The tidal forces on the earth associated with attraction of the sun can be derived in a manner entirely similar to that of Art. 2.042. In this case the motion of the center of the earth-moon system in its orbit about the sun must be taken into account. This leads to a centrifugal force per unit mass at any point on the earth equal to
where 
is the mass of the sun and 
is the distance
between the earth-moon center and the sun. This distance varies
by about 3 per cent during the course of the year due to the
eccentricity of the center of the orbit from the center of the sun.
However, as a first approximation may be regarded as a
constant.
The final expressions for the vertical and horizontal tidal forces associated with the sun by analogy with Eq. (5) are
The greater distance from the earth to the sun than from the earth to the moon offsets the effect of the greater mass of the sun. By inserting the appropriate constants from Table 2.02-II we find
which is about 0.46 times that for the moon. Thus, the tide producing effect of the sun is roughly half that due to the moon.
The angle 
given in Eqs. (52) represents the angle
between the line joining the center of the earth with a point
on the earth's surface and the line between the centers of the earth and
sun. For a given point on the earth the agnles 
and
have different values depending upon the relative
positions of the moon and the sun at a given time. Furthermore,
at a particular point on the earth's surface the angles
and change periodically with time in a rather
complicated manner due to the combined effect of the rotation of
the earth about an axis inclined to the earth/sun ecliptic
plane and the varying aspects of the moon and sun to the earth.
In addition to these effects, the plane of the moon's orbit
is inclined somewhat (about 5 deg.) to that of the earth/sun
ecliptic plane, leading to an additional complicating feature
with regard to the possible combinations of the
angles and .