Category Archives: astronomy

Astronomy Picture of the Day – Dark Molecular Cloud Barnard 68

See Explanation.  Clicking on the picture will download
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Image Credit: FORS Team8.2-meter VLT AntuESOExplanation: Where did all the stars go? What used to be considered a hole in the sky is now known to astronomers as a dark molecular cloud. Here, a high concentration of dust and molecular gas absorb practically all the visible light emitted from background stars. The eerily dark surroundings help make the interiors of molecular clouds some of the coldest and most isolated places in the universe. One of the most notable of these dark absorption nebulae is a cloud toward the constellation Ophiuchus known as Barnard 68pictured here. That no stars are visible in the center indicates that Barnard 68 is relatively nearby, with measurements placing it about 500 light-years away and half a light-year across. It is not known exactly how molecular clouds like Barnard 68 form, but it is known that these clouds are themselves likely places for new stars to form. In fact, Barnard 68 itself has been found likely to collapse and form a new star system. It is possible to look right through the cloud in infrared light.




Astronomy Picture of the Day – Eclipsosaurus Rex

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Eclipsosaurus Rex 
Image Credit & CopyrightFred Espenak ( We live in an era where total solar eclipses are possible because at times the apparent size of the Moon can just cover the disk of the Sun. But the Moon is slowly moving away from planet Earth. Its distance is measured to increase about 1.5 inches (3.8 centimeters) per year due to tidal friction. So there will come a time, about 600 million years from now, when the Moon is far enough away that the lunar disk will be too small to ever completely cover the Sun. Then, at best only annular eclipses, a ring of fire surrounding the silhouetted disk of the too small Moon, will be seen from the surface of our fair planet. Of course the Moon was slightly closer and loomed a little larger 100 million years ago. So during the age of the dinosaurs there were more frequent total eclipses of the Sun. In front of the Tate Geological Museum at Casper College in Wyoming, this dinosaur statue posed with a modern total eclipse, though. An automated camera was placed under him to shoot his portrait during the Great American Eclipse of August 21.



Astronomy Picture of the Day – Global Aurora at Mars

See Explanation.  Clicking on the picture will download
 the highest resolution version available.Global Aurora at Mars 
Image Credit: MAVENLASP, University of ColoradoNASAExplanation: A strong solar event last month triggered intense global aurora at Mars. Before (left) and during (right) the solar storm, these projections show the sudden increase in ultraviolet emission from martian aurora, more than 25 times brighter than auroral emission previously detected by the orbiting MAVEN spacecraft. With a sunlit crescent toward the right, data from MAVEN’s ultraviolet imaging spectrograph is projected in purple hues on the right side of Mars globes simulated to match the observation dates and times. On Mars, solar storms can result in planet-wide aurora because, unlike Earth, the Red Planet isn’t protected by a strong global magnetic field that can funnel energetic charged particles toward the poles. For all those on the planet’s surface during the solar storm, dangerous radiation levels were double any previously measured by the Curiosity rover. MAVEN is studying whether Mars lost its atmosphere due to its lack of a global magnetic field.



Hubble Hones In on a Hypergiant’s Home


Image credit: ESA/Hubble & NASA Text credit: European Space Agency

This beautiful Hubble image reveals a young super star cluster known as Westerlund 1, only 15,000 light-years away in our Milky Way neighborhood, yet home to one of the largest stars ever discovered.

Stars are classified according to their spectral type, surface temperature, and luminosity. While studying and classifying the cluster’s constituent stars, astronomers discovered that Westerlund 1 is home to an enormous star.  Originally named Westerlund 1-26, this monster star is a red supergiant (although sometimes classified as a hypergiant) with a radius over 1,500 times that of our sun. If Westerlund 1-26 were placed where our sun is in our solar system, it would extend out beyond the orbit of Jupiter.

Most of Westerlund 1’s stars are thought to have formed in the same burst of activity, meaning that they have similar ages and compositions. The cluster is relatively young in astronomical terms —at around three million years old it is a baby compared to our own sun, which is some 4.6 billion years old.

Galaxy Cluster Abell 2666


Image Credit & Copyright: Bernhard Hubl, CEDIC 2017Explanation: The galaxies of Abell 2666 lie far beyond the Milky Way, some 340 million light-years distant toward the high flying constellation Pegasus. Framed in this sharp telescopic image, the pretty cluster galaxies are gathered behind scattered, spiky, Milky Way stars. At cluster center is giant elliptical galaxy NGC 7768, the central dominant galaxy of the cluster. As the cluster forms, such massive galaxies are thought to grow by mergers of galaxies that fall through the center of the cluster’s gravitational well. Typical of dominant cluster galaxies, NGC 7768 likely harbors a supermassive black hole. At the estimated distance of Abell 2666, this cosmic frame would span about 5 million light-years.

Spacetime Diagram

The spacetime diagram (“a position vs time graph”) is a valuable tool for modeling and interpreting situations in relativity. As I like to say, “A spacetime diagram is worth a thousand words.” Many problems and “apparent-paradoxes” (or better “puzzles”) can be resolved by drawing a good spacetime diagram. However, because Minkowski spacetime geometry is not Euclidean, there is a hurdle to interpreting the spacetime diagram. As Alfred Schild eloquently stated,

“When it comes to metrical concepts, our Euclidean intuition is no longer valid in space-time—it cannot be trusted. Here we have to re-educate our intuition and learn to think in terms of new pictures. Thus, equal lengths in Minkowski geometry will not look equal, right angles will not look like right angles.”

(Side comment: Before we get into special relativity, it is worth noting that PHY 101’s “position vs time graph” also has a underlying geometry that is not Euclidean. However, practically everybody has learned to read the position-vs-time graph—without knowing anything about this geometry. To help students better understand special relativity, we may have to become more aware of this geometry… but that’s a story for another day.)

Where are the tickmarks?

Although we may be given the tickmarks of the inertial observer drawing the spacetime diagram, a common question is “how does one know where to mark off the ticks of another observer’s clock and meterstick?” More precisely, “given a standard of time marked on an observer’s worldline, how does one calibrate the same standard on the other observer’s worldline?”
Traditionally, this is answered algebraically using the Lorentz Transformation formulas… which is rather abstract for a novice. Geometrically, one may use two-observer diagrams or hyperbolic graph paper—which are rather restrictive. [We use the usual conventions where the time axis is vertical and where the units are chosen so that light signals are drawn at 45 degrees.] The two-observer diagram can only accommodate two frames of reference, and the diagram must be prepared for the velocity of the “moving” frame (here, <span class="MathJax" data-mathml="vBob=3/5″ id=”MathJax-Element-1-Frame” role=”presentation” style=”position: relative;” tabindex=”0″>vBob=3/5vBob=3/5). The hyperbolic graph paper can handle more general velocities, but distinguishes the meeting event at the “origin”. For simple problems, either of these is probably sufficient. But what features are they emphasizing? Are these unnecessarily complicated? Unnecessarily expensive?

We propose a new type of graph paper—actually, a new use of plain old graph paper:
Rotated Graph Paper.
The grid lines are aligned with the light cones in spacetime. So, light signals are easier to draw.

But how do we get the 4 ticks along Bob’s worldline that we get from the other graph papers? The paper uses a physical argument based on the Doppler Effect and Bondi’s k-calculus. Here, we will use a geometrical argument (also found in the paper).

Diagramming Alice’s ticking Light Clock with “Clock Diamonds”

We begin the construction by interpreting the unit boxes in the rotated grid. Consider an inertial observer, Alice, at rest in her reference frame, carrying a mirror a constant distance away. Alice emits a light flash (traveling with speed c) that reflects off the distant mirror and returns (at speed c) to her after a round-trip elapsed time. If this returning light flash is immediately reflected back, this functions like a clock, called the light clock.
On the rotated grid, we draw the spacetime diagram of Alice and two such mirrors, one to the right (the direction in which Alice faces) and the other to the left. The parallelogram OMTN represents one tick of Alice’s longitudinal light clock, where the spatial trajectories of the light signals are parallel to the direction of relative motion. Henceforth, we will refer to this parallelogram as Alice’s “clock diamond.”
By tiling spacetime with copies of her clock diamond, Alice sets up a coordinate system. She measures displacements in time along a parallel to her worldline (along diagonal OT, which happens to be vertical on our rotated grid). She measures displacements in space along her “line of constant time” (parallel to diagonal MN, which happens to be horizontal on our rotated grid). According to Alice, events M and N are simultaneous. Lightlike displacements are measured parallel to the edges of her clock diamond.

Building Bob’s Clock Diamonds

Now consider another inertial observer Bob. For convenience, suppose <span class="MathJax" data-mathml="vBob=3/5″ id=”MathJax-Element-2-Frame” role=”presentation” style=”position: relative;” tabindex=”0″>vBob=3/5vBob=3/5.
How should Bob’s light clock and clock diamonds be drawn?
This is the Calibration Problem.
Given Alice’s worldline and one tick of Alice’s clock (clock diamond OMTN), how should one draw event F on Bob’s worldline so that timelike segment OF corresponds to one tick on Bob’s clock (clock diamond OYFZ)?

It turns out that
Bob’s clock diamond OYFZ
has the same area as
Alice’s clock diamond OMTN.

Geometrically, this is because events T and F lie on a hyperbola centered at O with asymptotes along the light cone of O. (Refer to the paper for physical arguments based on the Doppler Effect and Bondi’s k-calculus.)
By subdividing the grid (into, say, a 6 x 6 subgrid) and drawing analogous clock diamonds with the same area, you can glimpse the unit hyperbola.
The velocity of a clock in this spacetime diagram is encoded by the width-to-height “aspect ratio” of its clock diamond. So, for Bob, we have:
Note that events Y and Z of Bob’s clock diamond OYFZ are simultaneous for Bob—but not for Alice. This is the “relativity of simultaneity.” In the geometry of the spacetime diagram, diagonal YZ is [spacetime-]perpendicular to diagonal OF, even though it may not look so to a Euclidean eye.

Visualizing Time Dilation and the Clock Effect (Twin Paradox)

With Bob’s clock diamonds determined, we can now construct the 4 ticks along Bob’s worldline that one obtains in the two-observer graph paper and hyperbolic graph paper. This triangle visualizes “time dilation”: Bob determines the elapsed time from O to Q (events on his worldline) to be 4 ticks, whereas Alice determines the elapsed time from O to distant event Q (Q, not on her worldline) to be 5 ticks.

(Side comment: We have highlighted a parallelogram in the grid with diagonal OQ, which we refer to as the “causal diamond” of OQ. The area of that causal diamond is equal to the square of the time interval from O to Q. This suggests another, more powerful method to construct Bob’s clock diamonds if we know that OQ is along Bob’s worldline. Refer to the paper for details.)

We can easily extend this diagram to visualize the “clock effect”, featured in the so-called twin paradox. Inertial observer Alice stays at home and logs 10 ticks between separation and reunion events O and Z, whereas Bob (a piecewise-inertial—but now a non-inertial—observer since he momentarily accelerated at Q to turn around and return to Alice) logs 4+4=8 ticks from events O to Z via Q, not on inertial segment OZ.

The Clock Effect visualized
Note that there are three inertial reference frames displayed here: Alice, outbound-Bob, and inbound-Bob. This is not easily constructed on the two-observer graph paper or on the hyperbolic graph paper, especially if Bob’s inbound speed if different from Bob’s outbound speed. (Note that the subdivided grid which displayed a glimpse of the unit hyperbola displayed clock diamonds for nine inertial reference frames.)

Final comments

Hopefully this construction makes it easier to draw, interpret, and calculate with spacetime diagrams. So, let’s draw them! Refer to the paper for details of this method, other textbook examples (length contraction, velocity composition, elastic collisions), and its relation to other methods (radar methods, Bondi k-calculus, Robb’s formula, standard textbook formulas).

Further Reading

“Relativity on rotated graph paper,” Roberto B. Salgado,
Am. J. Phys. 84, 344-359 (2016);
[see also the references within]

“The Clock Paradox in Relativity Theory,” Alfred Schild,
Am. Math. Monthly, 66, 1-18 (Jan., 1959);

Relativity and Common Sense, Hermann Bondi (Dover, 1962).
“Space-time intervals as light rectangles,” N. D. Mermin,
Am. J. Phys. 66, 1077–1080 (1998);

“Visualizing proper-time in Special Relativity”, Roberto B. Salgado,
Phys. Teach. (Indian Physical Society), 46, 132–143 (2004);
available at

Free Astronomy Books

Free Astronomy Books – Primarily for education.

Feel free to add your own links to free books. Let me know if there are broken links or copyright issues.

Reference to

Solstice Illuminated: A Year of Sky

Explanation: Can you find which day is the winter solstice? Each panel shows one day. With 360 movie panels, the sky over (almost) an entire year is shown in time lapse format as recorded by a video camera on the roof of the Exploratorium museum in San FranciscoCalifornia. The camera recorded an image every 10 seconds from before sunrise to after sunset and from mid-2009 to mid-2010. A time stamp showing the local time of day is provided on the lower right. The videos are arranged chronologically, with July 28 shown on the upper left, and January 1 located about half way down. In the videos, darkness indicates night, blue depicts clear day, while gray portrays pervasive daytime cloud cover. Many videos show complex patterns of clouds moving across the camera’s wide field as that day progresses. The initial darkness in the middle depicts the delayed dawn and fewer daylight hours of winter. Although every day lasts 24 hours, nighttime lasts longest in the northern hemisphere in December and the surrounding winter months. Therefore, finding the panel with the longest night will locate the day of winter solstice — which happens to be today in the northern hemisphere. As the videos collectively end, sunset and then darkness descend first on the winter days just above the middle, and last on the mid-summer near the bottom.

Solstice Illuminated: A Year of Sky 
Video Credit & Copyright: Ken Murphy (MurphLab); Music: Ariel (Moby)

The Milky Way Galaxy

Our magnificent Milky Way Galaxy sprawls across this ambitious all-sky panorama. In fact, at 800 million pixels the full resolution mosaic strives to show all the stars the eye can see in planet Earth’s night sky. As part of ESO’s Gigagalaxy Zoom Project, Serge Brunier recorded images with a digital camera over several months of 2008 and 2009 at exceptional astronomical sites—the Atacama Desert in the southern hemisphere and the Canary Islands in the northern hemisphere. The individual frames were stitched together and mapped into a single, flat, apparently seamless 360 by 180 degree view. The final result is oriented so the plane of our galaxy runs horizontally through the middle with the bulging Galactic Center at image center. Below and right of center are the Milky Way’s satellite galaxies, the Magellanic Clouds. The Andromeda galaxy is just below center about 1/6 of the way from the left edge. Also visible are bright planets (with spikes around them) and even a comet.

The Dark Energy Survey

The Dark Energy Survey  aims to answer that question, and UCL, Cambridge and other UK astrophysicists are heavily involved in the collaboration.This film explains the project – and features Prof. Ofer Lahav (UCL Physics & Astronomy), one of the leading figures of the DES science programme.