[agalashan (OP)]

Why do we not feel the effect of centrifugal force caused by the orbit of the Earth around the Sun making us heavier during the day by pulling us towards the Earth and less at night by pulling us away from the Earth?

[waytogo]

Nice question and what about the Earth itself?

[RD]

Why do we not feel the effect of centrifugal force caused by the orbit of the Earth around the Sun making us heavier during the day by pulling us towards the Earth and less at night by pulling us away from the Earth?

For a 70Kg person the force is equivalent to approximately 0.000000000000000024 times Earth's gravitational pull at its surface (g),  i.e. completely negligible : for the 70Kg person the force is approximately 30 millionths of the weight of a head hair , (do you notice the weight loss when a hair falls from your head ?).

[ someone should double-check my maths as it's 2:30am ...  http://www.calctool.org/CALC/phys/newtonian/centrifugal ]

Nice question and what about the Earth itself?

What about it ?

[CliffordK]

If you consider the gravitational pull of the sun experienced at the Earth, it is about 6mm/s², compared to 9.8 m/s² from the Earth.  It is small due to the distance we are from the sun, about 150 million km.

If the Earth was just hanging in one place in space, this would still be quite noticeable. 

However, the Earth is in orbit around the sun.  I.E, the Earth is in constant freefall towards the sun, and the centrifugal (force to follow a straight line), and the centripetal (force of gravity from the sun) balance out.

Consider if you were in a space ship in orbit around the Earth (or around the sun).  The space ship is constantly falling towards the Earth, compensated by the space ship moving forward.  The gravity, say in Low Earth orbit is nearly the same as on the surface of Earth (about 9 m/s²), however, one experiences it as Zero-G since both the occupants and the space ship are falling at the same rate.

Likewise, one would expect the Earth, and all the people on it to be in free fall with respect to the sun, and have the experience of zero-G (centrifugal and centripetal forces balance) with respect to the sun (of course, one still has the Earth's gravity).

We do, however, experience slight solar tides on Earth.  So you would expect your weight to decrease at noon and midnight and increase at 6AM & 6PM.  But, as Evan mentioned, it is less than the weight of a hair.  And, of course, the solar tides are less than the lunar tides.

So, if the Earth is in zero-G freefall with respect to the sun, what actually causes the tides.?

I think it is that the sun side of the Earth actually is traveling a shorter distance around the sun, and thus is traveling too slow to orbit, and thus stuff there is a tendency to fall towards the sun.  Or, you could consider it as being closer to the sun, and thus experiencing a slightly higher gravity from the sun than the middle of the earth, and thus slightly lighter.

On the opposite side, it is traveling a longer distance, and thus traveling faster than the orbit.  Likewise, there would be a tendency to move away from the sun.  Or, you could consider it as being farther from the sun, so the far side of the Earth experiences slightly less gravity from the sun than the middle of the Earth.

Regardless, while tides are noticeable when moving bodies of water over a mile deep, and covering vast ares of the Earth, they are generally insignificant when considering the weight of the human body.