Why does any orbiting space craft appear to travel in a sine wave path?

Question

Does the path shown on TV news require steering in this pattern or perhaps the flat map is distorted and the space craft only appears to follow a sine wave?

Answer 1

It appears to be a sine wave because the background you are looking at is the Earth projected in two dimensions.   Basically, the sharpest sine wave will be generated by polar orbits.  As the angle of the orbit tilts progressively to get closer and closer to the plane of the Earth's equator, the sine wave will get longer and longer.  A perfect equatorial orbit will look flat when projected in two dimensions.

Imaging you are out in space.  You see the Earth, behind it the sun.  The satellite you see is at the equator immediately in front of you.  But the Earth is tilted on its axis.  When the satellite gets to the other side, it will no longer be over the equator.  

If you flatten the Earth out and project the satellite, over the flattened picture, that by itself will generate a sine wave.

The other thing that generates a sine wave is the planet's rotation.   Suppose you have a satellite in a perfect polar orbit.  It goes over the north pole, the south pole.  It makes one revolution every four hours or six revolutions per day.  If you graph that, you will see that the planet is turning *underneath* the orbiting satellite.  It goes over Miami on the first pass, the world turns, and it goes over San Franciso (actually to the W of San Francisco) for the second turn.  If you graph that you will get a sine wave of the planet's movement over the Earth's surface in two dimensions.

If the satellite was in a perfect equatorial orbit it would be "tilted" like the Earth's axis and stay on the equatorial position.  It would go round and round and not make anything but a line at the equator, when projected in two dimensions.  If it were geostationary, it would just make a dot over the same place.   Any other orbital path, and any other orbital speed, would make some kind of sine wave, when projected against the surface of the Earth in two dimensions.  

Hope that helps,

GN

Answer 2

Because the shuttle (and other spacecraft) do not orbit at the equator.  Instead the orbit is inclined off the equator.  It still makes a full circle around the earth but when you flatten the globe into a flat map of the earth the orbit looks like a sine wave.

See link below.  Easier understood when illustrated as they do there.

Answer 3

I like your question.

Because that was the starting point for me to figure out the intricacies of an "Orbit". Once I computed the path as a sine wave and ended up in a lot of bull. I used

(Lambda) = Sin (time from asc.node X 360d/orbital period)

Then I went to the books, studied and figured it out. Now I know better, it is

Tan(Lambda) = Tan(iota)*Sin (thetaX 360deg/orbital period)

where

'theta'= time from asc.node

iota = orbital inclination at asc.node

Armed with this formula I have learnt a good amount of spherical astronomy. It defines a great circle with known iota & theta and equator as reference. I have solved many spherical trigonometry problems with my calculator. Murphy said 'If you have only a hammer, everything looks like a nail'. if that is so, I am that workman.

Answer 4

You guessed it, it only looks like a sine because it's projected onto a flat map. If you traced the orbital path you see on the news onto a globe, you'd see that it's circular.

Answer 5

Imagine a plane passing through the earth ,centered around the equator. The angle is the launch angle . Now that is how it looks like a sign wave. About 23000 miles up U can get into a synchronous orbit which to the observer on earth it makes a figure infinity centered around the equator.