does a plane shadow move faster than the plane?

Question

i have wondered this for a long time really because the plane is away from the ground so if it was going all the way round the world then it is a greater distance but then i wondered how you calculate for the fact that in different parts of the world the shadow would be further away oh i dont know can you help me get this out of my head please thank you xxx

Answer 1

The shadow will appear on the ground to go at the same speed as the plane.

Answer 2

Think of it this way: the plane is flying TOWARDS the sun, and the sun is above and in front of the plane. The shadow is BEHIND the plane.
The plane passes "under" the Sun (vertical): the shadow is now under the plane.
Now the sun is behind the plane, and the shadow is IN FRONT of the plane. So the shadow has made more distance than the plane... and has been moving faster.
Now if the plane goes "away" from the sun: the sun is behind the plane, and the shadow is in front. The further the pilot goes away from the sun, the steeper the angle between the plane and the ground: the shadow stays in front... and moves faster!
The only time the shadow moves at the same speed is when the sun is right above the plane.

Answer 3

1. Imagine a line of kids holding hands with a pole in the center. They are directed to proceed in a line around the pole. Those close to the center will have to move slower, those at the edge have a big circle to make..so they have to move faster (like the plane) All this makes one assumption that is not really valid..that the sun is directly overhead, and the shadow is directly below.

2. When the sun is at an angle an object may have a shadow that is longer than itself. If an object moves toward the sun, the shadow might not really move much, if it moves in another direction the shadow will cover more distance on the ground than is actually moved because it is streched out kind of.

Go out in the sun on an afternoon, place a pencil point on the ground then pick it up one inch, then measure the distance from the shadow's original location to it's new location...it will be more than one inch, and the distance will vary depending on if you move it an inch towards the sun, or away. If you moved it one inch per second...it's shadow would move more than one inch in the same second...faster.

The angle of the sun will very seldom be close to 90 degrees...only in the tropics and only at noon, even then only along a specific line of latitude. If you live in a temperate climate you never ever will see a 90 degree angle.

3. The earth is turning too...towards the East...15 degrees /hour (111km/hr at the equator). If you travel east your speed is reduced, if you travel west it is increased adding your speed to the earth's speed.

All in all...the shadows are going to be the biggest factor. The shadow could move faster or slower than the actual plane.

Answer 4

Thisis a tricky one. It depends on a few factors:

1) Speed of plane. If the plane is supersonic it will move FASTER than the Earth turns, so the Sun will go from West to East so the shadow will move slower

2) The time of day. If it's at night there is NO shadow, if the time is late then the shadow will be longer or if the time is mid-day then the shadow will move roughly the same speed as the plane.

3) Where the plane is. If the plane is at a pole then it will be in perpetual day light, or perpetual night

Even with these take into consideration I don't think the shadow will move as fast. It would be easier to explain with a picture, but I ccan't so I will try to explain with words:

the speed of light is 299 792 458 m / s so from the light coming from the Sun hitting our atmosphere to the plane it would take a couple of Milliseconds, so it would take a couple of milliseconds for a shadow to form on the ground. Because the plane (an opaque object) blocks all light it would take a very short amount of time for it to block the light already in the air, bouncing off particles. It would therefore take the shadow a fraction of a second longer to appear than it would for the plane to move above that area. The shadow therfore would move slightly slower than the plane.

Answer 5

They both move at the same speed, it would take a very long flight for the angle of the sun to have a significant impact to make a noticeable difference in speed.

In any case, the aircraft in the air only seams to go slower because of the distance. The further away you are the smaller a distance looks to you (try covering the sun with your finger), so even if it looks like the aircraft is moving slowly, it is actually traveling the same speed as it's shadow.

Angular difference will also be negligible considering the great distance the sun is from the earth and the relatively small distance the aircraft is from the ground.

Answer 6

Sure it can. The people who said "no" were correct only for a plane travelling over level ground. Imagine moving your hand across a card table out in the sun. Your hand's shadow would travel at the same speed as your hand.
Now imagine getting a big board (bigger than the table), and tilting it so that it's shadow perfectly fits onto the card table. If you waved your hand horizontally over the tilted board, at the same speed as before, your shadow would flash across the board in the same time as before. But the board is bigger than the table, so the shadow moved faster along the board.

So a plane's shadow travelling down a mountainside travels faster than the plane.

Incidently, although Einstein said nothing could travel faster than light, he meant mass or information. If you tilted the board at a great enough angle, couldn't the shadow travel faster than light? Think about it!

Answer 7

I could see how if a plane was taking off or landing or flying low, especially on a true east-west axis, at sunrise or sunset, the rapid change of the angle of the sun could make the shadow *appear* to go faster, as the different angles would cause the shadow to fall in different places in relation to the plane itself--but the ACTUAL speed of advance of the shadow can be no more than the speed of advance of the plane itself.

Answer 8

If the plane flew once around the world (following the sun and always casting a shadow) you would expect the shadow to be in the same place after one complete revolution as when it started. For this revolution the time would be the same but the distance the plane flew would be greater as its going around a bigger circle so the plane must be slighly faster.

R=Radius of earth = 6378.1 km
r= Plane flys at 22000 feet = 6.7 km

comparing 6378 km to 6385 km
(speed of 1669 km/hour (shadow) compared to 1670 km/hour (plane)km/hour in example given above (2 * Pi * R km / 24hours)

Answer 9

Both the plane and shadow move at the same speed - the shadow cannot part from the actual plane

Answer 10

depends on the distance the plane travels, the angle of the sun and time of day, location of the plane etc.

taking into account all of the above the shadow may move VERY slightly faster or slower than the plane its self.