Final answer:
The gravitational force on a spaceship at a distance of two Earth radii from the center of Earth is given by the formula F = GMm / (2R)². This is derived from Newton's law of universal gravitation with the separation being two times Earth's radius. Option A is correct.
Step-by-step explanation:
When a spaceship is at a distance of two times the radius of Earth from the center of the Earth, the gravitational force on that spaceship is given by Newton's law of universal gravitation:
F = G×M×m / r²
Where F is the gravitational force, G is the gravitational constant (6.674 × 10-11 N·m²/kg²), M is the mass of the Earth, m is the mass of the spaceship, and r is the separation between the center of masses of the two objects. If r is equal to two times the radius of Earth (2R), the equation becomes:
F = G×M×m / (2R)²
Therefore, the correct answer is a. F = GMm / (2R)².
The correct formula to calculate the gravitational force on the spaceship when it is at a distance of two times the radius of Earth is F=GMm/(2R)².
Here, G represents the gravitational constant, which is a universal constant that is the same everywhere in the universe. Its value is 6.67 × 10^-11 Nm²/kg².
M represents the mass of Earth and m represents the mass of the spaceship. R represents the radius of Earth.
By substituting the given values into the formula, you can calculate the gravitational force on the spaceship.