Final answer:
To determine the new gravitational potential energy when the distance between stars in a double-star system is doubled, we use the formula for gravitational potential energy which shows that the potential energy is inversely proportional to the distance. As a result, the potential energy would be one-fourth of its original value. However, without knowing the initial potential energy or masses of the stars, we cannot provide an exact answer from the options given.
Step-by-step explanation:
To calculate the gravitational potential energy (GPE) of a double-star system where the distance between the two stars is doubled, we can use the formula for GPE between two masses, which is given by:
GPE = -G(m1m2) / r,
where G is the gravitational constant, m1 and m2 are the masses of the two stars, and r is the separation between the two masses. When the distance r is doubled, the new potential energy will be one-fourth of the original value since GPE is inversely proportional to the distance.
If the original gravitational potential energy of the system at the initial separation was represented by some value, doubling the distance would reduce this value to a quarter of its magnitude.
However, without the original GPE value or masses of the stars, we cannot calculate the new GPE value. The options given (A, C, D, E) cannot be evaluated as correct without additional information about the initial conditions of the system.