wrong size comparisons of planets

[Stormyman]

There is a bug I dont understand.
I splited the window in 2 parts...then I looked at Mercury from a distance of 10 000 km and at Venus from a distance of 10 000 km in order to compare sizes. If I measure the radius of both planets now the one of Venus is about 186 % bigger. But in reality the radius of Venus is 6052 km and the one of Mercury 2440 km..this means Venus is supposed to look 248 % bigger seeing it from a distance of 10 000 km... or how can this be explained ?

[HankR]

I don't seem to have this problem.

- Hank

[selden]

You are observing them from much too close a distance.

Try looking at them from 100,000 km and 1,000,000 km.

What kinds of results do you get then?

Hint: this is a problem in Euclidian geometry involving circles and tangents.

[HankR]

Hint: this is a problem in euclidian geometry involving circles and tangents.

Selden,

I also thought this might be the problem, but now I'm not so sure. First, when I compared the planets from 10000 km, the proportions looked okay to me. Second, when I looked at the geometry of the problem, I concluded that the apparent diameter should be 2*asin(r/R) where r is the planet radius and R is the distance of the viewpoint from the planet center. When I computed the apparent diameters with R = 10000km and r = 2440km (Mercury) and 6052km (Venus), the ratio was not that different. Also, since the viewpoint is proportionately farther from Mercury, it actually looks comparatively smaller than it should, not larger.

Unless, I've made some mistake (always possible).

- Hank

[selden]

Hank,

Here's a crude diagram of the problem.



The apparent radius is the orange line.
The actual radius is the cyan line.

[HankR]

Selden,

Your diagram is precisely the situation I had in mind. The formula I gave for the apparent diameter was the angular measure. Notice that if you project the orange line from the viewpoint onto the plane through the object's center, it maps onto the extension of the cyan line to its intercept with the red ray. This is always longer than the cyan line alone, and gets comparatively longer as the eyepoint approaches the object. Thus being proportionately closer to the object exagerates its projected diameter. Since at a given distance one is proportionately closer to Venus than to Mercury (because Venus is larger), the projected diameter of Venus will be more exaggerated than that of Mercury. So Venus should look larger compared to Mercury than it actually is, not smaller. That's why I don't think the geometry explains the phenomenom described by Stormyman.

- Hank

[Calculus]

I made some shots of relative size planets. I remember that I experienced the "bug". When you split the window, Celestia does not have the same window size reference (I can't remember if this is verically or horizontally). So when you look at a planet from the same distance, you don't have the same size.
I took into account this "bug" when I made this shot:
http://www.shatters.net/gallery/view_photo.php?set_albumName=Calculus&id=22_celestial_bodies_and_their_relative_sizes_from_Earth_to_Ceres

[Christophe]

I made some shots of relative size planets. I remember that I experienced the "bug". When you split the window, Celestia does not have the same window size reference (I can't remember if this is verically or horizontally). So when you look at a planet from the same distance, you don't have the same size.
I took into account this "bug" when I made this shot:

Indeed, it is not really a bug, just an interface weirdness. The current reference for FOV is the window height.

This will be fixed in the next version of Celestia, the FOV is now automatically set from the screen resolution and your distance to the screen (which you obviously have to enter manually). This gives you a consistent apparent focal length across views.

[Stormyman]

I think the graphic Selden made explains the phenomena. When you look at a planet from a bigger distance you are able to see it from Pole to Pole...while when you are close to it with a 45° FOV you see only a part.
This is obvious when you look at earth, the American contient for instance ...first from a distance of 10000 km with a FOV of 45° you see Patagonia to Northern Alaska...when you look at it from distance of 3 million kilometers and a FOV of 15' you can see it from Pole to Pole...the one from a bigger distances shows a significantly bigger area of the surface of earth.
When a planet is smaller you are relatively more distant, thats why Venus seems smaller than it is when you compare it to Mercury looking at both from the same distance.

[HankR]

Stormyman,

I don't believe this explanation is correct. The apparent size of an object on the screen is the size of its projection onto the view plane. As you move closer to an object, the size of its projection onto the view plane increases, even though the actual size of the area you see decreases (because of the horizon effect).

Thus Venus actually seems larger than it is compared to Mercury when viewing at both from the same distance.

Of course, if the field of view is different in the two views, then all bets are off. By changing the field of view you can make either planet appear as large or as small as you want.

Also, as Christophe points out, changing the vertical dimension of a view currently changes its effective field of view, because the field of view is expressed in terms of the vertical dimension.

So to compare the appearance of two planets from the same distance, you must ensure not only that the distances are the same, but that the indicated fields of view and the vertical dimensions of the views are also the same.

If you do this, I believe you will find that Venus looks larger than it should compared to Mercury when viewed from the same distance.

- Hank