how does a crow or a radio waves follow the great circle path between two distant places?
A crow probably doesn't
Radio waves spread out in a straight line in all directions from the source. To get over the horizon they can bounce between the surface and ionosphere but they don't follow a great circle.
The only way to get a radio wave to follow a great circle is to use a highly directional antenna. The as mgb said, you'd have to use a frequency that would get you the correct atmospheric bounce (usually lower than VHF).
Actually, I would say that as a matter of geometry a radio wave always travels in a great circle route between antenna and transmitter (insert caveat about bouncing off things...). Since radio waves spread out in all directions, they go in a straight line between transmitter and receiver and a great circle route is a straight line on a curved surface.
yes radio waves follow a great circle ,similarly crow also flies a great circle
what i wanted to know is that does the crow continuously changes its direction to follow the great circle or fly straight to its destination. To follow the great circle it has to continuously change its direction.
Actually you follow great circle if you just fly straight, without changing direction. It is a geodesic path. What changes is your course in respect to the points of the compass. But I don't know how a crow manages to fly straight unaffected by the atmosphere. And depending on wind conditions it is not always the fastest route anyway, especially for a bird.
At certain (very low) frequencies the refraction due to varying atmospheric density will just match the curvature of the Earth and radio waves can "hug the ground" traveling in great circles (if directional).
You can also set up standing waves between the ionosphere and surface and the atmosphere acts as a wave-guide. This basically was how N. Tesla was transmitting power.
(Many naive people look at the receiver patent not appreciating that it required a transmitter elsewhere and create a whole conspiracy theory about Tesla's "free energy" device being suppressed by "them". His idea was for power transmission not tapping some mysterious reservoir of natural atmospheric energy.)
As far as crows go, they simply fly in one (lateral) direction at a fixed altitude. If they turn neither left nor right then they will follow a geodesic = great circle path. However I suspect in reality crows and other birds use visual (and sometimes magnetic) navigation references instead and in fact do not travel along exact great circles.
Example: If you follow a given magnetic heading, say NW you will spiral in around the magnetic north pole. Similarly if you follow a NW path via Polaris you will spiral in around the axial north pole. Likewise if you (or a crow) head due East or West you follow a non-great=non-geodesic circle of constant latitude. Only if you're on the equator will this be a great circle. Note Mercator maps are conformal and straight lines on the map are lines of constant heading on the globe. But these will not be geodesic (great circle) paths.
No - as I said in the post directly above yours, a great circle route is a straight line projected on a curved surface. Don't confuse that with what your compass tells you - your compass doesn't point you in a straight line.
That is only in the sense that it doesn't fly off into space but continues at a constant distance above the Earth. So its changing its direction by turning downward. Remember on a map geodesic lines are curved because the map is a distorted projection of the spherical Earth. Take a piece of string and stretch it between two points on a Globe and you get a great circle (segment). Assume the Earth has no hills or valleys and start walking in a straight line and you'll follow a geodesic (great circle) path.
Remember a Great Circle is where the seam would be if you cut a sphere exactly in half (through the center) at some arbitrary angle.
Thanks it was nicely explained.
Separate names with a comma.