Answer:
The magnitude of the gravitational force that each part of the space probe exerts on the other in space, far from any other objects, is approximately 6.27 x 10^-6 N.
Step-by-step explanation:
To find the magnitude of the gravitational force that each part of the space probe exerts on the other, we can use the equation for gravitational force:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67 x 10^-11 N m^2/kg^2), m1 and m2 are the masses of the two parts of the space probe, and r is the distance between their centers.
Given that the masses are proportional to the weights, we can rewrite the equation as:
F = (G * w1 * w2) / r^2
where w1 and w2 are the weights of the two parts.
Substituting the given values into the equation:
F = (6.67 x 10^-11 N m^2/kg^2) * (10500 N) * (3000 N) / (23 m)^2
Simplifying the equation:
F = (6.67 x 10^-11 N m^2/kg^2) * (10500 N) * (3000 N) / (23 m)^2
F ≈ 6.27 x 10^-6 N
Therefore, the magnitude of the gravitational force that each part of the space probe exerts on the other in space, far from any other objects, is approximately 6.27 x 10^-6 N.