Consider
a star located on a line perpendicular to the plane of the Earth’s
orbit about the Sun. The
distance to the star is much greater than the diameter of the Earth’s
orbit. We have to show
that, due to the finite speed of light, a
telescope through which the star is seen must be tilted at an angle
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Solution: Click For PDF Version The orbital speed of the Earth in the frame of reference of the star is
Let us call
the frame of reference in which star is at rest
The relativistic equation for the aberration of light is
where
As the light
from the star reaching the Earth is being emitted in the
Therefore,
As
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to the perpendicular, in
the direction the Earth is moving. This
phenomenon, called aberration, is noticeable and was first explained
by James Bradley in 1729.
.
and the frame of reference in which Earth is moving in the x
direction, which is parallel to the
direction, S.
and
are the directions of propagation of light as seen from the frames S
and
direction
.
That
is the telescope through which the star is to be seen needs to be
tilted at an angle
from the
direction, that is the vertical, toward the direction of the Earth’s
orbital velocity.