# Why are the sun and moon percieved as being almost exactly the same size?

During a solar eclipse the moon covers the sun almost perfectly. It seems like a really rare circumstance given the profound distances and variability of the size of objects in the solar system.

Is it rare in our solar system for the sun and local moon to appear to be so similar in size when viewed from the planets surface?. For example, if I stand on the surface of mars during an eclipse, will one or both of the moons seem similar in size to the sun?

Yes, it is rare. In fact, it hasn’t been true during much of Earth’s history, either, and it will eventually cease to be true as the moon moves further from the Earth.

No, it won’t. From what I’ve heard, they would look more like stars.

The Sun is 870,000 miles in diameter and roughly 93 million miles from the Earth. The Moon is 2,160 miles in diameter and about 238,857 miles away on average. That’s the basic reason they look the same size.

I’m sure there’s some kind of formula you could use to figure out if Phobos or Deimos could eclipse the Sun if you were standing on Mars, but I don’t know what it is…

Even better, download Celestia (freeware) and go see for yourself! I love this program.

You can use basic trig to figure it out, just draw out the triangles.

Suppose D is the distance to the star. d is the distance to the moon.
Suppose S is the diameter of the star. s is the diameter of the moon.

tan-1(S/D) / tan-1(d/s) = the apparent difference in size during the eclipse…
right…right?

sigh My BA in math is rolling over in its grave

From Astronomy Picture of the Day:
http://antwrp.gsfc.nasa.gov/apod/ap030329.html

I understand the concept of percieved size based on relative distance. I guess what I’m asking is-- how probable is it that a moon would Almost Perfectly!! blot out a sun.

It seems so highly improbable that is makes me wonder if it has something to with the relationship of gravitational pull between the Sun and the Earth on the moon, or perhaps a light refracting effect of the atmosphere–or is it that we are just very, very lucky?

I’m not sure if wolfstu was trying to make this point, but when you consider how many places you have to stand on some planets, that makes it a lot more likely that you could see a ‘perfect’ eclipse somewhere. Jupiter has dozens of moons and so many places to stand that I wouldn’t be at all surprised if some of them, temporarily, could perfectly block the Sun if you were at the right point on Jupiter’s surface.

Opportunity took pictures of a martian eclipse on March 10, 2004:
Transit of Phobos from Mars

I saw the images that wolfstu posted, but still I wonder. If you were standing in that shadow on the surface of mars and looking at the sun would you see a small black dot in the middle of the sun, or would the entire sun be blotted out like an eclipse on earth?

Right, though we can just use: Diameter/Distance = approximate subtended angle in radians, valid when the ratio is much less than 1. You can safely ignore the trig functions in this case.

From the Martian surface, the Sun’s subtended angle is (1,392,000 km) / (228,000,000 km) = 6.1 milli-radians.

The subtended angle of Phobos is about (23 km) / (9378 - 3397 km) = 3.8 mrads. (Its orbit radius is 9378 km, but the radius of planet you’re standing on must be subtracted off.)

The subtended angle of Deimos is about (12 km) / (23459 - 3397 km) = 0.6 mrads. Not even close.

So no, the Martian moons never make a total eclipse of the Sun. I suppose you might notice a partial eclipse by Phobos — though here on Earth, it’s surprising how much of the Sun needs to be blocked during a solar eclipse before you notice the unusual darkness. In this case, Phobos could block no more than about half of the Sun’s apparent disk.

It’s only a coincidence, though a plenty remarkable one, and we just happen to be around at a lucky time. There’s no feedback mechanism to keep the Moon where it is though. In fact, the Moon is relentlessly drifting (slowly) away, and one day there will be no more solar eclipses.

If we’re still counting Pluto as a planet these days (and not everyone wants to), then it might be the only other terrestrial planet, as in the kind you can actually stand on, where total eclipses can be observed. On Pluto, the Sun subtends an angle of 0.24 milli-radians. Its moon Charon subtends an angle of (1186 km) / (19600 - 1195 km) = 64 mrad, which easily blocks out the Sun.

Why suppose? Look at the picture of Phobos eclipsing the sun that I linked to.

Highly improbably. The moon is by far the larges satellite relative to the size of its primary. The Earth-Moon system could really qualify as a double planet.

By “I suppose you might notice,” I really meant notice without assistance from technology. (Sorry I didn’t make that clear.) Yes, you can certainly see a Phobos eclipse with a camera. But you might not notice it if you were living on Mars and were just “looking around”, and no one had told you there was going to be an eclipse that day.

Okay, for all those willing to make angular size calculations here is a darned good calculator at my website:
www.1728.com/angsize.htm

In this case–allthough I’m not familiar with milli-radians–it seems that the moon charon would appear much larger than the sun. I think it is amazing that our moon appears neither larger nor smaller than our sun, but so close to the same size.

You might be the person to ask. What angle does the Sun subtend to and what angle does the moon subtend to on earth in mrad–is it close? If so, how long has it been that way?

It isn’t the size of the satellite relative to the primary that matters, it’s the absolute size of the satellite, the distance between the satellite and the primary, and the distance from the primary to the Sun. With a small telescope you can watch total eclipses from all four Galilean satellites on the surface of Jupiter. The satellites are farther from Jupiter than the Moon is from Earth, but the Sun is smaller from Jupiter. Callisto is only a little bit bigger than the Moon, and about five times as far from Jupiter, and Jupiter is five times as far from the Sun as Earth, so Callisto must block the Jovian Sun without too much overlap.

Right, I hadn’t thought of that. The total eclipses are really small fractions of the Jupiter hemisphere but they are sure enough total.

I agree, it’s an amazing fluke.

Sorry if my units seem a little odd. I could convert to degrees, or milli-degrees, or arcminutes, or what have you, but since the exercise here is simply to compare angles, I figure only the relative values matter.

The Sun’s diameter is 1.392 million km, and its distance from us ranges from 147 to 152 million km — meaning that the angle it subtends varies from 9.2 to 9.5 mrads. The Moon’s diameter is about 3474 km, and its distance from Earth’s surface ranges from 357 to 399 thousand km — meaning its subtended angle varies from 8.7 to 9.7 mrads.

So depending on where the Moon is in its orbit, and where the Earth is in its orbit, the Moon can appear either slightly smaller or slightly larger than the Sun. Hence we sometimes have annular eclipses, and sometimes total.

As to how long things have been this way, with that interesting overlap of the ranges, I don’t know exactly. The Moon is currently moving away at a rate of about 4 cm per year, but that rate is not constant. Still, if you assume that the rate is fixed anyway, you can reckon that the Moon first began to permit annular eclipses sometime in the past few hundred million years, very roughly. Before that, it would have been too close.

Here’s a page discussing the opposite case: the distant future, when there’ll be no more total eclipses.

I’m still amazed by this sun/ moon coincedence—

This person seems to think a similar experience may exist in our solar system with the moon Callisto off Jupiter --as in perfectly blocking the sun during ecliplse.

Are we the only planet that has near perfect eclipses? Better ask Jupiter.