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I recently watched Another Earth and I would like to know what the actual distance between the two earths is, using the size of the disks as illustrated in this photo: enter image description here

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feel free to explain your downvote so I can improve the question –  sarge_smith Dec 15 '12 at 16:30
    
I didn't downvote the question but one reason to downvote would be that asking for a mathematical method for deriving the distance is probably off-topic. Asking for the distance itself would be on-topic assuming it can be derived from what is presented in the movie. –  Kyle Jones Dec 15 '12 at 18:08

3 Answers 3

up vote 7 down vote accepted

To compute the distance you need to know two things, the real diameter of the object in the sky and the degrees of arc its disk subtends in your field of vision. Google says Earth's diameter is 12756.2 kilometers so we'll assume the second Earth has the same diameter.

We'll have to guess at the degrees of arc subtended because we can't know for sure without knowing at least the focal length of the lens used to make the photograph. My assumption is that the whole image covers roughly 34 degrees of arc, as if shot by a 70mm lens on a 35mm camera. The Earth in the sky covers about 11 percent of that image laterally, yielding 3.8 degrees of arc in the visual field.

Divide the diameter of the Earth by the sine of the angle subtended and you get the distance to the second Earth. Using the figures above, the result is around 190000 kilometers, which is way too close for comfort. The tides would be like tsunamis and volcanoes would be erupting worldwide on both planets. People seem not to be running and screaming in the movie trailer, so I assume these effects were ignored in the movie.

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+1 | I was going to do the same things you did. I got a picture of the Earth from the Moon and compared the two images. I assumed it was within the orbit of the Moon as well. Nice work! –  Thaddeus Dec 15 '12 at 19:59
    
Mmmm math. Yum yum yum –  OghmaOsiris Dec 16 '12 at 22:24

Looks closer than the moon. Earth radius is about 3.6 times moon radius, so at same distance, earth should appear 3.6 times as large. In pic, earth looks at least 8 times bigger, so half lunar distance, or so. Incidentally, that'd destabilize the heck out of the moon's orbit. We'd probably end up extinct.

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We have another moon in the picture, which we could use as a reference, but we can't tell from the picture whether it is our moon or Another Earth's moon. We especially can't tell because both are full, which means that the sun should have already set and be behind the camera, but it appears to be still light and to the right--look at the bars on the fence on the left of the image.

We know that the ratio of the diameters of the earth to the moon is 3.67, and if you measure carefully you find that in the picture the ratio is about 7.3. So if that's our moon, it's twice as close--190 thousand km. In contrast, if that's their moon, then they are twice as close to us as their moon is to us. Since their moon is ~384000 km from them, that means they're 384000 km from us (and their moon is 768000 km from us).

I slightly favor the latter interpretation since given that the sun is to the right, there's no way that the objects in view are on or near the ecliptic as our moon is. But really, either way, the moon and other Earth should be only partially full, so without that being correct there's no good way to know what is supposed to be depicted.

(Note also that the second earth is almost exactly the same diameter as the person is tall, so we can infer with a high degree of certainty that the other Earth is about 7,500x farther away than the person is.)

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Given the lighting issues, I'd guess the writers/effects people just didn't pay much attention and forgot the other Earth has a moon as well... –  Izkata Dec 16 '12 at 21:23
    
@Izkata I assumed the moon next to the other Earth belonged to the other Earth. It's present every time we see the other Earth, at least in the movie trailer. The size and separation from the other Earth would vary depending on where the second moon was in its orbit. –  Kyle Jones Dec 16 '12 at 22:25

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