The change in the value of acceleration of earth towards sun, when the moon comes from the position of solar eclipse to the position on the other side of earth in line with sun is: (mass of the moon = $$7.36 \times 10^{22}$$ kg, radius of the moon's orbit = $$3.8 \times 10^8$$ m).

Position 1: Solar Eclipse

The Moon is located between the Earth and the Sun. In this case, both the Sun and the Moon pull the Earth in the same direction (towards the Sun).

$$a_1 = a_s + a_m$$

Position 2: Other side (Full Moon)

The Moon is on the opposite side of the Earth, away from the Sun. The Sun pulls the Earth towards itself, while the Moon pulls the Earth in the opposite direction.

$$a_2 = a_s - a_m$$

The change in the value of acceleration ($$\Delta a$$) is $$\Delta a = |a_1 - a_2|$$

$$\Delta a = (a_s + a_m) - (a_s - a_m)$$

$$\Delta a = 2 \cdot a_m$$

The change is simply twice the acceleration produced by the Moon on the Earth.

The acceleration produced by the Moon on the Earth is given by Newton's Law of Universal Gravitation:

$$a_m = \frac{G \cdot M_{moon}}{r^2}$$

$$a_m = \frac{6.6 \times 10^{-11} \cdot 7.36 \times 10^{22}}{(3.8 \times 10^8)^2}$$
$$a_m = \frac{48.576 \times 10^{11}}{14.44 \times 10^{16}}$$
$$a_m \approx 3.364 \times 10^{-5} \text{ m/s}^2$$

$$\Delta a = 2 \cdot a_m$$

$$\Delta a = 6.73 \times 10^{-5} \text{ m/s}^2$$