According to Einstein's theory of relativity, as an object approaches the speed of light, its relativistic mass increases. The formula to calculate the relativistic mass of an object is:
m' = m / sqrt(1 - (v^2/c^2))
Where: m' is the relativistic mass, m is the rest mass (in this case, 1 kilogram), v is the velocity of the object (99.9% of the speed of light), and c is the speed of light.
To calculate the new mass of a 1-kilogram object moving at 99.9% of the speed of light, we can substitute the values into the formula:
v = 0.999c (where c is the speed of light, approximately 3 x 10^8 meters per second)
m' = 1 / sqrt(1 - (0.999c)^2/c^2)
m' = 1 / sqrt(1 - 0.998001/c^2)
m' = 1 / sqrt(1 - 0.998001/1)
m' = 1 / sqrt(1 - 0.998001)
m' = 1 / sqrt(0.001999)
m' = 1 / 0.0447
m' ≈ 22.38 kilograms
Therefore, the new mass of a 1-kilogram object moving at 99.9% of the speed of light would be approximately 22.38 kilograms.