If the Universe contains trillions of stars in every direction, why isn't the night sky as bright as day?
Olbers' 'paradox' and JO's query sound similar, but are not exactly alike, JO's question differs because its very phrasing contains the answer. It also resolves Olbers' Paradox.
The resolution pertains to the Universe's age. The Universe is not infinitely old, but, instead, as JO indicated, is about 13 billion years old. The Universe hasn't been generating stars forever, only for billions of years. Consequently, the cosmos hasn't had sufficient time to fill the sky with stars. Lord Kelvin (1824-1907) proposed this age solution, which was corroborated years later by Big Bang theorists George Lemaître and Edwin Hubble. The dark night sky is direct observational evidence that we live in a Universe that was born at a specific time.
Or, in other words, the Universe doesn't have enough stars to fully illuminate our skies. While the Universe contains trillions of stars distributed through billions of galaxies and also dispersed through intergalactic space, the distances between us and most of those stars is unfathomable. The light intensity diminishes with the square of the distance. So, not every line of sight will connect with a star that we can actually see.
Of course, if you ever have a chance to observe the night sky through binoculars, you will see far more stars than are visible with the unaided eye. The sky is truly alight with stars, although some of them are hidden from our view.
How did they determine the relationship between a Cepheid variable's brightness and variability period?
Like all variable stars, Cepheids exhibit a variable brightness. Over the course of time (between 1-70 days), a Cepheid progresses through a complete cycle from maximum brightness to minimum and then back to maximum again.Outer layer pulsations alternately increase and decrease the star's size and temperature, both of which affect the star's luminosity, or energy output. As Henrietta Swan Levitt discovered, a Cepheid's variability period relates directly to its luminosity. The longer the variability period, the more luminous the Cepheid. Through observations of Cepheid variables, astronomers have determined the distances to other galaxies. They compare the Cepheid variable's apparent brightness with its intrinsic brightness. The difference between observed and actual brightness yields the distance.
Henrietta Swan Leavitt discovered the Period-Luminosity Relation by observing Cepheid variable stars with the Small Magellanic Cloud. This "Cloud" is a satellite galaxy to the Milky Way at an estimated distance of 160,000 light years from Earth. Even though the SMC has an diameter of 7,000 light years, we can assume that all the stars are at more or less the same distance from us. Similarly, we can assume that every citizen of Los Angeles County is at the same distance from Portland, Maine.
Professor Leavitt surveyed the Cepheid variables within the SMC and noticed that the brightest Cepheids exhibited the longest variability periods. Through careful observations, she determined a correlation between the Cepheid variable's brightness and variability period. These observations served to established a relationship only. Direct distance determination of Delta Cephei, the very first Cepheid discovered - hence, the name - provided astronomers with that Cepheid's luminosity. This knowledge provided them with the key to establishing the actual period luminosity relation.
[Note: by measuring Delta Cephei's distance through parallax, they could compare its apparent brightness and distance to determine the star's actual brightness, or luminosity. Distance, apparent brightness and absolute brightness are the three factors involved in the "distance modulus" equation. The determination of two yields the value of the third.]
Are there as many stars below our feet as exist above our head?
This image shows the Sun and the stars within the immediate vicinity. Produced by National Geographic, this chart illustrates that our Sun and the other stars all "float" in the void. For convenience, the graphic artists placed Sol in the dead center, to enable us to gauge the up/down positions of the proximate stars.
Let's imagine that Earth were a transparent glass globe so that we could look through the ground to observe the stars as easily as we observe them above us. On this imaginary sphere, one finds stars in every direction. Many of those stars we see below our feet are those stars that can never actually see at the mid-northern latitudes, such as Pavo, the Peacock, Crux (the Southern Cross) or Tucana, the Tucan. With Earth obscuring internal material taken away, we can see most everything, apart, of course, from those stars around the Sun. Of course, as we're delving in our own imaginary Universe, we can snap the Sun off, too, if we so choose.
The Milky Way Galaxy is about 10,000 light years thick around its halo. This thickness tapers down to about 1000 light years toward the outer spiral arms. Our Galaxy is a barred spiral. In such galaxies, curling arms extend away from a central bar structure. The Sun and it attendant bodies occupy a minuscule niche within the Orion Arm about 23,000 light years from the center. Within our neighborhood, stars are most abundant along the spiral arms, but are also scattered "above" and "below'" the arms. It is for this reason that we see the richest star fields within the "Milky Way" bands and far fewer stars away from these bands. However, we still see quite a few stars in all directions because our solar system is part of a great swarm within this galactic region.
So, the void falls away into the infinite under our feet just as it does above our heads. Fortunately, the planet's gravity holds us fast to its surface. It gives us a ground that ultimately, is spinning and turning in the boundless vacuums of the cosmos.
How far away could we travel from the Sun while still being able to see it with the naked eye?
If we were to travel away from the Sun, it would become fainter. At Pluto's distance, the Sun will still be many millions of times brighter than the night sky's brightest star, Sirius. At the distance of Proxima Centauri, the Sun would be about as bright as Procyon, the brightest star in Canis Minor and the 8th brightest star in our sky. The faintest stars that most people can see are about 185 times dimmer than Procyon. For the Sun to appear this faint to us, we would have to be about 58 light years away from it. Some people have keener eyesight than most of us and they can see fainter stars. However, if we were all in a space vessel that was 58 light years from the solar system, we could still just barely see the Sun. We'd likely need a highly detailed star chart to locate it.
The closest "invisible" star, called Barnard's Star, is only six light years away. Barnard's Star is a low mass red dwarf. A red dwarf is a star that is just massive enough to have ignited and sustained thermonuclear fusion reactions in its core. A star is considered "active" if its core active fuses lighter elements into heavier ones. A star's luminosity, or energy output per unit time, depends on its mass. The more massive the star, the higher the luminosity. A low luminosity star is comparatively quite faint.
Barnard's Star is about 25 times fainter than the faintest stars visible to the unaided eye. In fact, Barnard's Star would have to be 1.2 light years from Earth to become as bright as the faintest naked eye stars. The closest star system to the solar system, Alpha Centauri, is 4.2 light years away.
We shouldn't be surprised by this answer, considering that less than ten of the thirty closest star systems to the Sun are visible to the unaided eye. Most stars are red dwarfs and therefore quite faint. We see only the biggest, brightest and, on occasion, the nearest.
To subscribe or unsubscribe from the Daily Astronomer: