Mass
In everyday usage, mass and "weight" are often used interchangeably. For instance, a person's weight may be stated as 75 kg. In a constant gravitational field, the weight of an object is proportional to its mass, and it is unproblematic to use the same unit for both concepts. But because of slight differences in the strength of the Earth's gravitational field at different places, the distinction becomes important for measurements with a precision better than a few percent, and for places far from the surface of the Earth, such as in space or on other planets. Conceptually, "mass" (measured in kilograms) refers to an intrinsic property of an object, whereas "weight" (measured in newtons) measures an object's resistance to deviating from its natural course of free fall, which can be influenced by the nearby gravitational field. No matter how strong the gravitational field, objects in free fall are weightless, though they still have mass.
Mass point geometry
Solution. We may arbitrarily assign the mass of point formula_37 to be formula_38. By ratios of lengths, the masses at formula_39 and formula_40 must both be formula_41. By summing masses, the masses at formula_23 and formula_26 are both formula_44. Furthermore, the mass at formula_31 is formula_46, making the mass at formula_34 have to be formula_48 Therefore formula_35 formula_50 and formula_51. See diagram at right.