Why is our moon exactly half when half?

[rogerk8]

Hi!

I looked up on the sky today while arriving home from work.

There was the moon but only exactly half of it was being visible.

With exactly half I mean, with regard to my poor english, that it was like a folded circular disc.

Seeing a "new-moon" like we call it here in Sweden, the moon look more like the moon on the turkish flag meaning that it is curved like the curvature of Earth actually is blocking the sun's rays.

But how can it be exactly half?

Shouldn't the curvature of Earth always make the moon curved, so to speak?

Roger

 

[cjl]

The moon doesn't appear half full because of the Earth's shadow (and this also applies when it is a crescent), the moon appears half full because it is lit from the side by the sun. This page has a fairly good diagram: http://www.moonconnection.com/moon_phases.phtml

There are times when the Earth blocks the sun's rays, causing the moon to go dark, but this is a separate phenomenon known as a lunar eclipse (and it can only happen when the moon would normally be full).

 

[rogerk8]

Thanks cjl!

Very nice and explanatory link!

I do however now feel stupid regarding my actual question.

But now I do not fully understand neither Gibbous nor Crescent :)

Do however not feel obligated to answer this.

Roger
PS
Why isn't it always a lunar eclipse at full moon as shown in the diagram?

Is the lunar orbit not in the same plane as the Earth orbit around the sun?

And is the lunar plane changing with time?

 

[Nugatory]

Is the lunar orbit not in the same plane as the Earth orbit around the sun?

Close, but not exactly the same... so usually the moon is a bit above or a bit below the earth/sun plane.

 

[sophiecentaur]

Thanks cjl!

Very nice and explanatory link!

I do however now feel stupid regarding my actual question.

But now I do not fully understand neither Gibbous nor Crescent :)

Do however not feel obligated to answer this.

Roger
PS
Why isn't it always a lunar eclipse at full moon as shown in the diagram?

Is the lunar orbit not in the same plane as the Earth orbit around the sun?

And is the lunar plane changing with time?

Take a ball (model Moon) and a torch (Model Sun) and turn off the lights. Shine the torch on the ball from a range of different angles and you will see that you can get all the shapes (including crescent and gibbous) that you see when you look over the Moon during its 28 day cycle.

The Sun, Moon and Earth are not in exactly the same plane all the time. The axes of orbits are in different planes. The only time you get a Lunar or Solar Eclipse is when they happen to be in the same plane and in line. To see the Eclipses, you also need to be on the appropriate side of the Earth during the Eclipse period. The Lunar Eclipse has to be during a full Moon because the Earth must be on a line between Sun and Moon but this only happens for some of the full moon. These things are easiest to appreciate using actual models in your hand or, almost as good, looking at animations. (There are dozens of them to find if you google).

 

[rogerk8]

Let's begin from scratch.

1) I have always thought of the whole planetary system as being in one plane
2) I have always thought of the planets moving in almost perfect circular orbits

I know our Earth's axis is off by some 16(?) degrees.

That our moon isn't moving in an orbit in the same plane as the Earth around the sun is new to me.

But now I have learned that that is the reason a lunar eclipse happens only sometimes and not always (at full moon).

Is there some kind of drift here regarding lunar plane vs earth/sun plane or is the "offset" constant?

The "shape" of the moon at Crescent (C) and Gibbous (G) however still makes me kind of confused.

I could for sure simulate it like you suggest, but I prefere being able to calculate it and thereby understanding it.

Roger

 

[sophiecentaur]

Your 1. and 2. placed you somewhere like five centuries out of date before you joined this thread - you have achieved some impressive time travel, subsequently.
You won't "calculate" it without a lot of information and number crunching.
Everything tends to affect everything else and the inclinations are shifting a bit, all the time afaik. There are no 'integer relationships' out there; hence all the problems with leap years and leap seconds - and that's only the tip of the iceberg.
The so-called plane of the Ecliptic is not really a plane but it does contain the orbits of the planets, within a few degrees, at least. Orbits are Ellipses with pretty low eccentricity (i.e. almost circles) but Keppler observed that they are elliptical, five hundred years ago and worked out his law which is still used, without knowing anything about gravity, too.
Something that really impresses me is that the 'ancients' and certainly the 'mediaevals' had this stuff tabulated and could predict Ephemeris and Tides and observe the positions of planets (in 3D) with a high degree of accuracy.
As for the "shapes" - do it with a model. The alternative is to get really good at spherical geometry and do the sums. (Good luck with that. haha)

 

[Chestermiller]

The Earth's axis is inclined at an angle of about 23 1/2 degrees to the axis of its orbit around the sun. The axis of the moon's orbit around the Earth is inclined at an angle of about 5 degrees to the axis of the Earth's orbit around the sun.

 

[rogerk8]

Your 1. and 2. placed you somewhere like five centuries out of date before you joined this thread - you have achieved some impressive time travel, subsequently.
You won't "calculate" it without a lot of information and number crunching.
Everything tends to affect everything else and the inclinations are shifting a bit, all the time afaik. There are no 'integer relationships' out there; hence all the problems with leap years and leap seconds - and that's only the tip of the iceberg.
The so-called plane of the Ecliptic is not really a plane but it does contain the orbits of the planets, within a few degrees, at least. Orbits are Ellipses with pretty low eccentricity (i.e. almost circles) but Keppler observed that they are elliptical, five hundred years ago and worked out his law which is still used, without knowing anything about gravity, too.
Something that really impresses me is that the 'ancients' and certainly the 'mediaevals' had this stuff tabulated and could predict Ephemeris and Tides and observe the positions of planets (in 3D) with a high degree of accuracy.
As for the "shapes" - do it with a model. The alternative is to get really good at spherical geometry and do the sums. (Good luck with that. haha)

I obviously know nothing :D

But that is a good thing, isn't it?

Because then I can view things in a way scientists simply aren't capable of because they know "too much".

And if I can't "view it" in a different way, I can always come up with more stupid questions :D

It's like growing old.

You learn so much along the road.

But when you have reached a certain age (like I have) you simply know too much about the consequences for doing this and that that you get repressed and kind of forget how to live.

Roger

 

[rogerk8]

The Earth's axis is inclined at an angle of about 23 1/2 degrees to the axis of its orbit around the sun. The axis of the moon's orbit around the Earth is inclined at an angle of about 5 degrees to the axis of the Earth's orbit around the sun.

Thank you for that exact data.

I thought it was less, obviously.

But I am surprised about the 5 degrees.

Does not sound so much.

How can there be a lunar eclipse out of that?

Roger

 

[micromass]

I obviously know nothing :D

But that is a good thing, isn't it?

Because then I can view things in a way scientists simply aren't capable of because they know "too much".

Nonscientists say this a lot. But it never had its bluff called. In the last 100 years, there was never a scientific discovery by nonscientists.

 

[rogerk8]

Hi micromass!

Don't take it so seriously.

I am just trying to boost my self confidence regarding me knowing so very little.

What is wrong with that?

Roger

 

[davenn]

Is the lunar orbit not in the same plane as the Earth orbit around the sun?

as nugatory say ... no

if it was, we would get a total eclipse of the Sun and the Moon every month of the year

Does not sound so much.

How can there be a lunar eclipse out of that?

we can get a lunar or solar eclipse because at periodic intervals during the ascending or descending nodes of the Moon's orbit they happen to be in line between the Earth and the Sun.

cheers
Dave

 

[rogerk8]

Jesus Dave, is this really you?

Dave from EP?

So you are interested in physics you too?

Ain't the world small :)

Take care and thank you for your input!

Roger

 

[rogerk8]

The Earth's axis is inclined at an angle of about 23 1/2 degrees to the axis of its orbit around the sun. The axis of the moon's orbit around the Earth is inclined at an angle of about 5 degrees to the axis of the Earth's orbit around the sun.

Hi Chestermiller!

I made some calculations regarding if 5 degrees was enough to not making the Earth cover the moon at full moon.

Here are my results:

[tex]r=LU=384 000 km[/tex]

[tex]R=6370 km[/tex]

[tex]\sin(5)=\frac{x}{r}[/tex]

[tex]x=r*sin(5)=33 500 km >>R[/tex]

Hense, a lunar eclipse has to be rear.

Roger

 

[davenn]

Jesus Dave, is this really you?

Dave from EP?
So you are interested in physics you too?
Ain't the world small :)
Take care and thank you for your input!
Roger

hahah yup its me :)
Yes, i have a love of astronomy, geology, electronics ...

cheers
Dave

 

[sophiecentaur]

Hi Chestermiller!

I made some calculations regarding if 5 degrees was enough to not making the Earth cover the moon at full moon.

Here are my results:

[tex]r=LU=384 000 km[/tex]

[tex]R=6370 km[/tex]

[tex]\sin(5)=\frac{x}{r}[/tex]

[tex]x=r*sin(5)=33 500 km >>R[/tex]

Hense, a lunar eclipse has to be rear.

Roger

At least, when it does occur, more people get a chance to see it than the few who, for a brief while, can glimpse the Moon's small shadow as it races over the Earth in a Solar Eclipse.

 

[rogerk8]

At least, when it does occur, more people get a chance to see it than the few who, for a brief while, can glimpse the Moon's small shadow as it races over the Earth in a Solar Eclipse.

Yes, it is a spectacular event!

Is the Solar Eclipse more rare(!) than the Lunar Eclipse?

If so, why?

With regard to the link above and what we have discussed, it feels like it shouldn't be.

Roger

 

[cjl]

They occur with approximately equal frequency, but a lunar eclipse is visible from a bit more than half the Earth's surface, while a solar eclipse is only visible from a narrow track (where the moon's shadow falls on the earth), so your chances of seeing a solar eclipse from any given location are much lower than your chances of seeing a lunar eclipse.

 

[technician]

Nonscientists say this a lot. But it never had its bluff called. In the last 100 years, there was never a scientific discovery by nonscientists.

I would suggest you look at DISCOVER...science for the curious magazine for a whole range of (usually older) enthusiasts who would not describe themselves as scientists.
But now I suppose they are!

 

[sophiecentaur]

Just think of the difference in size between the Moon's Shadow and the Earth's Shadow. It's like being in the shadow of a large truck or the shadow of a small car, illuminated from the headlights of a distant car.
Very often the Moon's shadow will just be grazing the edge of Earth. Only a very few people will see that (just the ones standing on the edge). Otoh, if there is even just a small 'nibble' taken out of the Moon, by the Earth's shadow, everyone on that side of the Earth can see it. So there are two factors of probability which make the visibility of a Lunar Eclipse much greater than for a Solar Eclipse.

 

[Integral]

Here is a pic of the moons shadow on the surface of the earth.http://www.google.com/imgres?imgurl=http://apod.nasa.gov/apod/image/9908/eclipse99_mir_big.jpg&imgrefurl=http://apod.nasa.gov/apod/ap990830.html&h=600&w=800&sz=54&tbnid=WoZlE2zBhRrXTM:&tbnh=91&tbnw=121&zoom=1&usg=__49Qml4LC2uFx8ZmSqdRgjUG-t2A=&docid=nz-KjmswZ78YPM&sa=X&ei=B2kSUsvtI8_SigKp9IGQDg&ved=0CEcQ9QEwBA&dur=112

 

[rogerk8]

They occur with approximately equal frequency, but a lunar eclipse is visible from a bit more than half the Earth's surface, while a solar eclipse is only visible from a narrow track (where the moon's shadow falls on the earth), so your chances of seeing a solar eclipse from any given location are much lower than your chances of seeing a lunar eclipse.

Thank you cjl!

If I have understood this correctly, the Moon's crossectional-area will cast a moving shadow onto the Earth as time passes by during this extraordinary event.

The radius of this shadow will equal the radius of the Moon:

[tex]R_m=1738km[/tex]

which is a bit small with regard to the Earth's radius:

[tex]R_e=6370km[/tex]

However, my hypothesis about the same frequency of a Solar Eclipse as that of a Lunar Eclipse seemed to be right.

You "just" need to be in the right place at the right time :)

One lazy but last question on this topic, what is the frequency?

Roger

 

[rogerk8]

Here is a pic of the moons shadow on the surface of the earth.http://www.google.com/imgres?imgurl=http://apod.nasa.gov/apod/image/9908/eclipse99_mir_big.jpg&imgrefurl=http://apod.nasa.gov/apod/ap990830.html&h=600&w=800&sz=54&tbnid=WoZlE2zBhRrXTM:&tbnh=91&tbnw=121&zoom=1&usg=__49Qml4LC2uFx8ZmSqdRgjUG-t2A=&docid=nz-KjmswZ78YPM&sa=X&ei=B2kSUsvtI8_SigKp9IGQDg&ved=0CEcQ9QEwBA&dur=112

Thanks for that very interesting link/picture!

I do however wonder why the shadow is so "tiny".

My calculations above suggests that around a quarter of the Earth (radius-wise) should be shadowed.

The picture shows maybe a tenth.

What is wrong with my calculations?

Roger

 

[rogerk8]

Just think of the difference in size between the Moon's Shadow and the Earth's Shadow. It's like being in the shadow of a large truck or the shadow of a small car, illuminated from the headlights of a distant car.
Very often the Moon's shadow will just be grazing the edge of Earth. Only a very few people will see that (just the ones standing on the edge). Otoh, if there is even just a small 'nibble' taken out of the Moon, by the Earth's shadow, everyone on that side of the Earth can see it. So there are two factors of probability which make the visibility of a Lunar Eclipse much greater than for a Solar Eclipse.

In short, it should be easier to cover the moon than to be covered by the moon, right? :-)

But I do think the equal frequency is interesting (but not so strange if I think about it).

Roger
PS
By the way, I liked you explanation of the Sun-issue. I am not on-line all the time so I didn't have the time to comment while the topic now is closed. Very interesting debate indeed!

 

[Travis_King]

Good question Roger,

Take a look at this link http://www.astroadventures.net/solar_eclipses.html for a pretty decent explanation.

Or this image:

 

[DrGreg]

The radius of this shadow will equal the radius of the Moon:

Can you see from this diagram why that is wrong?

Image credit: FSogumo on Wikimedia Commons, CC BY-SA 3.0

Sorry this is labelled in Portugese, but it's the best diagram I could find on Wikipedia.

 

[technician]

Can you see from this diagram why that is wrong?

Image credit: FSogumo on Wikimedia Commons, CC BY-SA 3.0

Sorry this is labelled in Portugese, but it's the best diagram I could find on Wikipedia.

I do not think that this diagram is drawn to scale! Which makes it not very convincing !

 

[davenn]

In short, it should be easier to cover the moon than to be covered by the moon, right? :-)

But I do think the equal frequency is interesting (but not so strange if I think about it).

Roger
PS
By the way, I liked you explanation of the Sun-issue. I am not on-line all the time so I didn't have the time to comment while the topic now is closed. Very interesting debate indeed!

actually not really equal

there usually 2 total lunar eclipses a year and only one total solar eclipse per year
and when you look at the size comparisons of the sun, moon and Earth its kinda easy to see why its a lot easier for the moon to go into the Earth's huge shadow, being so close to the earth, than it is for the small disc of the moon to cover the small disc of the sun

Dave

 

[rogerk8]

Thank you both for your answers!

I was actually on the verge of calculating something like that but then I came to my wrong "intuitive" conclusion.

But it is fun to be stupid. As long as you understand that you are stupid :D

Let's recalculate:

[tex]R_s=7*10^5km[/tex]

[tex]R_m=1738km[/tex]

[tex]R_e=6370km[/tex]

[tex]LU=LunarUnit=1.3 lightseconds=1.3*300,000=390,000km[/tex]

[tex]AU=8 lightminutes=8*300,000*60=1.44*10^8km[/tex]

Using DrGreg's picture and setting

[tex]A=0[/tex]

yields

[tex]tan(\alpha/2)=\frac{R_s}{AU}=\frac{7*10^5}{1.44*10^8}=4.9*10^{-3}[/tex]

which makes the total eclipse angle, alpha equal

[tex]\alpha/2=0,28 deg=4.9*10^{-3} rad[/tex]

Now the Moon has to be closer than:

[tex]tan(\alpha/2)=\frac{R_m}{LU}[/tex]

or

[tex]LU<\frac{R_m}{tan(\alpha/2)}=\frac{1738}{4.9*10^{-3}}=355,000km<390,000km[/tex]

Strangely enough, this states that there actually should not be any Solar Eclipse visible because the moon has to be closer than it is to actually give a shadow on the Earth's surface.

Once again I have probably calculated wrongly.

Roger

 

[cjl]

I do not think that this diagram is drawn to scale! Which makes it not very convincing !

It isn't to scale, no, but the geometric effect is still correct. To scale, you'd have a very hard time making out much of anything, since the sun would be so far away.

 

[cjl]

actually not really equal

there usually 2 total lunar eclipses a year and only one total solar eclipse per year
and when you look at the size comparisons of the sun, moon and Earth its kinda easy to see why its a lot easier for the moon to go into the Earth's huge shadow, being so close to the earth, than it is for the small disc of the moon to cover the small disc of the sun

Dave

Not true at all - there are anywhere from two to five solar eclipses per year. Actually, from what I can find with some quick googling, it looks like solar eclipses may in fact be more frequent than lunar eclipses, though I would have to stare at the geometry for a while to figure out why that may be (I don't know off the top of my head).

 

[sophiecentaur]

In short, it should be easier to cover the moon than to be covered by the moon, right? :-)

But I do think the equal frequency is interesting (but not so strange if I think about it).

Roger
PS
By the way, I liked your explanation of the Sun-issue. I am not on-line all the time so I didn't have the time to comment while the topic now is closed. Very interesting debate indeed!

"And some fell on fertile ground"
I don't think PF got what I was on about - but at least one of you did!

 

[sophiecentaur]

It isn't to scale, no, but the geometric effect is still correct. To scale, you'd have a very hard time making out much of anything, since the sun would be so far away.

The Sun doesn't actually need to be in the picture for the effect to be clearly shown. The Penumbra is a very secondary issue but even that could be included without showing the actual source of the illumination.
It could also be a good idea to show pictures of what the two Eclipses would look like to someone on the Moon - for completeness.

 

[technician]

To show the scale of things it is worth making a model of the Sun, Earth, Moon system
The Sun is about 100x the diameter of the Earth so if you have a cardboard disc 100cm dia the Earth would be a disc about 1cm dia (a typical coin?). The Moon is about 1/3 the dia of the Earth so a 3mm disc (a small pea?)
Take this lot outside, place the Sun disc 100m away..place the moon disc about 25cm away...this set up is a fair scale representation of the Earth, Moon, Sun.
If you are involved in education this is a great demonstration for kids to see and to get a feeling for the distances involved.