal ("Cosmic distances calibrated to 1% precision with GAIA EDR3 parallaxes and Hubble Space Telescope photometry of 75 Milky Way Cepheids confirm tension with ACDM", Adam G Riess, Stefano Casertano et al, 5 January 2021, https://arxiv.org/pdf/2012.08534.pdf), the team of astronomers call it 73.2 km/s/Mpc. Which means the age of the universe is not 14 billion, but only 13.4 billion years. Not a huge difference? What's a half billion years here or there, you think? But it's from these numbers and ideas that we come to grips with where we are in this vast cosmos, that we gain some perspective on our existence. And that's why the ever-greater precision is important. There's more, hinted at by the word "tension" in the title of the paper. If galaxies are all receding, that means the universe is expanding. There are ways to predict how fast they should be receding, but the Hubble Constant suggests they are faster still. Why? Of this so-called Hubble tension, another time. -- My book with Joy Ma: "The Deoliwallahs" Twitter: @DeathEndsFun Death Ends Fun: http://dcubed.blogspot.com -- You received this message because you are subscribed to the Google Groups "Dilip's essays" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web, visit https://groups.google.com/d/msgid/dilips-essays/CAEiMe8rYH2Jh31hMAyq%3DoVb0UFWkGiFgJZgwtaeUO1KQbZmuiQ%40mail.gmail.com.
