To determine the gravitational force of an object located 10re from the center when the original force at 2re is 200 N, we can use Newton's law of gravitation. The law states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Mathematically, the gravitational force (F) between two objects with masses m1 and m2, separated by a distance r, is given by:

$$F = \frac{Gm1m2}{r^2}$$

where G is the gravitational constant (approximately 6.674 × 10^-11 N m^2 kg^-2).

In this case, let's assume the masses of the objects remain constant. If the distance between the objects changes from 2re to 10re, we can calculate the new gravitational force (F') using the formula:

$$F' = \frac{Gm1m2}{(10re)^2}$$

Since the masses are constant, we can write:

$$F' = \frac{F}{(10)^2}$$

Substituting F = 200 N:

$$F' = \frac{200 N}{(10)^2} = \frac{200 N}{100} = 2 N$$

Therefore, the gravitational force of the object located 10re from the center is 2 N.