Space Oddity

by zebra on 16 October 2012 · 9 comments

Just when I was reflecting that a post on the Mule was long overdue and I really should get on to writing something, guest poster James Glover has come to the rescue to share his reflections in a guest post on space jumping.

You may have seen media reports of “Fearless” Felix Baumgartner, an Austrian, who takes BASE jumping to a whole new level (literally). He ascended to a height of 40km over the US in a helium balloon and then free-jumped back to Earth, eventually landing safely and breaking several long held records in the process. What I found curious when I looked at the photos though was how far away from the Earth he looked. You might disagree, after all 40km is a long way up. Curiously it is just under the standard distance for a marathon (42km). Humans though have a curious mental process aberration –  vertical heights appear much more significant than horizontal ones. That’s why we get scared at the top of a 20m building but think nothing of that as a horizontal distance. If I said a man had just run 40km you’d think him a marathon runner and not having just completed a singular feat of human daring, unless you were actually at Marathon on Greece in 490BC when the first “marathon” supposedly took place.

In fact given the Earth has a radius of 6,400km, 40km represents less than 1% of that. If the Earth were a globe 30cm across (I hear that such things exist!) then his jump would be from a height of 1mm. From that height the Earth is still pretty up close and in your face. By comparison the International Space Station or ISS has an average height of 360km and that is considered to be only in “near Earth orbit”. That vision you see of astronauts floating around the ISS in zero-g isn’t because they are outside the Earth’s gravitational field. At 360km gravity is 90% what is in on the Earth’s surface. They float because the orbital velocity of the ISS, about 7.7kms-1, needed to stop it falling, means they are in free fall – albeit on a trajectory that means they don’t head straight down.

I have been on a bit of an Earth geometry kick lately so I applied some trigonometry to this problem. Firstly I worked out that at 40km the angle the Earth subtends to a viewer is 167 degrees, compared to 180 degrees at the surface. By contrast at the moon (distance from Earth approximately 380,000km) the angular width of the earth is 2 degrees. In fact you can also show that the distance Fearless Felix could see on the Earth’s surface from (his) horizon to horizon is 1,400km or about the distance from Adelaide to Sydney. From the top of the Sydney Tower (height 260m) the horizon is about 58km away or approximately the distance to Penrith. This also explained why when in Tokyo you can see about 80% of Mt Fuji (height 3776m), from the ground, even though it is 104km away and hence well over the standard horizon. Actually I tried to see it from the top of Roppongi Tower (height 238m) and from there you can potentially see 96% of Mt Fuji. Unfortunately I got there at midday and to see it you have to get there before the smog thickens, by about 11am.

So what of the picture of the jump by Fearless Felix? Well using the same geometric principles and applying some advanced beer coasterology I think the picture is a fake. Fake in the sense that they have used a special lens to deliberately increase the apparent curvature of the Earth to make it look like he was jumping from deeeeep spaaaaace! It is the astronomical equivalent of photo shopping on a few curves to a model to improve her wow factor (though I understand, in practice, the opposite usually occurs).

Felix Jump

To see why consider the image of FF himself. Assuming he was about 2m tall I would estimate that the apparent diameter of the Earth in the photo would be about 5ff (a new astronomical unit I invented). It is possible to show that for that to be a true image the picture must have been taken at a distance of 56cm from Felix. Judging by the craft next to him my guess is it was taken at least 4m away. (If in the picture Earth was only 3ff wide it would need to have been taken at a distance of 34cm)

For that to be a true image, from 4m away, geometry shows, he would have to be not 40km but 500km above the Earth. At that height the Earth would subtend an angle of about 135 degrees which also seems to fit the picture as the human field of vision is about 120 degrees. In fact if the impression they are trying to give with the photo is that he could just see the whole image of the Earth floating in space before him, in his normal field of vision, then he would need to be at least 1,000km above the Earth, not a ground hugging 40km.

My suspicions were confirmed when I saw some vision on the tv news that night shown as FF descended. Whenever the camera pointed to the horizon it was almost flat but when it pointed straight down suddenly the Earth appeared as a ball. It is the camera lens rather than some advanced photo shopping to blame. While this does not detract from the fearlessness of Felix’s jump it is a sad indictment that the organisers of the jump felt the need to up the wow factor so as to make it seem more impressive. I guess they never learned their lesson from when NASA faked the moon landings.

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{ 9 comments… read them below or add one }

1 Magpie October 16, 2012 at 10:41 pm

Hey Zebra,

Although I can’t say that I did any calculation, I had the same nagging suspicion.

In my case, the feeling came from simply seeing the images: any footage from ISS, from NASA orbital flights (or even from people who’ve launched private unmanned balloons) shows the horizon much flatter than it could be seen from Baumgartner’s capsule.

It’s a daring feat, though.

Are you, too, interested in space?

2 Andy October 16, 2012 at 11:30 pm

Ditto. I was instantly suspicious of this.

3 Wisdomtooth October 17, 2012 at 12:04 pm

YES! I knew it!! (thanks for demonstrating it, Mule)

What’s to say the whole thing isn’t a fake?

Oh, because it’s backed by a credible institution such as… Red BULL! (are you kidding me?)

How does the NAA guy even know it was him falling, and not a fabricated image??

4 Thomas October 17, 2012 at 2:30 pm

I’ll give them the benefit of the doubt. Judging from the angle, I think the choice of lens was probably limited to some extreme fish-eye which, needless to say, generates a great deal of distorsion. So to me at least, I wasn’t surprised to see the curvature in the horizon. Also I hear that on the Concorde people can see the curvature of the earth, that’s at 60,000 ft. This fellow was at twice the altitude, so I am fairly sure the curvature could be observed. What really striked me was how black the sky above was!

5 zebra October 17, 2012 at 8:34 pm

@thomas – you raise an interesting point and one which I have in fact been thinking about for several years. What do we mean we say the Earth is more curved the higher we get? Do we really notice the Earth’s curvature? And more importantly why weren’t the ancients able to discern that we lived on a sphere (or at least a discworld) rather than an infinite flat plain? Clearly at the distance of the moon it is a perfect circle. At ground level I may agree the horizon looks the same distance in all directions but does that mean it’s a sphere? Your airline comment made me think. If we are looking out the window of a plane at altitude to the horizon and then project the circle we see onto the window can we detect the curvature???? Well it appears you can solve this problem. For smallish heights “h” (in km) above the Earth’s surface which has a radius = 6400km it is simple. Suppose we are looking out the window, which is 20cm wide, from a distance of 10cm. Then it can be shown if we held a ruler horizontally to the window so that it was tangential to the earths horizon and compared the amount the horizon had curved away at the edge of the window from the ruler, then for smallish h the formula is: y=100mm x sqrt(h/D) where D=12,800km is the diameter of the Earth.

At the cruising height of the Concorde (h=20km) we get y=4mm. That’s a 4mm drop off in 100mm so I think it would require a discerning eye to notice. At the ISS’s 360km where y=16mm in 100mm I can imagine it’s quite easy to discern. Especially as the windows are wider…

At Felix’s height of 40km, y=6mm which I think is borderline but certainly nothing like what appears in the photo.

6 Dimitar November 12, 2012 at 9:48 pm

NASA faked the moonlandings? Do you have a proof on that ?

7 Stubborn Mule November 12, 2012 at 10:00 pm

@Dimitar perhaps you missed the irony.

8 Dimitar November 12, 2012 at 10:03 pm

I didn’t. I asked because a lot of people claim that the moonlandings wass fake so I was curious if U have a proof on that. I mean, it would be interesting for me to read your opinion on that post :)

9 Thomas February 1, 2014 at 4:41 pm

Here’s an awesome video:

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