Splitting The Sun In Two

Let's imagine the Earth orbiting two stars that are separated by a distance of \(1 \text{ AU}\), each with half the mass of the Sun. When the distance between the Earth and both stars is \(1 \text{ AU}\), the net gravitational force acting on Earth is \(F_2\).

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

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

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