# AnalyticBridge

A Data Science Central Community

# Job interview question: what is wrong with this picture?

Earth and Moon seen from 1 billion miles away:

There is no way this picture is taken from 1 billion miles away. Or if it is, this is a huge zoom in, maybe by a factor 500, on the original NASA picture.  First, 1 billion miles is 5,000 times the distance between Earth and moon. So Earth and moon should appear as one single dot and be indistinguishable. Second, could you see a celestial body the size of Earth 1 billion miles away from Earth, from your home? No way: Saturn is about 1 billion miles away from Earth (at its closest), far bigger than Earth, and never visible with the naked eye.

In addition, there should be thousands of stars, much more shiny than Earth, visible in the picture. Where are all these stars??

Note posted on August 17, 2013: Saturn can actually be seen from Earth with the naked eye. The statement that it is not, is erroneous. Also, the question is not properly formulated due to a translation issue from French to English (read comments below for detail). The question would make sense if Earth and Moon seen from a billion miles was replaced by Earth and Moon seen with the naked eye, from a billion miles (which is what the author meant) and the image shown by the interviewer to the interviewee is the image posted in this article (where Earth and Moon are 1 centimeter apart), not the original image, where Earth and Moon are far less than 1 millimeter apart.

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### Replies to This Discussion

It is clear that those who posted this picture never lived a billion miles away from Earth, and have a very Earth-centric point of view. I would think that Earth, seen from one billion miles away (that is, about one billion miles away from the sun) would appear very close to the sun, and obscured by the sun's glare. Just like you can't see Mercury from Earth (with the naked eye) because it's too close to the sun.

I am not an astronomer or anything, but neither the Earth nor the Moon emit light, they at most reflect the light they receive from the Sun and probably from such a distance  (1 billion miles away) could not possibly be this bright . . .

Could it be two space rocks, fairly close to the camera (the camera itself located genuinely a billion miles away from Earth), mistaken for Earth and Moon?

It is deceptively presented as "a view from one billion miles away" in the press, but it is a magnified image, the colors/brightness have been added, Earth and moon sizes are artificially exaggerated,  and all sorts of image processing, making it appearing indeed  as "a view from a few million miles", despite being truly taken from a billion miles away.

If it was really a natural (unprocessed) "view from a billion miles", the sky would be covered with tons of stars, and both Earth and moon would be totally invisible. It would not be published, or if it was, would generate very little traffic. In short, it's just hype used for marketing purposes. The same picture could have been taken from 10 million miles away (or far that matter, even from 800,000 miles away if instead of a zoom in, you used a zoom out).

The image was magnified 5x to make it easier to see, but you could indeed see the earth and the moon in the original image, because it was through a hi-resolution camera. The brightness was altered because the brightness of the earth exceeded the sensory range of the narrow angle lens. They used the brightness readings from the wide-angle lense to calibrate. The "all sorts of image processing" is the standard stuff done with Cassini (and other probe) images, as they use multiple shots with different filters to maximize the capabilities of their sensors.

The notion that the sizes exaggerated assumes that the picture is somehow to a particular scale. That seems like a pretty crazy notion considering it is a digital image appearing on a variety of displays with varying rendering algorithms and pixel densities, let alone the fact that most photos we get these days from NASA/JPL are very high resolution.

There aren't a lot of stars visible because the earth & moon are a fair bit brighter (or more accurately, their reflection of the Sun's light is a fair bit brighter) than most in the surrounding area, which at 1 billion miles away with that much distance between the earth and the moon, is actually a very small portion of space. Even if there were a broader view of the sky, there actually aren't that many stars that could compare to the earth and the moon. Keep in mind that Saturn is almost as bright as the brightest stars in our skyline, and the light from it has traveled from our sun to Saturn and back. One should expect light that bounced off the earth towards Saturn to be significantly stronger.

That the picture was taken from a billion miles away is indeed significant. No one else has been able to get such a technologically capable sensor so far away from earth to take such a photo. It no doubt generated a disproportionate amount of public interest for the obvious reasons, but if anything the lack of interest in the other work from the Cassini probe is far more artificial than the response to this photo.

There seems to be an assumption here that if the picture does not match exactly the full view a human might see if gazing out in the direction of the earth from one billion miles away, that there is something "wrong" with the photograph. By that measure, one should throw out all photos you've ever seen from the space program, not to mention pretty much every photo you've ever taken (particularly any digital photo with JPEG compression). They're all "wrong".

The photo is a composite drawn from electrical signals. Those signals came from light that travelled nearly a billion miles from earth, which then generated electrical charges on CCD's, which were then combined, processed, colour translated, brightness corrections were made, filtered, compressed, etc., before being sent to your computer screen, where they were again decompressed, filtered, colour corrected, brightness adjusted, etc. The process is very similar to what takes place when you take a photo with a digital camera and then display it on your screen, though perhaps with better technology (the Cassini CCD's and lenses were pretty state of the art in the early 90's, but a lot of progress has been made since then).

I'm kind of shocked with the boldness of stating, "there is no way this picture is taken from 1 billion miles away." when in fact the evidence shows it was taken from just under 900 million miles away and common sense dictates that it wouldn't look much different if it were taken from 1 billion miles away.

As an interview question this is about as worthy as, "please explain the top five ways we know the Apollo 11 landing was fake" or "please explain how a banana is proof of intelligent design".

Christopher, I think you did not get the message that I am trying to communicate. Newspapers publish an image with two circles about  1 cm apart, the radius of the bigger circle is about 0.5 mm, the background is all dark, and they write "Earth and moon seen from a billion miles". Critical judgment (which is what the hiring manager is testing here) would suggest that it does not add up and that there are multiple discrepancies. The hiring manager most likely would draw the picture on a piece a paper anyway, the fact that the device that took the picture was truly 1 billion miles away does not matter. What is misleading is either the title or the image, there is a conflict between both of them. The purpose of the exercise is to assess whether a candidate takes for granted any nonsense journalists publish in a newspaper without any questioning at all.

Of course I know and everybody know that the camera was really a billion miles away, but that's not the point. Likewise, if someone would publish a great, detailed picture of (say) Pluto and wrote "Pluto as seen from Earth" but indeed seen from Earth using a powerful telescope, false colors and other enhancements, wouldn't you say that the story is misleading?

To put it differently, why showing an image of the moon and Earth, which everybody knows, with a bit of computation (the purpose of this job interview question) that they are invisible with the naked eye from such a distance? Why not showing an image of the Sun (probably visible with the naked eye) or details of Saturn rings? That would be much more interesting than an image of Earth that could as well.have been taken from 10,000,000 miles away. Or why not rename the title as "magnified image of Earth from a billion miles" or "Earth as seen through xyz device 1 billion miles away".

I probably wouldn't hire anyone who thinks that the picture is somehow a human's view from 1 billion miles away... but then again, I'm not sure I'd hire someone who thought that was what the headline suggested.

Actually, the real story is quite interesting . . .  http://www.jpl.nasa.gov/news/news.php?release=2013-229.

The picture is a real picture taken by the Cassini space craft, using the wide angle lens.  Presumably, the image is quite magnified.  I wonder if the blue in the blue fuzzy dot is true color -- after all, the earth would probably have a blueish tint from so far away.

This, apparently, is one of the most distant photos of the earth ever taken (at last that shows the moon as a separate entity).  The earth would need to be "on the other side of the sun" relative to Saturn, when the photo was taken, in order for it to be so bright (it is reflecting back the sunlight).

From a billion miles, or from a trillion quadrillion miles, or from a far away galaxy, with the naked eye, Earth can't be seen. Even by the human being with the best vision and night sky navigating skills.

It would be interesting to see when (how far) Earth becomes invisible for 99% of human beings. Is it from 100 million miles away? I'm sure simulations could be done, to render Earth as it would be seen from any distance, ranging from a few million miles to a billion miles away.

It would also depend on a number of factors, such as the position of the sun, the Earth and you. What would be the best configuration for Earth to be seen with the naked eye from as far away as possible?

I will just address this one statement "Saturn is about 1 billion miles away from Earth (at its closest), far bigger than Earth, and never visible with the naked eye" and not address its relation to the original question at hand (Saturn being much larger than Earth, etc.).

Maybe you have really bad eyesight or have never been outside of a heavily light-polluted area, but Saturn, with apparent magnitude in the ballpark of 0 to +1, is one of the brightest objects in the sky, and can be readily viewed from a good location by people with even mediocre vision.

Definitely, something to consider for the understanding of the perspective is the time and position in space, from where the picture was taken, besides the limitations of the technology (in an euclidean space). This reminds me when observing the Fish Tail peak-mountain of the Annapurna Range in the Himalayas, from a village named Nirmal Pokhari in Pokhara, Nepal. The Fish Tail is the highest peak of the range, however, from this perspective, it looks lower than other peaks.