Weight and Mass, Revisited

As stated previously, the weight of an object is defined as the magnitude on the gravitational force acting on it. Its relationship to inertial mass, by Newton's law of gravitation is therefore given by

  W = mg

where g is the gravitational acceleration. Since g, can be different at different locations (eg different heights above the Earth, or near different planets), the weight of any object also changes with location. Weight and mass are only interchangeable if the gravitational acceleration is fixed. The inertial mass of an object is always the same, no matter where you are.

As an example, suppose that you are buying groceries on a space station a distance of 1500 km above the Earth, and you see a special on cheese. You can get 2.2 lbs of cheese for $4.00 or you can get 1 kg of cheese for the same price. Which should you buy? The amount of cheese (eg the food energy it would provide if you ate it) is determined by its inertial mass. You know that on the surface of the Earth, 1 kilogram weighs precisely 2.2 lbs. However, on the space station, the gravitational acceleration is less than at the surface of the Earth. Thus, 1 kg of cheese weighs less on the space station than it does on Earth. Conversely, in order to weigh in at 2.2 lbs, you need more than 1 kg of cheese. At a height of 1500 km, the gravitational acceleration is down by a factor of two, so that 2.2 lbs of cheese has an inertial mass of 2 kg, and would weigh 4.4 lbs on Earth. So you should definitely by the 2.2 lbs of cheese for $4.00.