The distance between London, where I live, and Oxford, where I used to live, is about 100 km (or 60 miles). It takes about 90 minutes by car and about 120 minutes by bus. I can easily make sense of that distance.
Harder to consider: the distance between the Earth and the moon, which is 384,400 km (240,000 miles). It’s a fact we’ve likely all learned in high school. Unlike the distance between London and Oxford, however, it’s not easy to comprehend what 384,400 km means in real terms.
Luckily, you don’t have to think too hard. A NASA spacecraft has solved that problem for us. In October, OSIRIS-REx, a spacecraft that’s bound to intersect an asteroid in August this year, took the photo above from about 5 million km (3 million miles) away from the Earth. NASA posted the picture on Jan. 2, providing the public with a unique view of our planet and its moon. The angle is great to get a grasp of what the distance between the two celestial bodies really looks like, but it’s not perfect.
Here’s a back-of-the-envelope calculation to explain why. For ease, we’re going to use round figures. The Earth’s diameter is about 13,000 km (8,000 miles). That means, in the 390,000 km distance between the Earth and the moon, we should be able to fit 30 Earths. But when I tried to Photoshop them in, I could only fit about 20 Earths:
Is NASA wrong? Nope.
Turns out the location of OSIRIS-REx when it took the image was not quite right. Had it been perpendicular to the line drawn between the Earth and the moon, we would have been able to fit in 30 Earths.
We can check the actual angle using high-school math. If the spacecraft, the Earth, and the moon form an obtuse triangle, then you can use this formula. Turns out the obtuse angle is about 139°, which is quite far from 90° that we would need to fit 30 Earths.
Nevertheless, it’s still a unique view of the Earth and the moon hanging in the empty black void of space. The real job of the OSIRIS-REx spacecraft is to study an asteroid, but I’m glad it turned back and took this image.