Sunday, November 06, 2005

[104] Parameters - Field of View #2

Using a tape measure, I came up with a better estimation of the distance from my screen to my eyes ... The difference isn't that big actually, only 2cm. But it translate into a change of the FOV value I have to use with Orbiter, from 28.6 to 27.58 degree, so around 1 degree. Armed with this more precise FOV, I thought that it will be interesting to check if I could somehow verify that what we see on our screen is properly scaled. This can be easily done by calculating the projected size of a distant object on my screen, knowing the simulated distance between my eyes and the object.

As I'm still orbiting in my trusty Apollo 7, I could use the S-IVB stage as the distant object and estimate the distance between it and my eyes using the docking MFD:



Or I could use the Moon and its known angular diameter in earth vicinity to calculate its size on the screen:



Using the Moon is actually a more interesting experiment which have already been partially answered by the good Doctor Schweiger in the Orbiter's FAQ. Let's see how we can calculate the expected diameter of the Moon in Orbiter.

The very handy small-angle formula tell us that the angular diameter of an object is related to its linear diameter and its distance:



The formula is the following:

Where the angular diameter is expressed in second of arc, the linear diameter and the distance in the same unit. The angular diameter of the Moon from the vicinity of earth being about 1800 arc seconds (0.5 degree), we can easily calculate the diameter of the Moon on a spacecraft window trought which we are looking, with the help of the small-angle formula:


Using 55cm as the distance, and 1800 for the angular diameter, we find that the linear diameter of the Moon is around 0.48cm. As I'm using a FOV (27.58) that is calculated for a distance of 55cm (from the screen to my eyes), I can measure, using a simple ruler, the on-screen diameter of the Moon ... and oh surprise, it's about 0.48cm! Thus Orbiter does render the Moon at a proper scale.

It's a bit hard to believe that Orbiter renders the Moon properly as if I step outside when the Moon is visible, it sure look way bigger than 0.48cm ... But in fact, Orbiter is right. The way the Moon appears to us is either an optical or a cognitive illusion ... There is still a fair amount of discussion on this problem that is not limited just to the Moon, but also to the Sun and constellations.

The small-angle formula is a pretty handy formula to know. There is a couple of web sites that provide online calculators for it, such as 1728.com.

Don't hesitate to comment on this post if you have any question, objection or comment related to its quality or content. Thanks.

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