Final answer:
The point at which the net gravitational force of Earth and the Sun on a spaceship is zero is known as the L1 Lagrange point. This point lies on the line joining the centers of the two bodies and will be closer to Earth due to the Sun's much larger mass. The exact position requires computation using Newton's law of universal gravitation.
Step-by-step explanation:
To determine how far from the center of the Sun the net gravitational force of Earth and the Sun on a spaceship would be zero, we employ the concept of gravitational balance or the point at which the gravitational pull of two bodies on a third one is equal and opposite, known as the Lagrange point.
The specific point we are interested in between the Sun and Earth is called the L1 Lagrange point. The gravitational forces are given by Newton's law of universal gravitation, which states that the gravitational force is proportional to the mass of the objects and inversely proportional to the square of the distance between them.
To find the exact position, we set the gravitational pull of the Sun and the Earth on the spaceship equal to each other and solve for the distance. The position will be closer to Earth since the Sun's mass is much greater than that of Earth.
However, without detailed computation or provided values, we cannot just select an answer such as 1.5 AU or 3.0 AU as the precise balance point depends on the specific values of the mass of the Sun and Earth, and their distance from each other.