The differences between the two birds are very subtle and difficult to spot. A good way to tell the difference between a Buzzard and a Golden Eagle is that an eagle hugs the hillside while a buzzard will tend to fly over open ground. Also, an eagle will fly in a straight line over open country. Other differences include the size, with the Golden eagle being much bigger. Look at the head in relation to the body and wingspan. The Buzzards head is more in proportion while the eagle's head looks small in comparison to its body. The white under the wing of the Golden eagle is less defined and especially in an adult bird is less bright.
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