Category Archives: Space

Tesla Orbiting Earth

Credit: SpaceX.

Explanation: Last week, a Tesla orbited the Earth. The car, created by humans and robots on the Earth, was launched by the SpaceX Company to demonstrate the ability of its Falcon Heavy Rocket to place spacecraft out in the Solar System. Purposely fashioned to be whimsical, the iconic car was thought a better demonstration object than concrete blocks. A mannequin clad in a spacesuit — dubbed the Starman — sits in the driver’s seat. The featured image is a frame from a video taken by one of three cameras mounted on the car. These cameras, connected to the car’s battery, are now out of power. The car, attached to a second stage booster, soon left Earth orbit and will orbit the Sun between Earth and the asteroid belt indefinitely — perhaps until billions of years from now when our Sun expands into a Red Giant. If ever recovered, what’s left of the car may become a unique window into technologies developed on Earth in the 20th and early 21st centuries.

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Why Alien Life Would be our Doom – The Great Filter

New video by Kurzgesagt – In a Nutshell. Sharing this as it’s very interesting for all to know 🙂


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Finding alien life on a distant planet would be amazing news – or would it? If we are not the only intelligent life in the universe, this probably means our days are numbered and doom is certain.

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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.

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

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.

Star Factory Messier 17

Image Credit & CopyrightData – ESO / MPIA / OAC, Assembly – R.Colombari

Sculpted by stellar winds and radiation, the star factory known as Messier 17 lies some 5,500 light-years away in the nebula-rich constellation Sagittarius. At that distance, this 1/3 degree wide field of view spans over 30 light-years. The sharp composite, color image, highlights faint details of the region’s gas and dust clouds against a backdrop of central Milky Way stars. Stellar winds and energetic light from hot, massive stars formed from M17 stock of cosmic gas and dust have slowly carved away at the remaining interstellar material producing the cavernous appearance and undulating shapes. M17 is also known as the Omega Nebula or the Swan Nebula.

Starburst Galaxy Messier 94

Image Credit: ESA/Hubble and NASA

Beautiful island universe 
Messier 94 lies a mere 15 million light-years distant in the northern constellation of the hunting dogs, Canes Venatici. A popular target for earth-based astronomers, the face-on spiral galaxy is about 30,000 light-years across, with spiral arms sweeping through the outskirts of its broad disk. But this Hubble Space Telescope field of view spans about 7,000 light-years or so across M94’s central region. The sharp close-up examines the galaxy’s compact, bright nucleus and prominent inner dust lanes, surrounded by a remarkable bluish ring of young, massive stars. The massive stars in the ring are all likely less than 10 million years old, indicating the galaxy experienced a well-defined era of rapid star formation. As a result, while the small, bright nucleus is typical of the Seyfert class of active galaxies, M94 is also known as a starburst galaxy. Because M94 is relatively nearby, astronomers can explore in detail the reasons for the galaxy’s burst of star formation.

Charon and the Small Moons of Pluto

Image Credit: NASAJohns Hopkins U. APLSwRI

What do the moons of 
Pluto look like? Before a decade ago, only the largest moon Charon was known, but never imaged. As the robotic New Horizons spacecraft was prepared and launched, other moons were identified on Hubble images but remained only specks of light. Finally, this past summer, New Horizons swept right past Pluto, photographed Pluto and Charonin detail, and took the best images of StyxNixKerberos, and Hydra that it could. The featured image composite shows the results — each moon is seen to have a distinct shape, while underlying complexity is only hinted. Even though not satisfyingly resolved, these images are likely to be the best available to humanity for some time. This is because the moons are too small and distant for contemporary Earth-based telescopes to resolve, and no new missions to the Pluto system are planned.

Galileo’s Europa Remastered

Looping through the Jovian system in the late 1990s, the Galileo spacecraft recorded stunning views of Europa and uncovered evidence that the moon’s icy surface likely hides a deep, global ocean. Galileo’s Europa image data has been newly remastered here, using improved new calibrations to produce a color image approximating what the human eye might see. Europa’s long curving fractures hint at the subsurface liquid water. The tidal flexing the large moon experiences in its elliptical orbit around Jupiter supplies the energy to keep the ocean liquid. But more making Europa one of the best places to look for life beyond Earth. What kind of life could thrive in a deep, dark, subsurface ocean? Consider planet Earth’s own extreme shrimp.

from NASA

The Creature from the Red Lagoon

What creature lurks near the red Lagoon nebula? Mars. This gorgeous color deep-sky photograph has captured the red planet passing below two notable nebulae — cataloged by the 18th century cosmic registrar Charles Messier as M8 and M20. Just below and to the left is the expansive, alluring red glow of M8, light-years distant. By comparison, temporarily situated below them both, is the dominant “local” celestial beacon Mars. Taken late last month while near its closest approach to the Earth, the red planet was only a few light-minutes away.from NASA IFTTT