My Handy "60-DEGREE RULE" for 1.4.1

[VikingTechJPL]

For those of us who still use 1.4.1 frequently, here's a handy trick if you visit neutron stars or pulsars.

In 1.4.1, when you have a star selected, the upper left corner of your screen displays the star’s radius in solar radii (Rsun) rounded to 2 decimal places. While precise enough for most stars, this breaks down for pulsars, other neutron stars and some white dwarfs, which are so small that CELESTIA must show their radii—rounded to 2 decimal places—as 0.00 Rsun! For example, white dwarf HIP 80300 in Scorpius (cel://Follow/HIP%2080300/2009-02-01T16:10:59.12299?x=MA+pF6DG9lfLNTb//////w&y=LCX/9RlJiHHpUUH//////w&z=YLBzBMyEgc7xIj4C&ow=0.984788&ox=-0.130024&oy=0.054454&oz=-0.101595&select=HIP%2080300&fov=34.228123&ts=1000.&ltd=0&rf=310679&lm=49154) and Sirius B in Canis Major (cel://Follow/Sirius%20B/2007-11-22T22:30:39.42067?x=pCRpqLa6evc3cuf//////w&y=qNOeyEFyrR4Ngqz//////w&z=kPPZsdFvaoupIJ7//////w&ow=0.833671&ox=0.532640&oy=-0.145092&oz=0.015368&select=Sirius%20B&fov=34.228123&ts=1000.000000&ltd=0&rf=310551&lm=49152).

Since CELESTIA shows their radii as 0.00 Rsun, just how large are these?

You can determine the sizes of small stars with good accuracy using the “60-Degree Rule.” It takes a few steps, but after trying it a time or two, you’ll do it without even thinking.

Step 1: Select a pulsar (or any other star) and center it on your screen by pressing the C key.

Step 2: Set your Field of View as close to 60? as you can using Shift + Right-Drag. As you do so, you’ll see the FOV change at the bottom right of your screen. An FOV of 60? is optimum, but don’t worry if you can’t set it exactly. Close is good enough.

Step 3: In CELESTIA’S menu, choose Render: View Options. . . When the View Options box appears, un-check Atmospheres, so they don't make it hard to see the object's diameter.

Step 4: Now change your distance to the pulsar you have selected so that it just fills your screen vertically. For finer control you’ll probably need to use Ctrl + Left-Drag.

Step 5: When you’re at the distance where the star just fills your screen vertically, read this distance in the upper left of your screen. THIS DISTANCE EQUALS THE DIAMETER OF THE STAR! Aren't geometry and trig grand!

Let’s look at a few examples.

A White Dwarf: PSR 1620-26 B
(cel://Follow/PSR%201620-26%20B/2009-01-31T17:12:33.23254?x=EOooDRfIYMqeWMr6/v///w&y=ZKciNEKOHkxkUD7D/////w&z=QZnzsRViSXQFSxOXAg&ow=-0.306434&ox=-0.063171&oy=0.948687&oz=0.045828&select=PSR%201620-26%20B&fov=60.000000&ts=0.000000&ltd=0&rf=310423&lm=49154)
Notice that CELESTIA does list its radius as 0.00 Rsun. So, with our Field of View set to 60? and our distance listed as nearly 4,000 km, this star therefore has a DIAMETER of almost 4,000 km, or a radius of almost 2,000 km! WOW! This stellar inferno is just a little larger than Jupiter’s moon Io!

Pulsar: PSR 1620-26 A
(cel://Follow/PSR%201620-26%20A/2009-02-07T08:27:58.17168?x=U0TWgP6gXkKkWMr6/v///w&y=q0qBYATDGH9uUD7D/////w&z=BBJi1X8wy9YASxOXAg&ow=0.132910&ox=0.748054&oy=-0.639347&oz=0.118263&select=PSR%201620-26%20A&fov=60.000000&ts=0.000000&ltd=0&rf=310423&lm=49154)
This is the companion star to the previous white dwarf, the two forming a binary. Using the 60-Degree Rule, we read the distance at the upper left and conclude that this wonder has a DIAMETER of only 20 km! A radius of only 10 km! That’s bareley larger than the asteroid Gaspra!

Here’s the white dwarf we mentioned earlier: Sirius B, tiny companion to the “Dog Star.”
(cel://Follow/Sirius%20B/2009-01-31T17:32:18.79807?x=1pRY7kGc9bcocuf//////w&y=lUVRGWqMc6AZgqz//////w&z=VCoPkkuGkqaiIJ7//////w&ow=0.976769&ox=-0.025452&oy=0.191600&oz=-0.092544&select=Sirius%20B&fov=60.000000&ts=100.&ltd=0&rf=310423&lm=49154)

The 60-Degree Rule works for stars, because CELESTIA defines the distance to any star as the distance to its center. Here you can see that it works for the Sun, which does indeed have a diameter of 1,392,000 km!
(cel://Follow/Sol/2007-11-17T05:48:42.00002?x=AMDb0T8Txp29DA&y=6r/SYUxpzfz//////////w&z=VVppaMLH5SI&ow=0.976853&ox=-0.024801&oy=0.189372&oz=-0.096344&select=Sol&fov=60.000000&ts=0.0&ltd=0&rf=302231&lm=49152)

You do need to be careful about one thing—the oblateness of some stars. Because the radius that CELESTIA displays is the equatorial radius, you’ll have to rotate any oblate star 90? before you alter its distance to fill your screen.

Does this work for planets too? Not with a 60? FOV, because CELESTIA defines the distance to a planet as the distance to its surface. But, if you change the FOV from 60? to 38.94? (38?56’24”), then it works for planets—and for any reasonably spherical moons and asteroids! Here’s the Earth to prove it!
(cel://Follow/Sol:Earth/2008-03-22T10:03:10.01569?x=sP5/jYKcAu+tDA&y=clDBxJBnAg&z=5mZF7RAzEpA&ow=0.682602&ox=0.140590&oy=-0.701962&oz=0.146761&select=Sol:Earth&fov=38.939991&ts=0.&ltd=0&rf=302231&lm=49152)

As we saw with stars, you do have to watch out for oblate objects like Jupiter. Tilting Jupiter 90? shows that it does work.
(cel://Follow/Sol:Jupiter/2008-03-22T12:52:07.89018?x=MAotWmC1R5PJDA&y=BUp6Oj46YxI&z=1Vf5ohz21pJR&ow=0.091905&ox=0.693657&oy=0.707298&oz=-0.100608&select=Sol:Jupiter&fov=38.939987&ts=0.&ltd=0&rf=302231&lm=49152)

However, it does not work for highly irregular objects (like the asteroid Ida), which lack the sphericity and to produce the "horizon-effect" that the rule depends upon. Fortunately, a “38.94-Degree Rule” is unnecessary for planets, moons and asteroids, because CELESTIA 1.4.1 lists the radii of even the smallest ones.

In 1.6.0, using the rule is not necessary because radii of neutron stars and pulsars are now given in kilometers. But, all of you 1.4.1 users can now find the sizes of any smallish stellar furnaces that populate CELESTIA's universe! Enjoy!

VikingTechJPL

[volcanopele]

hmm, wouldn't this give you the radius of the star, not the diameter?

[VikingTechJPL]

Hi Volcano,

Glad you took a look. Did you try the examples?

It works because of the following. If you move away from the center-point of any circle by a distance equal to the circle's diameter, and then draw the two tangents back to the circle, the two tangent-lines will always subtend a 60? angle. In fact, that's a great way to draw an equilateral triangle "by construction". Just connect the ends of the tangents. Ah, geometry is a wonderful thing.

I'm new to the forum, so I'm not yet sure how to embed an image in this post, so I didn't add one. I'll be happy to e-mail one to you if you like, but by following the description above you'll be able to verify it easily enough.

One more fun fact about circles. Say you have a circle and you draw a diameter through its center. Then, choose ANY point on the circle except for the two ends of the diameter you drew. If you now draw two new lines from your chosen point back to the ends of the diameter, those two new lines always form a Right Angle (90?). It works for any point on the circle other than the endpoints of the diameter. (Theoretically it also works there if you use calculus, as they form the limits of the function.)

And thanks for taking a look at the "60-Degree Rule." If you still use 1.4.1 at all, you may find the rule helpful.

Regards,
--VikingTechJPL

[John Van Vliet]

--- edit ---

[VikingTechJPL]

Hi John,

You don't have to be using 1.4.1 for it to work. It works in 1.6.0 also. But 1.6.0 does give sizes of small stars like white dwarfs (or is that dwarves?), pulsars and neutron stars in kilometers, so it's not necessary when using this version. Of course, you might want to use it even in 1.6.0 just to check that star and planet sizes are being rendered by Celestia properly.

Enjoy!

--Gary