1. Newbie
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## Satelite flight path.

Good morning all,

I have recently joined this forum and have found the depth of knowledge and experience documented in the many threads I have read simply amazing.

Now I have a question which I suspect many will consider extremely elementary but its one which has been annoying me for some time.

Why is it that satelite (or shuttle) flight paths around the earth shown as elongated wave rather than a straight line?

See I told you it was a dumb question!

2. Originally Posted by Rowan
Good morning all,

I have recently joined this forum and have found the depth of knowledge and experience documented in the many threads I have read simply amazing.

Now I have a question which I suspect many will consider extremely elementary but its one which has been annoying me for some time.

Why is it that satelite (or shuttle) flight paths around the earth shown as elongated wave rather than a straight line?

See I told you it was a dumb question!

3. Banned
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YOU try flying around in space and see if you don't get a little dizzy!

.

Right off the bat- I would say Course Corrections.
The Shuttle and satellites are not Huge like Moons are. Their gravity is small, the Earths magnificent.
They will drift inward and then fire a pulse and get back up to altitude... drift again.. fire thrusters again...

4. Originally Posted by Rowan
Why is it that satelite (or shuttle) flight paths around the earth shown as elongated wave rather than a straight line?

See I told you it was a dumb question!

Do you mean the orbital path looks like a curving arc when shown on a flat map?

If so, it is because the Earth is not flat.

5. It's what a circular orbit looks like when the spherical globe surface is mapped onto, projected onto, a rectangle.

The curve you get depends on the projection you use.

You could manipulate the projection to make the landtrack straight, but then the normal projection of land masses would look just as warped as the orbit track usually looks.

NASA: Orbital Mechanics 101

Most ground track maps appear on Mercator projections of the Earth. These are flat representations of the globe. When drawn on a globe, an orbit looks like a closed loop around the Earth.

When drawn on a Mercator map, it looks like an S-shaped curve with half of the S being above and half of the S being below the equator. Consider the equator itself, which on a globe is a circular loop around the center of the Earth but which, on a Mercator map, is a straight line.

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Originally Posted by aurora
Do you mean the orbital path looks like a curving arc when shown on a flat map?

If so, it is because the Earth is not flat.
OH!
I hadn't thought of that... I was thinking 3D...

Maybe a picture of the question?

7. Established Member
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What you are seeing is the ground track of the orbit, not really the orbit itself. A shuttle orbit is nearly circular, and as the earth turns underneath it the sine pattern shows up. This will vary with inclination and orbit period. A spacecraft in a geosynchronous orbit for instance, would theoretically have a ground track that is a point on the equator.

I'd recommend getting the free version of Satellite Tool Kit and playing with it. It will give you a better intuitive feel for orbits.

http://en.wikipedia.org/wiki/Satellite_Tool_Kit

8. Originally Posted by Karl
What you are seeing is the ground track of the orbit, not really the orbit itself. A shuttle orbit is nearly circular, and as the earth turns underneath it the sine pattern shows up.
The rotation under the satellite is more the reason the curved path isn't closed, that the ends don't meet up. It the Earth did not rotate under the satellite, you'd still get a curved path with common projections.

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Originally Posted by 01101001
The rotation under the satellite is more the reason the curved path isn't closed, that the ends don't meet up. It the Earth did not rotate under the satellite, you'd still get a curved path with common projections.
Now, I'm confused. How do you say this is so?
Once I realized what picture he was talking about..
As the Earth rotates, it also has a slight wobble...
I was thinking this was the cause- that the ground itself was moving underneath the orbiter with the observer on the ground.

10. Order of Kilopi
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A circular orbit directly over the equator gives a ground path on a Mercator
map which is a straight line directly on the equator. A circular orbit which is
inclined to the equator gives a sine curve on a Mercator map. The rotation
of the Earth means that a satellite has to make more than a full orbit before
it crosses the same line of longitude again, so the ground path of an inclined
circular orbit on a Mercator map is a sine curve with a period shorter than
the map's full width by about 22.5 degrees, or 1/16 of the way around the
Earth, since satellites in low orbits, like the International Space Station, orbit
the Earth about 16 times per day.

-- Jeff, in Minneapolis

11. Originally Posted by Neverfly
As the Earth rotates, it also has a slight wobble...
I was thinking this was the cause- that the ground itself was moving underneath the orbiter with the observer on the ground.
The wobble doesn't have anything to do with it really. I didn't really understand it myself. I used to kind of wonder why satellites seemed to go north and south, even though I knew logically that they were going in a straight line. But I think I get it now. If the earth did not rotate, the path of a satellite would be north of the equator for 180 degrees, and then south for 180 degrees. But because the earth rotates, it doesn't work, because by the time the satellite has made its 180 degrees, the earth has moved under it, so it ends up getting out of "sync".

12. I'm trying to understand this...
Is this true: The frequency of the sine wave would be determined by the speed at which the satellite orbits as compared to the rotating Earth below.
http://www2b.abc.net.au/science/k2/s...pic331829.shtm

13. Originally Posted by Neverfly
I was thinking this was the cause- that the ground itself was moving underneath the orbiter with the observer on the ground.
That picture above from NASA shows exactly the situation if the Earth didn't rotate under the satellite: the ends meet up, so the path is closed, always passing over the same points on Earth on each orbit. Note that the ground track projection is still a wave -- because it is projecting an inclined circle (or ellipse) onto a flat rectangle.

All that is due to the Earth rotating under the satellite is to make different Earth features pass under the orbit each time around. The ground track then isn't a closed path, but each wave overlaps (or underlaps) the previous slightly.

With or without Earth rotation, the ordinary projection of an inclined satellite's ground track is a wave.
Last edited by 01101001; 2008-Jul-29 at 03:16 AM.

14. Originally Posted by ginnie
I'm trying to understand this...
Is this true: [I]The frequency of the sine wave would be determined by the speed at which the satellite orbits as compared to the rotating Earth.
I'm not an expert, but I think that is correct. If the satellite is very fast (i.e., in low orbit) and the earth (hypothetically) rotated very slowly, then the frequency would be close to 360 degrees. However, if the satellite is going very slowly, then the earth would rotate relatively quickly under it, and the frequency would become much shorter.

15. Originally Posted by Rowan
Good morning all,
Welcome to BAUT!
Why is it that satelite (or shuttle) flight paths around the earth shown as elongated wave rather than a straight line?
Others have explained it, but I'd like to remind you about how a sine curve arises from circular motion anyway: if a particle follows a circular path with constant speed around the x/y origin, then the graph of its x coordinate over time is a sine curve. A similar thing is happening here.
Originally Posted by Jens
I'm not an expert, but I think that is correct. If the satellite is very fast (i.e., in low orbit) and the earth (hypothetically) rotated very slowly, then the frequency would be close to 360 degrees.
By frequency, do you mean wavelength? The length of its wave would correspond to 360 degrees of longitude on the earth, is that it?
However, if the satellite is going very slowly, then the earth would rotate relatively quickly under it, and the frequency would become much shorter.
The wavelength would become longer? The frequency smaller?

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One way to help visualise this is to get a globe and a rubber band. Stretch the rubber band around the globe at its widest, say, around the Equator, or from Pole to Pole. The rubber band now represents the ground track of a satellite, though it assumes the Earth isn't rotating. Look at the countries or continents that the rubber band crosses. Now look at a Mercator map of the Earth, and trace out that path on the map. If the orbit is inclined to the Equator, you'll get a sine wave just like you see on the picture boards.

An interesting example of these ground tracks to look at are the Apollo ones. The spacecraft lifted off from Florida, did a couple of orbits of the Earth, then fired its rockets again to go to to the Moon.

If you trace the ground track, you can see the spacecraft arc out over the Atlantic Ocean, cross the Equator somewhere over the Indian Ocean or Africa, probably cross Australia, then cross the Equator again, finally completing one orbit, but not by passing over Cape Kennedy (as the Earth had rotated under the spacecraft, remember). But the really interesting bit is when the spacecraft heads off for the Moon. The ground track swings around and actually starts to slowly double back, because now its orbit is so elliptical that it orbits around the Earth more slowly than the Earth rotates.

17. Originally Posted by hhEb09'1
The wavelength would become longer? The frequency smaller?
We need to be sure how we define our terms here.

We commonly define frequency as the number of cycles a wave motion completes in a given amount of time.

Wavelength is the distance between successive crests or troughs of the wave pattern.

In the case of the plot of a satellite's path on a map as it moves in an inclined orbit, the relationship between frequency and wavelength is very different from that of waves that propagate at the same forward speed despite having different frequencies. The frequency decreases as the orbital period increases, but so does the wavelength as Earth's rotation shortens the observed track more for a slower orbit. When the frequency drops to one cycle in 24 hours what had been a roughly sinusoidal track morphs into a figure-eight analemma in which the satellite's longitude oscillates around a fixed point. For still higher and slower orbits, the track on the map will be retrograde and the wavelength of the trace will increase with decreasing frequency, but not in a simple reciprocal manner.

Clear as mud? I realize that verbal descriptions like these can be difficult for someone who does not already have a strong grasp of the geometry and trigonometry that are involved.

18. Originally Posted by hhEb09'1
By frequency, do you mean wavelength? The length of its wave would correspond to 360 degrees of longitude on the earth, is that it?
I fully admit, I need to study my terms. It's been a looooong time since high school trigonometry. I'm not sure of the difference between frequency and wavelength, but I'll get on it.

19. Order of Kilopi
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Jens,

I'm astonished that you could hang around in a science discussion forum
for so long and still be unsure of the difference between frequency and
wavelength. They are so fundamental to soooo many things! And they
are so much fun! Harmonic oscillations! They even sound fun!

What other dark secrets have you been hiding?

-- Jeff, in Minneapolis

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Originally Posted by Karl
A spacecraft in a geosynchronous orbit for instance, would theoretically have a ground track that is a point on the equator.
That's a geostationary orbit, which is a subset of geosynchronous orbits.

Only the geostationary orbit remains over one location on the equator at all times. That's required for satellite TV, as the receivers must remained fixed on one small point in the sky. The inclination of a geostationary orbit is zero.

A geosynchronous orbit is simply one that matches the Earth's sidereal period of rotation. Thus, it can be geostationary, or it can have an inclination, which actually has a figure-eight as a ground track. Either way, once per day, a geosynchronous orbit returns to exactly the same place in the sky at exactly the same time.[/QUOTE]

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