POINT OF VIEW: MASS

If we travel inside a space ship, regardless of its speed, the masses of all the objects in the ship with us appear normal as long as our ship is not accelerating. However, from the vantage point of Earth, the mass of the ship and the masses of all the atoms inside it increase as its speed increases.

Let m be the mass of the moving ship as a multiple of its mass when it is stationary relative to an observer. Let u be the speed of the ship as a fraction of the speed of light. Then
m = 1/(1 - u²)^1/2
= (1 - u²)^-1/2
This is the same as the factor k that we defined a little while ago. It is always greater than or equal to 1.
Look again at Fig. 1. As the space ship moves faster, it “scrunches up.” Imagine now that it also becomes more massive. The combination of smaller size and greater mass is a “double whammo” in regard to the density of the ship.
Suppose that the rest mass (the mass when stationary) of our ship is 10 metric tons. When it speeds by at half the speed of light, its mass increases to a little more than 11 metric tons. At 80 percent of the speed of light, its mass is roughly 17 metric tons. At 95 percent of the speed of light, the ship masses about 32 metric tons. At 99.9 percent of the speed of light, the ship’s mass is more than 220 metric tons. And so it can go indefinitely. As the speed of the ship approaches the speed of light, its mass grows larger and larger without limit.

Fig. 1. As an object moves faster and faster, it grows shorter and shorter along the axis of its motion.