How high is the Death Star above Endor?

Question

This is part of the answer to How did the Death Star 2 stay in orbit above Endor when it did not have functional ion engines nor a functional hyperdrive system?. The answer is so large I decided to split off this piece and make it its own question that I can self-answer for reference.

Answer 1

tl;dr: Using on-screen cannon, about 16,350 km to 35,550 km above the surface of Endor or 18,800 km to 38,000 km from its center.

We can calculate this by comparing their actual diameters with their apparent diameters on screen.

Actual diameters

Wookiepedia has this covered.

• Death Star 2: 160 km
• Endor: 4900 km

Apparent diameters

To calculate their apparent diameters we need a clear shot of both Endor and the Death Star. We get this as the Rebel fleet comes out of hyperspace. Couldn't ask for better.

That's no moon moon, it's a space station!

Since we only need a ratio, we can just measure in pixels.

• Death Star 2: 29 pixels
• Endor: 290 pixels

A nice 10:1 ratio. Their actual ratio is 4900/160 or about 30:1.

We can also observe that for Endor to appear that small it is quite far away from the Millennium Falcon, much further away than a low orbit.

What is the angular diameter of Endor? One can approximate it by holding out their hand at arms length and covering up the object. 1 pinky finger is about 1 degree, 3 fingers is about 5 degrees, a fist is about 10 degrees.

I'd say Endor is between 3 fingers and a fist so 5 to 10 degrees. If someone knew the diameter of the Falcon's windows and their distance from the pilot's chair we could be more precise.

Let's run the numbers at both 5 and 10 degrees.

If Endor's angular diameter is 5 degrees...

Using the 10:1 ratio of apparent diameter...

• Endor: 5 degrees
• Death Star: .5 degrees

Plugging this into Wolfram Alpha to convert this angular diameter into distance from the Falcon, we get...

• Distance to Endor: 56,000 km
• Distance to Death Star: 18,000 km

This gives us a height of the Death Star above the center of Endor of 56,000km - 18,000km or 38,000 km. To get its height above the surface we subtract the radius of Endor 38,000 km - 2,450 km = 35,550 km above Endor's surface.

If Endor's angular diameter is 10 degrees...

Using the 10:1 ratio of apparent diameter...

• Endor: 10 degrees
• Death Star: 1 degree

And plug that into Wolfram Alpha we get...

• Distance to Endor: 28,000 km
• Distance to Death Star: 9,200 km

This gives us a height above the center of Endor of 28,000km - 9,200 km or 18,800 km. Subtract the radius of Endor and we get 16,350 above Endor's surface.