Splitting The Sun In Two

Let's imagine the Earth orbiting two stars that are separated by a distance of 1 AU1 \text{ AU}, each with half the mass of the Sun. When the distance between the Earth and both stars is 1 AU1 \text{ AU}, the net gravitational force acting on Earth is F2F_2.

If the gravitational force applied by the Sun on the Earth at an orbital distance of 1 AU1 \text{ AU} is F1F_1. What is F2F1\dfrac{F_2}{F_1}?

Note: 1 AU1 \text{ AU}, which stands for "Astronomical Unit," is the actual average orbital distance between Sun and Earth.

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