Ponder This

[NtrentT]

Skiing with the kids, you get off the lift at the top of the mountain and pause for a moment to take in the view. Looking down the mountain, you see the shadow of a cloud hovering overhead and point it out. Your daughter asks, "Hey Dad, if we could measure both the shadow and the cloud, would they be the same size?" Well, would they?

[RR]

No, in the case of a thunderhead anyway. A 45,000' thunderhead could cast a shadow well over 20 miles long...and...if it was against gently rising land, gain a little width.

[Affix Snow]

Ummm.....can i go to the bathroom teach?

[DMC]

Ummm.....can i go to the bathroom teach?

#1 or #2 ?

[PWDR8S]

Owwww! My brain hurts! http://www.timefortuckerman.com/forums/images/smilies/doh.gif

[Sledhaulingmedic]

The shadow would be infinitesimally larger than the cloud. This is because the difference in the distance between the cloud and the earth and the distance between the cloud and the sun is so great that the sun's rays are for all intents and purposes are parallel.

[PWDR8S]

I would say it all depends on which way the sun was shining down and the relative shape of the clouds as RR eluded to. My brain still hurts!

[M@]

SledHauler if pretty much dead on.

Fact: An airplane's shadow is the same size as the airplane, no matter how high it is. The distance from the sun to the airplane compared to the distance from the airplane to the ground is insignificant, so the shadow is the same size.

Clouds, however, are three dimensional and you have to worry about angles, a big thunder head can cast quite a big shadow late or early in the day.

Regardless, how old is your daughter, I ask becuase of an Einstein quote: "If you can't explain it to a 6 yr old, you don't understand it."

M@

[Justin]

The shadow would be infinitesimally larger than the cloud. This is because the difference in the distance between the cloud and the earth and the distance between the cloud and the sun is so great that the sun's rays are for all intents and purposes are parallel.


Sleds right on with light traveling in a straight line. You can see such in sunsets:http://www.optics.arizona.edu/Nofziger/UNVR195a/Class2/sunset6.jpg

<Begin technical answer>
Ask any photographer and he'll most likley answer your question by refering to what's called the inverse square law (http://hyperphysics.phy-astr.gsu.edu/HBASE/vision/isql.html#c1) . It states, any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius (r) is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena. Point sources of gravitational force, electric field, light, sound, or radiation obey the inverse square law.
<end technical answer>

It's commonly applied everyday in such studio photography I and many others do every day. Another example of this is a lunar eclipse...

Sorry, I totally just geeked out there.

[PWDR8S]

......

<Begin technical answer>
Ask any photographer and he'll most likley answer your question by refering to what's called the inverse square law (http://hyperphysics.phy-astr.gsu.edu/HBASE/vision/isql.html#c1) . It states, any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius (r) is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena. Point sources of gravitational force, electric field, light, sound, or radiation obey the inverse square law.
<end technical answer>

It's commonly applied everyday in such studio photography I and many others do every day. Another example of this is a lunar eclipse...

Sorry, I totally just geeked out there. Owww! Too early! Too early in the morning! http://timefortuckerman.com/photopost/data/774/1659cantfocus.gif http://www.timefortuckerman.com/forums/images/smilies/tongue.gif

[M@]

It's commonly applied everyday in such studio photography I and many others do every day. Another example of this is a lunar eclipse...

Yeah, but in a studio the distance from the object casting the shadow and the light source is a variable - it's not with shadows cast by the sun. The moon's shadow is still effectivly the same size as the moon when it's cast on the earth:
Moon -> Earth: 245,000 miles
Earth -> Sun: 93,000,000 miles

So the difference is less than a single percent.

M@

[DMC]

The suns gonna shine on my back door someday...

[Justin]

SledHauler if pretty much dead on.

Fact: An airplane's shadow is the same size as the airplane, no matter how high it is. The distance from the sun to the airplane compared to the distance from the airplane to the ground is insignificant, so the shadow is the same size.

Clouds, however, are three dimensional and you have to worry about angles, a big thunder head can cast quite a big shadow late or early in the day.

Regardless, how old is your daughter, I ask becuase of an Einstein quote: "If you can't explain it to a 6 yr old, you don't understand it."

M@

Airplanes are subject to the same shadow casting of clouds but the results are smaller b/c it's a smaller object and more noticeable b/c it has hard edges and doesn't diffuse light. Think about making had shadow puppets with your hand. Size and sharpness is directly related to 2 things; the size of the lights source. A larger light source creates softer shadows where as a smaller creates harder ones. The second is the distance between the light source and the shadow "caster" compared to the distance between the shadow caster and the ground ( wall, cieling, car or whatever it might be)

[M@]

Size and sharpness is directly related to 2 things; the size of the lights source. A larger light source creates softer shadows where as a smaller creates harder ones. The second is the distance between the light source and the shadow "caster" compared to the distance between the shadow caster and the ground ( wall, cieling, car or whatever it might be)

The sharpness of shadow's is something I wish I understood better - for photography. Most of the time I don't want any shawdows, but once in a while a crisp shadow adds somthing to the photo.

M@

[Bannick]

The suns gonna shine on my back door someday...

so you gonna snowboard the ravine naked this weekend? ;)
no butt checking!

[Justin]

Yeah, but in a studio the distance from the object casting the shadow and the light source is a variable - it's not with shadows cast by the sun. The moon's shadow is still effectivly the same size as the moon when it's cast on the earth:
Moon -> Earth: 245,000 miles
Earth -> Sun: 93,000,000 miles

So the difference is less than a single percent.

M@

Right, the difference is hardly variable when speaking in terms of %. I'm not sure you could even achieve a 1% variance even when comparing a high noon in mid june to 4pm in January.

[M@]

so you gonna snowboard the ravine naked this weekend? ;)

Yeah - getting the shadows right in those kinda photo's is critical... makes a big difference in who you can show them too.

M@

[DMC]

so you gonna snowboard the ravine naked this weekend? ;)
no butt checking!

I'm not the naked guy type...

[Justin]

The sharpness of shadow's is something I wish I understood better - for photography. Most of the time I don't want any shawdows, but once in a while a crisp shadow adds somthing to the photo.

M@

If you've got a grasp on what we've been talking about than your 1/2 way there.

like i said already there are 2 large factors in shadow "strength"

Small light source = sharp
Large = soft

2nd has pretty much been covered with the "Cloud, airplane riddle" ;)

[Bannick]

Yeah - getting the shadows right in those kinda photo's is critical... makes a big difference in who you can show them too.

M@

gotta carry big ski poles ;)

[RR]

The shadow would be infinitesimally larger than the cloud. This is because the difference in the distance between the cloud and the earth and the distance between the cloud and the sun is so great that the sun's rays are for all intents and purposes are parallel.

True..when the blinders are on. A tall skinny cloud...a thunderhead for example will cast a different size shadow a bit after sunrise or a bit before sunset than it will at noon:
http://timefortuckerman.com/photopost/data/500/415CloudShadow.bmp
Lived in Kansas as a boy. Noticed cloud shadow length a lot.

[abacab]

Hmm...This is all very interesting...

Sometimes the cast showdow will infact be much larger than the object itself, but that has everything to do with the shape and angle formed between the sun/object/and what the shadow is cast on.

Take a look at your shadow cast on the ground at sunrise or sunset with your back to teh sun...the shadow is much larger than you are....but stand in front of a wall (perpindicular to the ground) and the shadow is the same size as you.

Its all relatively relative.

[NtrentT]

I like M@'s answer and the following too....


I really like this answer, although I can not take credit for it, yet agree with it.

The Sun is, on average, 93,000,000 miles away. Let’s say the cloud has an altitude of 1 mile (just over 5,000 feet). Let’s say the cloud is 1/5 of a mile across, for the sake of this argument. Let us also consider the Sun as a point source for the moment. Now the math…

We need to calculate the angular separation, in degrees for the clouds width at a distance of 93,000,000 miles from the radius. That is, two lines 93,000,000 miles long, separated by 1/5 mile (0.2 miles) at their ends. For brevity we will consider the resulting triangle as a right angle since the error is so small.

tan = rise/run = 0.2 / 93,000,000 = 2.15054 e-9

Ang = arctan (2.15054 e-9) = 1.2322 e-7 degrees or 0.00000012322 degrees for dramatic effect.

Let’s assume the cloud’s shadow is projected onto a flat surface that is perpendicular to a line that passes from the Sun through the center of the cloud. The angular separation is still the same, the distance is no longer 93,000,000 miles, it is 93,000,001 miles. If the cloud is 0.2 miles wide, how wide is the shadow?

Again, let’s assume a right triangle since the angular error is so small.

We know the angle is 0.00000012322 degrees and the length of the long side is 93,000,001 miles. We can calculate the length of the other triangle’s side as follows:

Rise = run * tan = 93,000,001 * (0.2/93,000,000) = 0.20000000215053763440860215053763 miles

So, if the Sun is considered a point source and the ground is both level and perpendicular to the line drawn from the Sun through the center of the cloud, the cloud’s shadow is larger than the cloud!

However, to your point, the Sun is not a point source! The diameter of the Sun is 870,000 miles, which is huge! However, the end effect can be calculated by a simple ratio and them multiply that by two and subtract the from the original calculation for the cloud’s shadow. I know you are chomping at the bit, so let’s go!

I love proportions, so that is what I will use. Think of a long lever that is 93,000,001 miles long with the fulcrum 93,000,000 miles away. Remember the cloud is 1 mile high. The long end moves 870,000 miles. How far does the short end move?

870,000 / 93,000,000 = X / 1.0

X = 1 * (870,000 / 93,000,000) = 0.0093548387096774193548387096774194 miles

We need to double that number since it effects both sides of the cloud’s shadow and subtract it from our original answer for a point source.

Shadow Width = 0.20000000215053763440860215053763 miles – (2 * 0.0093548387096774193548387096774194 miles)

Shadow Width = 0.18129032473118279569892473118216 miles

Wow! The shadow is smaller by about 9%!

Why? Because the angular size of the Sun is larger than angle that is made by two lines drawn from the center of the Sun to each side of the cloud, so the cloud is slightly larger than its shadow under theoretical conditions

[pulverschwein]

I agree with Pwdr8s - OUCH! I can follow the Bannick / DMC part, but only wish I could understand the NTrentT / Justin dialogue.
All right brain, I don't like you and you don't like me - so let's just do this and I'll get back to killing you with beer.

[DMC]

The sun is a mass of incandescent gas
A gigantic nuclear furnace
Where Hydrogen is built into Helium
At a temperature of millions of degrees

The sun is hot, the sun is not
A place where we could live
But here on Earth there'd be no life
Without the light it gives

We need its light, we need its heat
The sun light that we seek
The sun light comes from our own sun's
Atomic energy

The sun is a mass of incandescent gas
A gigantic nuclear furnace
Where Hydrogen is built into Helium
At a temperature of millions of degrees

The sun is hot...

The sun is so hot that everything on it is a gas
Aluminum, Copper, Iron, and many others

The sun is large...

If the sun were hollow, a million Earth's would fit inside
And yet, it is only a middle size star

The sun is far away...

About 93,000,000 miles away
And that's why it looks so small

But even when it's out of sight
The sun shines night and day

We need its heat, we need its light
The sun light that we seek
The sun light comes from our own sun's
Atomic energy

Scientists have found that the sun is a huge atom smashing machine
The heat and light of the sun are caused by nuclear reactions between
Hydrogen, Nitrogen, Carbon, and Helium

The sun is a mass of incandescent gas
A gigantic nuclear furnace
Where Hydrogen is built into Helium
At a temperature of millions of degrees

[pulverschwein]

The sun is a mass of incandescent gas
You know, Frank, scientists have found that the sun is a huge atom-smashing machine.
The heat and light fron the sun are caused by the nuclear reaction between hydrogen and you, Frank O'Toole.

Scientists have found that the sun is a huge atom-smashing machine,
the heat and light from the sun come from the nuclear reaction between
hydrogen, nitrogen, helium, carbon, boron, chloron, flu, moron and estrogen.

[direwolf]

The suns gonna shine on my back door someday...


Woohoo!! a great Dead quote to follow up all those Genesis quotes from earlier. I was way too lost in this thread until i got IKYR running through my head :D

[M@]

Whenever life gets you down, Mrs. Brown, and things seem hard or tough,
And people are stupid, obnoxious or daft,
And you feel that you've had quite enough...

Just remember that you're standing on a planet that's evolving,
And revolving at nine hundred miles an hour,
That's orbiting at nineteen miles a second, so it's reckoned,
A sun that is the source of all our power.
The sun, and you and me, and all the stars that we can see,
Are moving at a million miles a day,
In an outer spiral arm at fourty thousand miles an hour,
In a galaxy we call the milky way.

Our galaxy itself contains a hundred billion stars.
It's a hundred thousand light years side to side.
It bulges in the middle sixteen thousand light years thick,
But out by us it's just three thousand light years wide.
We're thirty thousand light years from galactic central point.
We go 'round every two hundred million years.
And our galaxy is only one of millions of billions,
In this amazing and expanding universe.

The universe itself keeps on expanding and expanding,
In all of the directions it can whiz,
As fast as it can go, the speed of light you know,
Twelve million miles a minute, and that's the fastest speed there is.
So, remember when you're feeling very small and insecure,
How amazingly unlikely is your birth!
And pray that there's intelligent life somewhere up in space,
'Cause there's bugger-all down here on Earth!

[TheMadBrit]

Whenever life gets you down, Mrs. Brown, and things seem hard or tough,
And people are stupid, obnoxious or daft,
And you feel that you've had quite enough...

Just remember that you're standing on a planet that's evolving,
And revolving at nine hundred miles an hour,
That's orbiting at nineteen miles a second, so it's reckoned,
A sun that is the source of all our power.
The sun, and you and me, and all the stars that we can see,
Are moving at a million miles a day,
In an outer spiral arm at fourty thousand miles an hour,
In a galaxy we call the milky way.

Our galaxy itself contains a hundred billion stars.
It's a hundred thousand light years side to side.
It bulges in the middle sixteen thousand light years thick,
But out by us it's just three thousand light years wide.
We're thirty thousand light years from galactic central point.
We go 'round every two hundred million years.
And our galaxy is only one of millions of billions,
In this amazing and expanding universe.

The universe itself keeps on expanding and expanding,
In all of the directions it can whiz,
As fast as it can go, the speed of light you know,
Twelve million miles a minute, and that's the fastest speed there is.
So, remember when you're feeling very small and insecure,
How amazingly unlikely is your birth!
And pray that there's intelligent life somewhere up in space,
'Cause there's bugger-all down here on Earth!

THERE YOU ALL GO AGAIN!! TALK OF PLANETS. TALK OF INTELLIGENT LIFE. DESCRIPTION OF EXTREME MATHEMATICAL COMPUTATION BEYOND 3RD GRADE. THIS FURTHER BACKS MY THEORY WE ARE ALL ALIENS. LETS CHANGE THE NAME OF THE FORUM TO TIME FOR TUCKERMAN TO PHONE HOME.

I REALLY HAVE LOST IT...... :troll:

[DMC]

Woohoo!! a great Dead quote to follow up all those Genesis quotes from earlier. I was way too lost in this thread until i got IKYR running through my head :D


Dark star crashes - pouring its light - into ashes
Reason tatters - the forces tear loose - from the axis
Searchlight casting - for faults in the - clouds of delusion

shall we go, you and I - While we can?
Through the transitive nightfall of diamonds

[RR]

...so the cloud is slightly larger than its shadow under theoretical conditionsSol's Light is refracted at sunrise and sunset...that is it does not always travel in a straight line from it's origin.

Further, clouds are three dimensional not unidimensional...infact, clouds have many different types and densities.

please see the drawing..the upper image. A thunderhead over Hays City, Kansas will cast a shadow all the way to the Rockies in the first five minutes after sunrise. Once the refraction is diminished the speed of the distal edge of the shadow racing back to Hays City is worth calculating.

enjoy :cool:

[Skilasnow]

Skiing with the kids, you get off the lift at the top of the mountain and pause for a moment to take in the view. Looking down the mountain, you see the shadow of a cloud hovering overhead and point it out. Your daughter asks, "Hey Dad, if we could measure both the shadow and the cloud, would they be the same size?" "So what trail would you like to hit this time, honey?"

[PWDR8S]

Did you know I have lint stuck between my toes? It's right there! Staring at me. Taunting me.

[Sledhaulingmedic]

True..when the blinders are on. A tall skinny cloud...a thunderhead for example will cast a different size shadow a bit after sunrise or a bit before sunset than it will at noon:
http://timefortuckerman.com/photopost/data/500/415CloudShadow.bmp
Lived in Kansas as a boy. Noticed cloud shadow length a lot.

Yes. I did make the mid day assumption. The shadow would be longer near Sunrise/Sunset, because of the angle the shadow is projected onto the earth. If it were being projected onto a perpendicular surface, it would still be same size.

"I got my head stuck in the cupboard!"

[direwolf]

Dark star crashes - pouring its light - into ashes
Reason tatters - the forces tear loose - from the axis
Searchlight casting - for faults in the - clouds of delusion

shall we go, you and I - While we can?
Through the transitive nightfall of diamonds


Eight-sided whispering hallelujah hatrack
Seven-faced marble eye transitory dream doll
Six proud walkers on jingle-bell rainbow
Five men writing in fingers of gold
Four men tracking the great white sperm whale
Three girls wait in a foreign dominion
Ride in the whalebelly
Fade away in moonlight
Sink beneath the waters
To the coral sands below
Now is the time of returning

Now all kinds of fun is running through me brain :cool:
If I wasn't at work, I'd have a couple o' :beer: and pretend that it was 4:20 :eek:
Then i'd certainly have a better chance of understanding all this "science stuff."

[DMC]

if i put bread in the toaster - and push the lever dwon - in a couple minutes it gets transformed into toast.... amazing...

[RR]

.."I got my head stuck in the cupboard!"The one where the tequila is kept??? Could be worse...

[abacab]

Yes. I did make the mid day assumption. The shadow would be longer near Sunrise/Sunset, because of the angle the shadow is projected onto the earth. If it were being projected onto a perpendicular surface, it would still be same size.

"


That is exactly what I meant...


"in the desert of shadowless death,
they pray for thunder clouds and rain,
but to the multitudes who stand in the rain,
heaven is where the sun shines....

[M@]

Speaking of shadows:

Here's a pix of the moons shadow on the earth, not very sharp:
http://antwrp.gsfc.nasa.gov/apod/ap040926.html

Here's another moon shadow on the earth, this one 500km long:
http://antwrp.gsfc.nasa.gov/apod/ap031127.html

And how about this, a valcano shadow on a cloud with the sun rising through it:
http://antwrp.gsfc.nasa.gov/apod/ap031127.html

Here's some kewl saturn ring shadows:
http://antwrp.gsfc.nasa.gov/apod/ap060503.html

I love the apod.

M@

[DMC]

I think I've had enough moon posts for one week M@... :)

[M@]

I think I've had enough moon posts for one week M@... :)
Rim shot + rep.

M@

[DMC]

Rim shot + rep.

M@

Who loves ya M@?


Sorry you wont be joining this weekend..

[M@]

Sorry you wont be joining this weekend..
Yeah, me too. I also wish I had season tickets to Fenway, but one has to make choices... I'm working the Jamfest though - hopefully we'll slide again in 2006!

M@