Bigger than you imagine

silhouette-of-man-standing-on-rock-formation-during-sunsetInspired by a quotation from J.B.S. Haldane, I would like to say that the Universe is not only bigger than we suppose, but bigger than we can suppose. Or perhaps I should say that it is bigger than we can fully comprehend.

The Universe is big. Really, really big. Frankly, it is hard to imagine how big it is, which is why so many people have little idea of its true size. I have been teaching astronomy in one form or another for 50 years, and I remain amazed at the difficult-to-comprehend distances involved. In this time I have learned that there are many, many misconceptions about space and the Universe, but probably the most common are misconceptions about size and distance.

I think a lot of students get very limited — if not downright incorrect — instruction on this in school, and then never pursue it any future, leaving that erroneous information embedded into their brains.

Not to mention the misleading graphics often found in elementary textbooks and educational material. Here is a section of a poster I had as a child on my wall long ago. It wildly distorts the distance. It makes the planets look as if they are right next to each other, when in fact they are separated by thousands of times their own diameters. For example, on average, Jupiter is separated from Earth by more than 5,000 times its own diameter!map-of-solar-system2

To be fair, though, distances and sizes on a poster like this must be distorted to be seen. If you plotted the solar system out to Neptune on a 3-foot poster in proper scale, nothing could even be seen except perhaps a tiny dot for the Sun. We see them in the real sky because they are glowing against a black

Anyway, I’ve used many analogies to try and illustrate the topic of scale in the Universe. First off, imagine a hydrogen atom, which consists of a tiny positive proton and a negative electron. A hydrogen atom, which usually exists as part of a molecule rather than alone, is so small that it would take roughly 1.7 billion billion billion to equal an average human. The diameter of a hydrogen atom is about one picometer, which is one ten millionth of a millimeter, far too small to be seen even the best optical microscope.

Now, what if I told you that the Earth compares to the known Universe as a single hydrogen atom compares to a human? Pretty amazing, huh? Well, it’s absolutely wrong. The Universe is actually much, much bigger than that. (See note about the size of the Universe below.)

Actually, the Earth compares to the known Universe, roughly as a hydrogen atom compares not to a human, not to the entire planet Earth, but to the Sun!

The Sun is 109 times the diameter of Earth and in volume is more than a million times larger. So the Earth compares to the known Universe as a single hydrogen atom compares to the Sun. But that is just a rough comparison. Actually, the known Universe is about 43% larger. Let that sink in.

If you wish to check it yourself, here’s the data.


These figures are rounded a bit, but you should be able to see clearly that the two ratios are in the same order of magnitude (signified by the E+19, which means 10 to the 19th power!).

Within the uncertainties inherent in the data and assumptions, the ratios are essentially the same. I assume a diameter of the known universe to be twice the light time distance to the observable boundary, which makes it 27.6 light years across, or about 2.6 times 10^29 millimeters. Truth is, the Universe is actually much larger than this, and perhaps even infinite, as explained in the note below.

So indeed, the Universe is really, really big. It is so big, in fact that the only way that any of use can begin to comprehend is through a little math.


To make this more palatable, I have made some simplifications that really do not affect the overall validity of the piece. There is a good bit of variation in the way words are used, but I have used the term “known” or “observable” Universe to refer to that part of the Universe that extends out to 13.8 billion light years in all directions. That distance, 13.8 billion light years, is the light time limitation of radiation that left near the time of the Big Bang. We can directly observe objects near that boundary, but only as they were that far back in time. So I have considered that distance as the boundary, and the known universe to be sphere of 13.8 billion light years, centered on Earth.

I did this for simplicity. However, it poses two non-trivial problems. First off, everything we can detect near that 13.8 billion light year boundary was moving away from us at that time, so consequently, even though we can observe it only as it was 13.8 billion years ago (Because of the restriction of the Speed of Light), it is actually much farther away now. In fact, most current estimates are that it is about 46 billion light years away, and hence the “known” Universe is at least 37 times the size (volume) larger.

You might think that this violates Relativity and the restriction of the speed of light. But it doesn’t. Those restrictions do not apply to space itself. The dimensions of space can increase much faster than the speed of light and Einstein would be just fine with that.

The second problem is that we tend to imagine the Universe as a big sphere. That is because the limit of our vision, the “cosmic horizon” is at the same distance all around us. Imagine being at the center of a basketball, where the inside edges of the balloon are all at a set distance (around 4.7 inches!) all around. You would think that the Universe is spherical because that would be how it would appear to you. You could not see beyond it, but that would not mean the there was nothing beyond it, or necessarily that whatever lay beyond your observable Universe was spherical.

Furthermore, by definition, the Universe is “everything.” In order to properly define the shape of the Universe, you would have to get outside it. But because anywhere you could go would still be inside the Universe — it’s everything, you know — that would be impossible.


Top Photo: Creative Commons Zero – CC0

J.B.S. Haldane reference:

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Aliens, aliens everywhere, but not a one to see

Is there Life — or to be more specific — Intelligent Life elsewhere in the Universe? I don’t know, but I strongly suspect — I believe — that there is. I have no direct evidence of it, but there is a great deal of circumstantial evidence.

I might also ask, is there a black, hand-sized rock in the shape of a frog within 500 km of Olympus Mons on Mars? I believe that there is, perhaps a large number of such rocks. It is just that we know from direct observation through probes such as the Viking landers and various rovers including Curiosity, that there are many, many rocks that size on Mars. Just random processes over billions of years could easily shape them into the appearance of a frog.

But I don’t have any direct evidence. Neither do we have any direct evidence of for Life in the Universe. We know that the chemicals for life (as we know it), including water, oxygen and more complex molecules such as amino acids (building blocks for proteins) are widely distributed and abundant.

Just as you are likely to find a frog-shaped rock on Mars if you have a large enough collection of rocks to search through, it’s likely – in my opinion — that we will discover intelligent life in the Universe if we look long enough and far enough.

Current estimates are that there are at least 20,000,000,000,000,000,000,000 (2 times 1022) stars in the observable Universe. Let’s say that only one is a million of those stars has a planet on which life as we know it is even possible. Of those stars, let’s say that only one in a million actually harbors some kind of life. Then lets say that only one in a million of these stars has developed an intelligent form of life. That means that there would be 20,000 planets with advanced intelligent life in the Universe.

But if those intelligent live forms were more or less evenly distributed in the Universe, they would be millions and millions of light years apart. Given the restrictions imposed by Einstein’s Relativity (which after more that 100 years has passed every test), communications not to mention direct contact would be essentially impossible.

Just the abundance of life-building materials and the mind-blowing size of the Universe make it next to certain that there is intelligent life out there, perhaps many, many species on many, many planets in many, many galaxies. But again, we have no direct evidence.

Given that life is probably widespread, the difficulties in us discovering it boil down essentially to size and distance. Most people really don’t realize how mind-numbingly big the Universe is.

How do you compare the Earth to the Universe? To give you an idea, consider a single atom. More than a trillion atoms could fit on the head of a pin. A “trillion” is a million times a million! Now compare an atom to a human body. No, wait! Compare that single atom to the entire planet Earth. No, wait! Compare that single atom to the Sun. Yes, comparing the Earth to the Universe is roughly the same as comparing a single atom to the Sun. The Sun is roughly one million times the volume of the Earth. So I think you can see that the Universe is a very, very, very big place. (How did I come to that comparison? Watch for the next blog entry.)

So even if there are thousands or millions or even billions of advanced civilizations in the Universe, they would be separated, on the average, by almost unimaginable distances.

What if they are “nearby” and actively “listening” for our signals? Even if they are within 100 light years — the rough distance at which any other intelligence could pick up our radio transmissions — it still represents a relatively small number of stars capable of being home to an advanced civilization.

The point is simply that given the truly enormous size of the Universe and the difficulty of travel and even communications imposed by the Theory of Relativity, it remains unlikely that aliens have ever visited Earth. Combine that with the complete lack of valid evidence, and you can understand why science rejects the claims of UFOs as alien spacecraft. Anything that does not violate the Laws of Physics is possible, but that does not make it likely.


1. NASA image of the Helix Nebula,×596.jpg

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The Betelgeuse Nebula

PIA16885_hiresDue to its recent dimming and apparent change in physical size, there has been speculation that the red supergiant star Betelgeuse may be on the verge of exploding in a supernova. If that were to occur – and it really is a question of when not if – it will likely become visible in the daytime sky for a few weeks, and may shine brighter than the Full Moon at night. It could happen before I finish writing this sentence, or it could be 100,000 or even a million years in the future. Any of that is “soon” in astronomical terms. We just do not know. To be honest, I don’t really expect it in my lifetime, but who knows? It certainly prompts some speculation.

Some observers  (not I) have claimed to be able to discern the visible disk of Jupiter with the unaided human eye. At closet approach, Jupiter spans about 50 seconds of arc. I have never made this observation myself this but I do not challenge the claim. It would be just on the verge of discernability.

So, my question is, when Betelgeuse goes supernova, how long after the explosion would a nebula likely be large enough to be just visible to the unaided human eye from Earth, at least by observers of exceptional ability?

I made a few quick, simplistic calculations that ignore a number of potentially important factors, using comparison values for just one other supernova. So don’t hold me to this… they’re just guesses.

In the case of Betelgeuse, you have to make some assumptions since we do not know some basic facts with certainty. Because of its particular characteristics, it is difficult to determine the exact distance. Estimates range from about 400 to about 800 light years for the distance to Betelgeuse. I will assume 640 light years, a commonly cited figure.

Assuming also that the supernova is a type II, how big would that nebula need to be to be seen as such by the human eye?

To find the diameter of an object of 60 arc seconds (1 arc minute, just slightly larger than Jupiter at its largest apparent size from Earth) at the distance of Betelgeuse, use the small angle formula.

Angle/206265 = d/D
d = (Angle/206265) * D

where Angle is in seconds of arc, 206265 is the number of arc seconds in a Radian, d is the actual size (diameter) and D is the distance, with both d and D in the same units. Here we use arc seconds for angle and Astronomical Units (AU) for distance. So if D is the distance to the object (Betelgeuse, 640 light years (ly) or about 40473241 AU) and the angle is 60 arc seconds, the diameter of the object (nebula) would be

d = (60/206265) * 40473241 AU = 11773 AU

Assuming a Solar System (SS) diameter out to Pluto of 80 AU, we have 11773/80 = 147. Thus the nebula would need to be about 150 times the diameter of the SS.

So according to my very crude and tentative calculations, a sufficiently illuminated distended object would need to be roughly 150 times the current diameter of the Solar System out to Pluto, to subtend an angle of about 60 seconds (1 minute) of arc.

But how long would this take? According to published information on type II SN1987A (, that object expanded to about .39 parsecs (pc) or about 80442 AU in less than 25 years. Given the expansion rate of SN1987A, which may or may not be typical, that would imply to me that it would take only a few years to get to 150 Solar System (SS) diameters (.06 pc if taken out to the orbit of Pluto). However, I have no idea how long any distended nebula would be overshadowed by the brilliance of the central supernova.

1) The image is a modification of an uncredited artist’s conception from JPL/NASA found on this page:
”Image credit: NASA/JPL-Caltech”

2) Type II supernovae involve the explosion of a single supergiant star. Other types (famously the Type Ia) involve the interaction of an old white dwarf star with a companion star.

3) Others would consider the SS as extending only to the orbit of the last known major planet, Neptune, while others consider it extending to the largest known TNO (“Trans Neptunian Object”) or KBO (“Kuiper Belt Object”) or to the Oort cloud or the Heliopause or some other preferred boundary. I chose the more traditional orbit of Pluto out of convenience.

4) Please feel free to correct me if you see an error, false assumption or other problem.

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The Family: Right Wing Bastardization of Biblical Teachings



This is a bit different from what I normally post here, and if it offends, I apologize. However, I think it needs to be considered.

Watching just the first two episodes of “The Family” on Netflix, two Biblical references struck with me with a kind of “Ah ha!” feeling. It was an epiphany or a  mini-revelation if you will. I Realized that this kind of thinking may be why Trump supporters so easily dismiss outrageous, vile, hateful, racist and anti-American behavior. They think that they can use biblical stories as precedent and justify it as “God’s will” as long as it gets them what they want.

But let me state that “The Family” is based on a book of the same name by Jeff Sharlet. It is supposedly his own personal experience, about in fact could be no more than a new conspiracy theory. Judge for yourself. The show on Netflix is here:

The first Biblical reference that concerned me was Psalms 137, verse 9, which in the King James Version of the Bible, reads: “Happy shall he be, that taketh and dasheth thy little ones against the stones.”

This refers, according to the commentators (Matthew Henry et al) basically to the wish of captive Jews in Babylon as something they prophesied or wished to happen to their captors — in this particular case, the children of their captors. To many of the commentators, this is justified as an expression of “God’s will.” Or God’s “righteous revenge” if you will.

No matter how I look at this, it seems intolerant, arrogant and hateful — hardly things I would like to associate with a loving God.

The other refers to David and Bathsheba (see 2 Samuel in the Old Testament). Just to make it short, Jewish king David (the same David who killed the giant Goliath) lusted after another man’s wife (Bathsheba), with whom he subsequently commits adultery (resulting in pregnancy). He then orders Bathsheba’s husband into battle specifically so he will be killed (he is). Later, he takes Bathsheba as his wife (apparently the favorite of his many wives, and the mother of famously wise Solomon). Despite his great sin and the blood on his hands, David repented and gained back favor from the Lord. He was said, in fact, to be an ancestor of Jesus.

In any event, although David is revered in Judaism, Christianity and Islam, his story to me is dripping with violence, intolerance, racism and callousness. And yet he repented, so all is forgiven.

Actually, the idea of being unconditionally forgiven if you are contrite (and in the case of Christianity, accepting Christ as your savior) is, of course, very tolerant and appealing. However, some simply take it too far. In my younger years, I heard preachers say effectively that you could live a life of evil as long as you repented after each vile act. Some even gave the impression that sincerity — specifically, a lack thereof — was not important as long as you went through the motions. Repentance became an empty ritual, which nonetheless unfailingly dismissed a multitude of vile deeds. It was like a murderer confessing his regret and remorse and being told, “Go and sin no more” — over and over and over again.

This has long bothered me, and doubtless is in part why I am not a believer anymore. It says, in effect, that you can do anything you want — any evil or illegal or immoral thing — and all you have to say those magic words and all will be well. It justifies anything!

Although the emphasis with the Family seems to be on Jesus (they promote “Jesus,” a book of just Jesus’s saying and a concept called “Jesus plus nothing), the teachings seem to emphasize some of the more violent and questionable sections of the Old Testament.

All you biblical scholars out there are welcome to correct me if you feel that I am wrong, but this appears to say that violence, murder, even genocide, is perfectly OK if done under the aegis of “God’s will.” Anyone can say some act or proposed act is “God’s will” and if he (or she) can get enough people to follow, any manner of evil can ensue.

This goes a long way in explaining — to me at least — how Trump got elected and how his supporters (in Congress and elsewhere) can glibly dismiss his foul deeds and shortcomings, as well as their own. They can claim it is “God’s will,” using biblical precedent. And in the end, if things go badly for them, they can just say, “I repent.”

Of course, thoughtful and sincere Christians, with whom I have no argument, can argue that this is not the message to take away here. But it is a matter of interpretation, which is exactly my point. It is, I fear, what is going on in Washington and elsewhere these days. (For the record, I don’t think it actually factors into Trump’s 5th grade thinking — I don’t think he gives a flying rip one way or another as long as he gets what he wants.)

Every American, and especially those who claim to be Christian, Jewish or Islamic, who does not speak out about this, is complicit in the result, in my opinion.

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Formula 1 (race) is going to Asia’s dog meat capital. Insist they help end the horror. Please sign this letter.

Shared via Formula 1 (race) is going to Asia’s dog meat capital. Insist they help end the horror. Please sign this letter.

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Guns and Violence

It has been a while since I have posted, and this is a bit out of context from what I normally post, but I feel I need to say it.

alone animal bird clouds

Photo by Gabriela Palai on

There is a logical argument to the statement that “Guns don’t kill people. People kill people.” That is technically correct. There is a sterile logic there. But it is incomplete. It does not take into account human nature. Sure, regurgitators of this phrase frequently say that we need more mental health screenings to keep guns out of the hands of the unstable — and then they do everything in their power to prevent any regulation or any attempt to screen out potential domestic terrorists.

Get real, people. The enemies are not the poor Hispanic folks hoping for a better life any more than they are our American ancestors who fled European tyranny. The real enemies are self-entitled, feeble-minded Americans fed a toxic hatred, a fear or foreigners, by equally feeble-minded, arrogant, narrow-minded but powerful leaders. You are better than that, aren’t you? You can think for yourself, right?

My memory of a better America does not include such insane, unthinking hatred. Sure, the past is not perfect, but my memory — and my sincere hope for the future –, is that we are better than the hatred, bigotry and the arrogance of the past.

In the end, people kill people, but they use guns and other weapons designed to kill to do it. Changing human nature is the long term goal. But if we do not stop the violence soon, what will it matter? We don’t have time to change human nature. It is an admirable goal, but a misplaced priority. We have to do something to curb the violence, then work on the causes. Or start working on the causes, but put the real emphasis right now on stopping the negative — and potentially fatal for all of us — effects.

Why should you or I care? Is your largely imagined “right” to own guns or other weapons without question worth the lives of thousands of Americans and hope-to-be Americans? Is it? If you believe in an afterlife, a great reckoning, how will you answer there?

I will be dead before the final outcome, but I do not want to think that I did nothing. I don’t want to think that I just sat back and watched it happen. What do you think?

When will we wake up? “Thoughts and prayers” will not help. Standing up to evil is the only solution. The longer you do nothing, the longer you oppose reasonable solutions, the more you support hatred, the closer we are to the end of the United States of America, and perhaps to a viable world. The choice is in your hands. The decision rests with you.

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Catch Jupiter Tonight!

CaptureIf you have never observed Jupiter — or at least have never knowingly observed Jupiter — this is the time to do it. It is easy, in fact so easy that I do not have to give any detailed other than this:

If it is clear, go out tonight and look to the South-southeast at about 10 pm local time. Other than street lights and airplanes, the brightest thing you will see in the sky is Jupiter. Period, that’s it.

No fancy equipment required. That bright, start-like dot is Jupiter, the largest planet in our Solar System and currently some 641 million miles from Earth. You should also be able to see the bright star Antares a bit to the right. Antares is in Scorpius the Scorpion. (Antares is a red supergiant star, the 16th brightest star e sky. It shines at a distance of about 604 light years, or very roughly, 3.55 X 10^15  or 3.55 thousand million million miles! For more see: Antares on

Jupiter2If you have a small telescope or even a very good pair of binoculars (and steady hands), you also may be able to see several tiny star-like points of light clustered very close around Jupiter. These are its “Galilean Satellites,” so named because they were first discovered and recorded by Galileo Galilei.

By the way, even though Jupiter will be easy to see all Summer, it is at it brightest right now (June 10, 2019). The satellites (moons) of Jupiter, change their positions every night (in fact you may notice some changes from hour to hour). On some evenings you can see all four, but on others one or more may be passing behind Jupiter and out of sight. For the record, Jupiter has many more moons — currently the total is 79 — but all but these 4 are too dim to be seen without at least a medium sized telescope, and in fact quite a few are known only from space probes.

So take a look.

(Charts courtesy of Stellarium)

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Have You Never Seen Uranus?

CaptureI was going to finish that title with “I can loan you a mirror,” butt some friends told me that younger folks wouldn’t get it and it would seem too rude for others. So forget I mentioned it.

So, if you have never seen the planet Uranus (preferable pronunciation today is “YOUR’-a-nus” rather than “your-A’-nus”), then your chance is at hand. Some people have told me that I could not find it with two hands, but you can, especially if you use those two hands to hold a pair of binoculars.

You see, Uranus is just barely at the limit of human ability to see with the unaided eye, and combined with its current location in the sky and the often hazy, polluted skies we contend with, you’ll need at least a pair of binoculars.

Because of its current location near bright planet Mars, and tonight with a Waxing Crescent Moon nearby, you should be able to do it.

Assuming that it is clear enough, look to the Southwest sky tonight at 7 pm local time to see the Crescent Moon. Then you should be able to pick out bright Mars nearby. Uranus will be too faint to see with just your eyes, but should appear as a faint bluish-green dot in the position noted on the graphic.

You can try again tomorrow (Monday night), but the Moon will be farther to the East (left) and a bit higher. You should still be able to find Mars, though, and Uranus will be in nearly the same place relative to Mars.

Good luck, and the next time someone says you couldn’t find Uranus with two hands, tell them you already did.


For more, see this link on EarthSky:

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Altitude & Azimuth, All Over Again

Altitude & Azimuth diagram

Altitude & Azimuth diagram

I posted a blog about Altitude and Azimuth in early 2017 (, but I thought I would try again:

One thing that tends to give students trouble is the concept of “altitude and azimuth,” a simple way to define the position of an object in the sky. Often abbreviated as “Alt-Az”, this concept has limited value overall for astronomy, but is very useful for any outdoor observations, especially over the much more complicated coordinate systems.

Let me start by very quickly by saying that you must know your cardinal point directions before you start. If you have a compass on your phone or device, that may be of some help, but I have found them not always to be accurate. If you know the North Star (it is decidedly NOT the brightest star in the sky, despite popular opinion), you can use it to define North. If you are not familiar with the North Star, but can find the Big Dipper, you can use this piece from EarthSky about six months ago:
(Note that the diagram in this that piece on EarthSky is for early Fall. However, You can turn it upside down to get approximately the position of the Big Dipper about 7-9 pm in early Spring or mid-Winter, as we are when this blog is being published.)

Basically, it is very simple as long as you know your directions — North-East-South-West. First face due North. The point on the horizon directly in front of you is “0 degrees azimuth.” Since you are also looking straight ahead at eye level, that point is at “0 degrees altitude.” Don’t strain your neck, but look straight overhead. The point straight overhead is “90 degrees altitude.” We call it the “zenith.” Then look halfway up in the sky, still facing due North. You would be looking at a point that is “0 degrees azimuth, 45 degrees altitude.”

Now, look again straight ahead to the North on the horizon. Make a quarter turn to your right. Now you are facing due East, which is “90 degrees azimuth.” While facing this direction, look one third of the way up in the sky. That point would be at “90 degrees azimuth, 30 degrees altitude.”

Returning now to straight ahead on the horizon (East), take another quarter turn to the right and you will be facing due South. That is “180 degrees azimuth.” We’ll skip the altitude here, and then turn another quarter turn to the right, which brings you to facing due West, which is “270 degrees azimuth.” From this orientation, if you look two-thirds of the way from the horizon to the zenith, you are looking 2/3rds of 90, which is 60 degrees up. So in this case the point you are looking at is at a location of “270 degrees azimuth, 60 degrees altitude.”

Finally, if you take one more quarter turn to the right, it brings you a full 360 degree circle back to the direction from which you started, due North, which reverts back to “0 degrees azimuth.”

The diagram posted here pretty much sums it all up.

Larry Sessions

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Kepler Telescope Bids ‘Goodnight’ with Final Commands

Reprinted from the Facebook page of the Laboratory for Atmospheric and Space Physics (Boulder, CO)

On the evening of Thursday, Nov. 15, NASA’s Kepler space telescope received its final set of commands to disconnect communications with Earth. The “goodnight” commands finalize the spacecraft’s transition into retirement, which began on Oct. 30 with NASA’s announcement that Kepler had run out of fuel and could no longer conduct science.
Coincidentally, Kepler’s “goodnight” falls on the same date as the 388-year anniversary of the death of its namesake, German astronomer Johannes Kepler, who discovered the laws of planetary motion and passed away on Nov. 15, 1630.

The final commands were sent by University of Colorado Boulder student command controllers over NASA’s Deep Space Network from LASP’s Kepler Mission Operations Center.

The Kepler and K2 Missions team disabled the safety modes that could inadvertently turn systems back on, and severed communications by shutting down the transmitters. Because the spacecraft is slowly spinning, the Kepler team had to carefully time the commands so that instructions would reach the spacecraft during periods of viable communication. The spacecraft is now drifting in a safe orbit around the Sun, more than 100 million miles away from Earth.

Kepler has had a profound impact on our understanding of the number of worlds that exist beyond our solar system. Through its observations, we’ve discovered there are more planets than stars in our galaxy. The data Kepler collected over the course of more than nine years in operation will be mined for exciting discoveries for many years to come.
NASA Ames Research Center
(Image credits: NASA/JPL-Caltech)

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