# All Alone In The Night

## Frequently Asked Questions

The song is called *Freedom Fighters* by **Two Steps From Hell**.

It was featured in the third trailer for *Star Trek* (2009).

The sequences are:

- (0:00) North-to-south down the western coast of North and South America.
- (0:48) North-to-south over Florida, the Bahamas and other Caribbean islands.
- (0:56) South-East Asia, approaching the Philippine Sea
- (1:04) Western Europe, from France through Italy, Greece, Turkey and the Middle East.
- (1:20) Aurora Australis, over the Indian Ocean, approaching Australia
- (1:36) Aurora Australis, over the Indian Ocean.
- (1:52) Aurora Australis, unknown location in the Southern Hemisphere.

The original sequences in the video were shot with each frame between 1 and 3 seconds apart. I slow down the sequences to about twice their original lengths. As a result, **1 second** of the video is about **15 seconds** of real time.

There were three main steps for this project.

- Downloading the individual high-resolution photos from NASA.
- Combining the sequences into a video file.
- Editing the sequences into the final video.

For **Stage 1**, it was a combination of custom **bash scripts** to download and request the high-resolution images, and an **FTP client** to download them from NASA.

For **Stage 2**, I used an app from the Mac App Store called **Time-Lapse** to compile each of the sequences into a single video.

For **Stage 3**, I used **Final Cut Pro X**. In particular, I used the **‘Optical Flow’** option for slowing down the sequences to about half their original speed. This helped smooth the journey, but resulted in some interesting ‘ripple’ artifacts.

The ISS’s altitude isn’t high enough to see the full curve of the earth. However, it can see a reasonably large segment of the earth, enough to see a curve on that segment. Here are some scale diagrams to help illustrate it:

Firstly, here is a scale diagram of the earth and the ISS (click to zoom in):

The red line is the visible horizon from the ISS at an altitude of **400 km**.

Next, here is an overhead view, looking down towards the ISS, with the red circle being the visible horizon from the ISS:

The red circle is the horizon, the same as the red line in the first diagram, looking down from 90º. The black **“Flat Horizon”** is a tangent to the Earth’s horizon, and is what would be visible as a straight line when looking at the horizon from the ISS. The orange lines indicate a field of view of **100º** when using a **15 mm lens** on a **35mm sensor**, as was the case for most of these sequences.

Here are the same details, from an off-centre perspective:

And here is the view you get from the ISS, looking directly at the horizon, with a field of view of 100º, which is what is present on a 15 mm lens:

And an actual photo from the ISS, taken with a 15 mm lens on a Nikon D3S, for comparison:

So, here is the math, if you want to dive in.

There are a few steps we need to take to figure this out mathematically. Here is what we know at the beginning:

- The radius of the Earth (
*R*):**6,367 km** - The altitude of the ISS (
*h*):**400 km**

Both the radius of the earth and the altitude of the ISS vary slightly depending on where you are. These numbers fit within the range.

Now, we calculate the distance to the horizon using this rule: the tangent between any point and a single point of a circle will be perpendicular to the centre of the circle. That point of tangency is our horizon, and we can calculate it using Pythagora’s classic theorum:

In our case *A* is the Earth’s radius (*R*), and *B* is the distance from the ISS to the horizon (*d*), and *C* is the distance from the ISS to the centre of the Earth (*h*):

So, we have a new value:

- The distance from the ISS to the horizon (
*d*):**2,292 km**

We can now calculate the angle between the *d* and the horizon line (*z*) (in red in the diagram):

- The angle between the ISS and the horizon line (
*z*):**19.8º**

Now, we can calculate the radius of the horizon line (*a*) and the distance between the ISS and the horizon line (*o*) like so:

- The radius of the horizon line (
*a*):**2,156.6 km** - The perpendicular distance from the ISS to the horizon line (
*o*):**776.3 km**

Knowing the radius of the horizon line and the distance of the ISS to that line means we can easily create a scale model on Earth.

If we divide the radius *o* by the ISS distance *a*, we get a ratio *y* for viewing height to the horizon radius:

We can now apply this to creating a flat circle of an appropriate scale to your eye level:

For example, if your eye level is at 6’, you can set up a circle on the ground like so:

When you stand in the centre of the circle and look at the horizon, you can see the curve of the horizon at roughly the same perspective as on the ISS.

All the sequences in the video are real photographs taken with a decent stills camera (typically a Nikon) with long exposure time. The only thing special about them is they are taken from a space station orbiting the Earth.

The original time-lapse sequences whip by pretty quickly, so I slowed them down in Final Cut Pro X using the ‘Optical Flow’ method. From the Apple website:

Optical Flow: Adds in-between frames using an optical flow algorithm, which analyzes the clip to determine the directional movement of pixels and then draws portions of the new frames based on the optical flow analysis.

Because the movement of pixels is quite rapid toward the bottom of the frame, the analysis has trouble tracking it, especially when it encounters a fixed object like the frame of the ISS. As such, you get some ‘rippling’ or ‘warping’ of the image in those areas.

Since this is a time-lapse, one might expect to see the clouds moving throughout the video. After all, we can see clouds moving from Earth in real time.

However, the ISS is a lot further away from the cloud layer than we are, and that distance changes how much movement is visible.

Cumulonimbus, or storm clouds, are at most **13 km** above us. The ISS is between **409 km and 416 km** above us, so let’s say it is **400 km** away from the cloud layer.

Let’s imagine we are taking **two square photos** of the same clouds at the same moment in time with the same type of camera - one **from earth** looking straight up, the other **from the ISS** directly above it looking straight down.

This will give us **two pyramids**, with the point being the camera, and the base being the cloud layer. Something like this:

If we calculate the dimensions of the bases, we can determine how much cloud area each photo will cover.

A typical **50 mm lens** on a **35 mm sensor** will have a field of view of about **46°**. If we divide the pyramid in two we get two right-angled triangles, so we can use some Pythagorean geometry to calculate the area of the base. Here is the formula:

*(tan(26) x h x 2) ^{2} = area of the base*

When we plug in **13 km** for the Earth-bound photo, we get an area of **122 km ^{2}**, or an

**11 km x 11 km**square.

From the ISS at **400 km**, we get an area of **115,315 km ^{2}**, or

**340 km x 340 km**of visible clouds.

That gives us a **ratio of 967:1** between the areas covered by the two photos. Here is what that would look like:

The **blue** is the area covered by the photo from the **ISS**. The **red** is the area covered by the photo from **Earth**. You will understandably lose a lot of detail.

Not only that, but given the speed of the ISS, a full orbit takes **90 minutes** travelling at **7.66 km/s**. As such it would take only **44 seconds** for something to appear on one edge of the photo and disappear off the other edge.

All those things combined mean you don’t see much change in clouds from the ISS.

If you were looking out the window of the ISS yourself, they would not be so intense.

The photos were taken with a long exposure (about 1-3 seconds per photo, depending on the sequence), which allows the camera to capture more light.

Additionally, the contrast and saturation were boosted to help them pop a bit more in the video.

The blue flashes you see in the first sequence are lightning.

If you slow down the video, you will notice that the lightning flashes appear for 2 or 3 frames at times. A time-lapse will only capture a single flash for a single frame.

However, to make the sequences last longer, they were slowed down to about 50%. As such, each frame from the original time-lapse lasts about 2 frames in this video. The video editing software created extra frames to fill in the gaps, so flashes get stretched across a couple of frames.

You can see another version of the sequence here which is at full speed. I preferred it a bit slower.

The individual frames are shot with a long exposure, with 1 photo every second, so the camera is able to capture light over more time. That increases the odds of seeing lightning in the sequences.

Most of the lights on the ground have a yellow how. But at 0:30, there is a patch of city lights that looks green.

It turns out that this is the country of Guatemala. In 2009, the government planned to replace street lighting with environmentally-friendly LED lamps. As indicated in this discussion it seems they had made some progress by 2011 when this sequence was recorded.

Satellites can be hard to spot by humans in space, but occasionally the camera does pick them up. You can see one in this video around the middle of the screen at 0:47.

You will notice that it appears just as the sun is beginning to rise in both this video and the one here. The light from the sun, at that angle, makes them easier to spot at that time.

Here is an image from the European Space Agency depicting how satellites are dispersed around the Earth:

So many satellites! Why can’t we see any in the video?

Keep in mind that the image above is not to scale. The satellites depicted are huge compared to reality. Even if they were a single pixel they would still be gigantic.

Let’s do some math and figure out how much distance will actually be between satellites on average.

According to the UN Office for Outer Space Affairs (yes, this department actually exists!), about **3056 satellites** are in **low Earth orbit** (an altitude of 180 km to 2,000 km).

Earth has a **circumference** of about **40,000 km**. If all **3056 satellites** were lined up around the equator at the same altitude, there would be **one every 13 km**.

However, they are dispersed all around the planet in a range of different orbits. The Earth has a **radius** of about **6367 km**. Add **400 km** for the altitude of the ISS and you get **6767 km**. Given the formula for calculating the surface area of a sphere is ** 4 x π x r^{2}**, that gives us a surface area of

**509,424,190 km**. Divide that by

^{2}**3056**and you get

**1 satellite**in every

**124,951 km**, or every

^{2}**353 km by 353 km square**, if you prefer to think of it that way.

That’s a lot of empty space.

Satellites do exist, and the ISS has to plan its orbit to generally keep out of the way of any known hazards, but it is not exactly a traffic jam up there.

In one of his many ‘mythbuster’ interviews, **Neil DeGrasse Tyson** mentions that the Earth is technically not a perfect sphere, but rather an ‘oblate spheroid’ and is in fact ‘pear-shaped’. Here is the video:

This is true. However, some construe this to mean that the Earth will look like an actual pear. If you watch the whole interview he clearly says that at a cosmic level, the Earth is practically a perfect sphere.

As indicated in this article, the diameter is **12,756 km** at the equator and **12,713 km** at the poles. That gives us a difference of **43 km**. In percentage terms, the diameter is only **0.34%** bigger at the equator - about 1/3 of 1%.

If the Earth was the size of a marble, we could barely detect mountains and oceans with our finger, let alone a slight bulge of less than 1%.