In anticipation of a holiday gift, I kept asking members of my research team every week whether they noticed any anomalous object among the nearly hundred thousand objects imaged by the Galileo Project Observatory at Harvard University over the past couple of months. The reason is simple.
Finding a package from a neighbour among familiar rocks in our backyard is an exciting event. So is the discovery of a technological object near Earth that was sent from an exoplanet. It raises the question: which exoplanet? As a follow-up on such a finding, we could search for signals coming from any potential senders, starting from the nearest houses on our cosmic street.
Summer Triangle, which consists of the three of the brightest stars in the sky–Vega, Deneb, and Altair. The Summer Triangle is high overhead throughout the summer, and it sinks lower in the west as fall progresses. For this star hop, start from brilliant blue-white Vega (magnitude 0), the brightest of the three stars of the Summer Triangle.
From Vega, look about 15 degrees west for the distinctive 4-sided figure in the centre of Hercules known as the keystone. On the north side of the keystone, imagine a triangle pointing to the north, with the tip of the triangle slightly shifted toward Vega (as shown in the chart below). This is the location of M92.
The opportunity for a two-way communication with another civilization during our lifetime is limited to a distance of about thirty light years. How many exoplanets reside in the habitable zone of their host star? This zone corresponds to a separation where liquid water could exist on the surface of an Earth-mass rock with an atmosphere. Also known as the Goldilocks’ zone, this is the separation where the temperature is just right, not too cold for liquid water to solidify into ice, and not too hot for liquid water to vaporize.
So far, we know of a dozen habitable exoplanets within thirty light years (abbreviated hereafter as `ly’) from Earth. The nearest among them is Proxima Centauri b, at a distance of 4.25 ly. Farther away are Ross 128b at 11 ly; GJ 1061c and d at 11.98 ly, Luyten’s Star b at 12.25 ly, Teegarden’s Star b and c at 12.5 ly, Wolf 1061c at 14 ly, GJ 1002b and c at 15.8 ly, Gliese 229Ac at 18.8 ly, and planet c of Gliese 667 C at 23.6 ly. These confirmed planets have an orbital period that ranges between a week to a month, much shorter than a year because their star is fainter than the Sun. This list must be incomplete because two-thirds of the count is within a distance of 15 ly whereas the volume out to 30 ly is 8 times bigger. Given that the nearest habitable Earth-mass exoplanet is at 4.25 ly, there should be of order four hundred similar planets within 30 ly. We are only aware of a few per cent of them.
But even if we identified all the nearby candidate planets for a two-way conversation, they would constitute a tiny fraction of the tens of billions of habitable planets within the Milky Way galaxy. Having any of the nearby candidates host a communicating civilization would imply statistically an unreasonably large population of transmitting civilizations for SETI surveys.
Most likely, any visiting probe we encounter had originated tens of thousands of light-years away. In that case, we will not be able to converse with the senders during our lifetime. Instead, we will need to infer their qualities from their probes, similarly to the prisoners in Plato’s Allegory of the Cave, who attempt to infer the nature of objects behind them based on the shadows they cast on the cave walls.
It is better not to imagine your neighbours before meeting them because they might be very different than anticipated. My colleague Ed Turner from Princeton University, used to say that the more time he spends in Japan, the less he understands the Japanese culture. According to Ed, visiting Japan is the closest he ever got to meeting extraterrestrials. My view is that an actual encounter with aliens or their products would be far stranger than anything we find on Earth.
Personally, I am inspired by the stars because they might be home to neighbours from whom we can learn. The stars in the sky look like festive lights on a Christmas tree which lasts billions of years. A few days ago, a woman coordinated dinner with me as a holiday gift to her husband, who follows my work. At the end of dinner, they gave me a large collection of exceptional Japanese chocolates, which I will explore soon. In return, I autographed my two recent books on extraterrestrials for their kids with the hope that they would inherit my fascination with the stars.
Here’s hoping that our children will have the opportunity to correspond with the senders of an anomalous object near Earth. During this holiday season, I wish for a Messianic age of peace and prosperity for all earthlings as a result of the encounter with this gift.
Feature Image Credit: Messier 92 is one of two beautiful globular clusters in Hercules, the other being the famous M13. Although M92 is not quite as large and bright as M13, it is still an excellent sight in a medium to large telescope, and it should not be overlooked. The cluster is about 27,000 light years away and contains several hundred thousand stars. www.skyledge.net
With enormous developments in Space sciences overtaking us, it is important to refresh our understanding of orbital mechanics from a basic perspective. Agrim Arsh, a young amateur enthusiast provides an easy-to-understand piece.
The curiosity to learn about our place and purpose in the Universe prompted us to look at it through sceptical eyes, and understand it through the scientific method of observation and application. We made models to explain the occurrences that we observed and continually refined them to make them fit our observations and worldview.
The earliest models of the Universe known to us were those proposed by ancient astronomers, including those in Greece, India, and China. With time, the models of the Universe have changed much in acceptance and prominence— from the Platonic Geocentrism that saw major additions from Eudoxus and Hipparchus, to the Ptolemaic model (Plato’s geocentric model with refinements), after a lengthy period, the Copernican Heliocentric Model and finally, our present models of the Universe, the most widely accepted currently being the ∧CDM Model (Lambda cold dark matter model) where ∧ refers to the cosmological constant, a constant coming into the model from the Einstein Field Equations.
But to understand astronomy, we must first understand the motions of the Earth. And as for every motion, we must choose a reference frame (observer) for our motion. So let’s understand the motions of the Earth concerning certain reference frames.
Relative to the Sun, there are three main motions of the Earth— Revolution (orbital motion), Rotation (rigid-body motion), and Precession (motion of the axis of rotation). The motion of the Earth is very much similar to the motion of a top always acted upon by a normal force.
Revolution
Revolution refers to the actual displacing motion of the Earth around the Sun. The path followed by the Earth is an ellipse, with the Sun situated at one of the foci. Amongst other properties of an ellipse is the fact that the sum of the distances of any point on the ellipse from the two foci is constant.
Image: All (that is needed) about ellipses (made with Geogebra)
If the Sun is placed at A, then the distance of the planet ranges from AF to AE. The planet is farthest from the Sun at F. This point is called the ‘Aphelion’, while the point E where it is closest to the Sun is called the ‘Perihelion’ (for any general body, these points are called ‘Periapsis’ and ‘Apoapsis’ and for the Moon, they are called ‘Perigee’ and ‘Apogee’ respectively).
[Proof¹ for the mathematically-inclined reader (requires calculus):
We can write the force equation for the planet in its orbit as:
and in calculus form:
We can eliminate ω with the help of the equation obtained from the conservation of angular momentum. Henceforth, we obtain:
This second-order differential equation can be solved by substituting u for 1/r and ɵ (angle) for t:
As you might know, the solution of this kind of differential equation is of the form A sin ɵ + C for some parameters. Similarly, this equation yields:
where A is a parameter depending on the initial conditions. This equation satisfies the polar equation of an ellipse (see image on ellipse). This proves the orbital path of planets to be an ellipse. ]
This law was put forth by Kepler (proof was given by Newton) and is known as Kepler’s First Law of Planetary Motion. Kepler’s Second Law states that the line separation vector between the Sun and the planet sweeps equal areas in equal intervals of time, i.e.
Kepler’s Third Law states that the square of the time of revolution of a planet is directly proportional to the cube of its semi-major axis:
Choosing T in years (specifically, Julian Year; 1 Julian year=(exactly) 365.25 days), and R in AU (astronomical unit, defined as the distance between the Earth and Sun; approximately 149.6 million km), the constant of proportionality equals 1.
Problem (for the mathematically inclined): Prove the above two results.
The Earth’s eccentricity is quite small (about 0.0167) and very slightly variable, as the Earth is affected by the gravitational forces of other Solar System Objects in its orbit. The plane of the orbit of a planet around the Sun is known as the Orbital Plane and is not necessarily the same for all the planets and moons (in fact, it is extremely rarely the case so). For example, the orbital plane of the moon is inclined to that of the Earth at about 5°.
All the planets revolve around the Sun in a counterclockwise direction when viewed from the top because this was just the way remnant material and accretion disk from the solar nebula started spinning, by chance, during the birth of the Solar System.
Earth’s one tropical year, defined as the time taken by the Earth to reach the same spot in its orbit again, is 365 days 5 hours 48 minutes 46 seconds with minute variations.
Rotation
Rotation is the rigid-body motion of the Earth, i.e. its motion on its axis. The plane passing normally to the line connecting the Earth’s pole and through its center of rotation, the Equatorial Plane, is inclined to its Orbital Plane at an angle of about 23.4° which is responsible for the change in seasons on the surface depending on which side of the Earth faces the Sun.
So what’s the Earth’s period of rotation? 24 hours? Some might be a “bit more accurate” and say 23 hours 56 minutes 4 seconds. In fact, both are right, depending upon the definition:
Image: Completion of a Sidereal Day (pos. 2) compared to the completion of a Solar Day (pos. 3) (in source: Wikimedia Commons, licensed under CC BY-SA 3.0
1 Sidereal Day is defined to be the time taken for a general star to come to a specific position in the night sky again and is equal to approximately 23 hours and 56 minutes. 1 Solar Day, on the other hand, is defined to be the time taken for the Sun to come to a specific position in the sky again and is equal to about 24 hours. How? Let’s not forget to count in the effect of the Earth’s revolution when calculating the period for a day with the help of the Sun. We know the Earth takes about 365 days to complete a revolution (360°) around the Sun. This means that in a day, it has covered (360°/365≈0.986°) in its orbit. This means that the Sun needs to cover 0.986° more to be at the same position it was the day before. Therefore, the difference in time between 1 Solar Day and 1 Sidereal Day = (0.986°/360°)×24 hours ≈ 0.066 hours ≈ 4 minutes. This is what we see as the “extra daytime” in 24 hours of the solar day. It is due to this difference in solar and sidereal timekeeping that we see the appearance of zodiac changes in the night sky.
Furthermore, the length of the Solar Day is also variable! Remember that Second Law given by Kepler in the previous section. That implies that the Earth revolves faster when it is closer to the Sun (near the Perihelion), implying that the Sun needs to cover slightly more than 0.986° to complete 1 Solar Day, implying that the length of the Solar Day is even larger. The opposite is true in the case of Aphelion and the length of the Solar Day reduces. Presently, the Perihelion takes place on about the 3rd of January. Thus, the actual longest day for the whole of Earth takes place in Northern Hemisphere’s winters (the Southern Hemisphere residents enjoy more daylight than the Northerners!).
The Earth spins in the same direction it revolves, i.e. counter-clockwise as seen from the top. This is what is known as Prograde motion. In fact, most of the planets in the Solar System are in a prograde motion. Why? As told previously, the solar accretion, by chance, came to be spinning counter-clockwise. Thus, when the planets were formed by the lumping of this accretion material, they had to conserve their angular momenta. This sped up their rotation (just like a skater speeds up when drawing his arms together) in the prograde direction. Uranus and Venus are the only planets that spin retrograde, i.e. in the opposite direction to their revolving directions. The cause for this is thought to be collisions of these planets early on in their lives (you see, they had a pretty ‘rocky’ start), which impacted their angular momenta adversely and changed their directions of motion.
Another interesting corollary of celestial motion is that the period of rotation of some satellites might be in sync with their period of revolution. This is what is known as ‘tidal locking’. This is an effect of the barycentre’s (center of mass’) gravitational effect on the satellite.
Image: Mechanism of Tidal Locking— The central body generates a gravitational torque on the satellite that stresses mass along the orbital direction of the satellite. The changed angular momentum as a result of this gravitational torque synchronizes the rotation period and the revolution period in a 1:1 ratio (for orbits with low eccentricity). For periods with a large tidal effect and eccentricity of orbits, the synchronization is not in a 1:1 ratio, but other simple ratios like 3:2 are more stable, for example in the case of Mercury’s tidal locking around the Sun. The given image shows the net torques about the surface of the body (in Public Domain.
You might have heard that we see only one side of the Moon. This is a result of the Tidal Locking of the Moon around the Earth in a 1:1 ratio. With repeated observation, about 59% of the Moon is visible from the Earth, due to the effects of liberation (change in perspective from different locations).
Precession and Fine Adjustments
A lot of the figures above are reported to be only a neat approximation. The reason for this is that these figures might undergo a slow periodic change. The cause of this change is the third type of motion of the Earth, Precession. Axial Precession is defined as the circular motion of the Earth’s axis of rotation. It is caused because of the gravitational effects of the Sun and the Moon on the equatorial bulge of the Earth (the shape of Earth). The Earth ‘precesses’ once in about 25,772 years. It is responsible for a large number of fine effects in the motions of the Earth.
Image: Axial Precession of the Earth (in Public Domain)
Because of the Precession of the Earth, the time of the seasons has been slowly changing. If the currently accepted Calendar Year would have been equivalent to the Solar Year, then in some time, Christmas in the Northern Hemisphere would have been celebrated in the heat of summer in July. This is known as the ‘Precession of the Equinoxes’. However, this situation is avoided because the Gregorian Calendar is based on the seasons themselves. However, precession will have a clear effect on the climate of the Earth. As of the present, the perihelion lies during the winter of the Northern Hemisphere, making them less severe and the summer of the Southern Hemisphere more severe. However, in some time, this will reverse, resulting in more severe winters in the Northern Hemisphere.
Axial Precession also changes the star alignment on the Earth. Our pole star will change from Polaris to Vega and then to Thuban before coming back to Polaris within the next 26,000 years.
There is also an Apsidal Precession of the Earth— changes in the shape of its elliptical orbit (its eccentricity) due to fine adjustments (gravitational effects of other planets), resulting in an approximately 112,000-year cycle.
This is not all. The precessional trajectory of the Earth is also not a perfect circle, but a kind of wavy one. This causes a periodic change in the axial tilt of the Earth. The resulting motion of ‘wavy precession’ is what is known as Nutation.
Image: Earth’s rigid-body motions: Rotation, Precession, and Nutation (in Public Domain)
Thus, quoting my previous sentence, the Earth’s motion is pretty much like the spinning of a top— rotation, precession, and nutation. However, there are also a large number of very, very fine adjustments in these periods, as an exactly precise measurement requires a solution to the ‘Three-Body Problem’ (more on it in later articles).
So this was pretty much everything about the motion(s) of the Earth from the Reference frame of the Sun, and as a rigid body on its own. In the next article, we will take this idea further and will look through the motions of other celestial bodies with different frames of reference.
All images used are in the public domain otherwise stated.
Thousands of galaxies flood this near-infrared image of galaxy cluster SMACS 0723. High-resolution imaging from NASA’s James Webb Space Telescope combined with a natural effect known as gravitational lensing made this finely detailed image possible.
Image Credit: NASA and STScI
Professor Avi Loeb, head of the Galileo Project and founding Director of Harvard University’s – Black Hole Project writes about the first pictures from NASA’s revolutionary James Webb Telescope. This article is published earlier in Medium.
From its vantage point L2, located a million miles away from Earth, the Webb Telescope just started to unravel new insights about the Universe. What is most exciting about the latest data caught in the “spider web” of the 18 hexagonal segments of its primary mirror?
The new Webb data shows evidence for water vapor, hazes and some previously unseen clouds, on the gas-giant planet WASP-96b. The planet’s mass is half of Jupiter’s mass and it transits in front of its star every 3.4 days, allowing a small fraction of the star’s light to pass through its atmosphere and reveal its composition to Webb’s instruments. This planet is not expected to host life-as-we-know-it because it does not possess a thin atmosphere on top of a rocky surface, like the conditions on Earth.
The image shows numerous red arcs stretched around a cluster of galaxies, named SMACS 0723, located about 5 billion light years away. NASA-administrator Nelson noted: “Mr President, we’re looking back more than 13 billion years”, an unusual statement to be heard in the household of DC politics which makes plans on a timescale of four years.
But there was also a “deep image” of the cosmos that was released in a dedicated White House event, hosted by President Biden and vice-President Harris. The image shows numerous red arcs stretched around a cluster of galaxies, named SMACS 0723, located about 5 billion light years away. NASA-administrator Nelson noted: “Mr President, we’re looking back more than 13 billion years”, an unusual statement to be heard in the household of DC politics which makes plans on a timescale of four years.
These amazingly sharp arcs were observed thanks to the unprecedented angular resolution of Webb’s optics. They feature ancient small galaxies from early cosmic times which happened to lie behind the cluster so that their images were deformed by the effect of gravitational lensing. Clusters of galaxies, like SMACS 0723, contain a concentration of about a thousand Milky-Way-like galaxies, buzzing around at five per cent the speed of light or a thousand miles per second. Most of the cluster mass is made of dark matter, an invisible substance which fills the dark gaps in Webb’s image. The luminous cores of galaxies are like fish swimming in a container filled with transparent water, bound together by gravity — which serves as the “aquarium” walls.
Ever since Fritz Zwicky observed clusters of galaxies in 1933, we know that most of the matter in them is invisible. While Zwicky inferred that dark matter must exist in order to bind the fast-moving galaxies, the same gravitational potential well can be probed directly through its lensing effect on background galaxies.
The Webb Telescope achieves unprecedented sensitivity to the faint galaxies that produced the first light during the dark ages of the Universe, hundreds of millions of years after the Big Bang. Its unprecedented ability to peer back in time stems from its observing site far away from the glowing terrestrial atmosphere, the area of its “light bucket” being 7.3 times larger than that of the Hubble Space Telescope, and its high sensitivity to the infrared band into which starlight from early cosmic times is redshifted.
In its released “deep image”, the 10 billion dollars Webb Telescope, is aided by the natural gravitational lens of SMACS 0723, graciously provided to us for free. The cluster lens magnifies distant sources behind it by bending their light. The combination of the Webb telescope and the cluster’s magnifying power allows us to peer deeper into the universe than ever before.
In a paper from 1936 titled “Lens-Like Action of a Star by the Deviation of Light in the Gravitational Field”, Albert Einstein predicted that a background star could be gravitationally lensed into a ring if it is located precisely behind a foreground star. This “Einstein ring” is an outcome of the cylindrical symmetry around the lens. A cluster of galaxies is not perfectly symmetric and so sources behind its center are lensed into a partial ring, or an arc — as evident from Webb’s image.
In 1992, I entered the neighboring office of Andy Gould, a postdoctoral fellow at the Institute for Advanced Study at Princeton, where Einstein wrote his lensing paper. Andy worked extensively on gravitational lensing by compact objects, considering the possibility that the dark matter is made of them. I asked Andy whether he ever considered the contribution of a planet to the lensing effect by a star. Andy responded promptly: “planets have a negligible mass relative to their host star and so their impact on the combined lensing effect would be negligible.” I accepted the verdict of the local lensing expert and retreated quietly to my office. Ten minutes later, Andy showed up in my office and said: “I was wrong … the Einstein ring radius of planets scales as the square root of their mass and so their effect is measurable and could serve as a new method for discovering planets around distant stars. Let’s write a paper about that.” And so we did in a paper titled: “Discovering Planetary Systems Through Gravitational Microlenses.” Today, gravitational lensing is the main method by which planets are discovered around distant stars where the transit method is less practical because the stars are too faint.
This anecdote from thirty years ago weaves together the themes of the two Webb images that were just unraveled.
A decade ago, I wrote two textbooks, one titled: “How Did the First Stars and Galaxies Form?”, and the second co-authored with my former graduate student, Steve Furlanetto, titled “The First Galaxies in the Universe”. Both books described theoretical expectations for what the Webb telescope might find in the context of the scientific story of Genesis: “Let there be light”. Last year, I co-authored a textbook with my former postdoc, Manasvi Lingam, titled: “Life in the Cosmos”. There is no doubt that I would be glad if the forecasts in these textbooks will be confirmed by future Webb data. But even better, I would be thrilled if Webb’s data will surprise us with new discoveries that were never anticipated.
This landscape of “mountains” and “valleys” speckled with glittering stars is actually the edge of a nearby, young, star-forming region called NGC 3324 in the Carina Nebula. Captured in infrared light by NASA’s new James Webb Space Telescope, this image reveals for the first time previously invisible areas of star birth.
Called the Cosmic Cliffs, Webb’s seemingly three-dimensional picture looks like craggy mountains on a moonlit evening. In reality, it is the edge of the giant, gaseous cavity within NGC 3324, and the tallest “peaks” in this image are about 7 light-years high. The cavernous area has been carved from the nebula by the intense ultraviolet radiation and stellar winds from extremely massive, hot, young stars located in the center of the bubble, above the area shown in this image.
In view of our upcoming event on ‘Scramble for the Skies: The Great Power Competition to control the Resources of Outer Space’, TPF is happy republish this old but excellent article under the Creative Commons License 4.0. Establishing outer space colonies and ‘mining the moon’ is a very distinct possibility in the near future. However, commercial scale of this process may take decades. Space resources, in terms of materials to be mined, will become the major focus in the coming decades.
This article by Paul K Byrne was published originally in The Conversation.
If you were transported to the Moon this very instant, you would surely and rapidly die. That’s because there’s no atmosphere, the surface temperature varies from a roasting 130 degrees Celsius (266 F) to a bone-chilling minus 170 C (minus 274 F). If the lack of air or horrific heat or cold don’t kill you then micrometeorite bombardment or solar radiation will. By all accounts, the Moon is not a hospitable place to be.
Yet if human beings are to explore the Moon and, potentially, live there one day, we’ll need to learn how to deal with these challenging environmental conditions. We’ll need habitats, air, food and energy, as well as fuel to power rockets back to Earth and possibly other destinations. That means we’ll need resources to meet these requirements. We can either bring them with us from Earth – an expensive proposition – or we’ll need to take advantage of resources on the Moon itself. And that’s where the idea of “in-situ resource utilization,” or ISRU, comes in.
Underpinning efforts to use lunar materials is the desire to establish either temporary or even permanent human settlements on the Moon – and there are numerous benefits to doing so. For example, lunar bases or colonies could provide invaluable training and preparation for missions to farther flung destinations, including Mars. Developing and utilizing lunar resources will likely lead to a vast number of innovative and exotic technologies that could be useful on Earth, as has been the case with the International Space Station.
As a planetary geologist, I’m fascinated by how other worlds came to be, and what lessons we can learn about the formation and evolution of our own planet. And because one day I hope to actually visit the Moon in person, I’m particularly interested in how we can use the resources there to make human exploration of the solar system as economical as possible.
A rendering of a possible lunar habitat. credit: Eos.org
Many countries have expressed a renewed desire to go back to the Moon. NASAhas a multitude of plans to do so, China landed a rover on the lunar farside in January and has an active rover there right now, and numerousothercountrieshave their sights set on lunar missions. The necessity of using materials already present on the Moon becomes more pressing.
Anticipation of lunar living is driving engineering and experimental work to determine how to efficiently use lunar materials to support human exploration. For example, the European Space Agency is planning to land a spacecraft at the lunar South Pole in 2022 to drill beneath the surface in search of water ice and other chemicals. This craft will feature a research instrument designed to obtain water from the lunar soil or regolith.
It’s worth noting that the Moon may not be a particularly suitable destination for mining other valuable metals such as gold, platinum or rare earth elements. This is because of the process of differentiation, in which relatively heavy materials sink and lighter materials rise when a planetary body is partially or almost fully molten.
This is basically what goes on if you shake a test tube filled with sand and water. At first, everything is mixed together, but then the sand eventually separates from the liquid and sinks to the bottom of the tube. And just as for Earth, most of the Moon’s inventory of heavy and valuable metals are likely deep in the mantle or even the core, where they’re essentially impossible to access. Indeed, it’s because minor bodies such as asteroids generally don’t undergo differentiation that they’re such promising targets for mineral exploration and extraction.
Artist’s impression of In Situ Resource Utilisation. Credit: Universe Today
Lunar formation
Apollo 17 astronaut Harrison H. Schmitt standing beside a boulder on the lunar surface.NASA
Indeed, the Moon holds a special place in planetary science because it is the only other body in the solar system where human beings have set foot. The NASA Apollo program in the 1960s and 70s saw a total of 12 astronauts walk, bounce and rove on the surface. The rock samples they brought back and the experimentsthey left there have enabled a greater understanding of not only our Moon, but of how planets form in general, than would ever have been possible otherwise.
From those missions, and others over the ensuing decades, scientists have learned a great deal about the Moon. Instead of growing from a cloud of dust and ice as the planets in the solar system did, we’ve discovered that our nearest neighbor is probably the result of a giant impact between the proto-Earth and a Mars-sized object. That collision ejected a huge volume of debris, some of which later coalesced into the Moon. From analyses of lunar samples, advanced computer modeling and comparisons with other planets in the solar system, we’ve learned among many other things that colossal impacts could be the rule, not the exception, in the early days of this and other planetary systems.
Carrying out scientific research on the Moon would yield dramatic increases in our understanding of how our natural satellite came to be, and what processes operate on and within the surface to make it look the way it does.
The coming decades hold the promise of a new era of lunar exploration, with humans living there for extended periods of time enabled by the extraction and use of the Moon’s natural resources. With steady, determined effort, then, the Moon can become not only a home to future explorers, but the perfect stepping stone from which to take our next giant leap.
Summer Triangle, which consists of the three of the brightest stars in the sky–Vega, Deneb, and Altair. The Summer Triangle is high overhead throughout the summer, and it sinks lower in the west as fall progresses. For this star hop, start from brilliant blue-white Vega (magnitude 0), the brightest of the three stars of the Summer Triangle.
From Vega, look about 15 degrees west for the distinctive 4-sided figure in the centre of Hercules known as the keystone. On the north side of the keystone, imagine a triangle pointing to the north, with the tip of the triangle slightly shifted toward Vega (as shown in the chart below). This is the location of M92.
