Traveling close to the speed of light does not cause the weight of an object to increase. Weight is a measure of the force exerted on an object due to gravity, and it remains constant regardless of the object's velocity.
What does change as an object approaches the speed of light is its relativistic mass, also known as the "apparent mass." According to the theory of special relativity, the relativistic mass of an object with mass m moving at a velocity v is given by:
m' = m / sqrt(1 - (v^2 / c^2))
In this equation, c represents the speed of light in a vacuum.
As the velocity (v) approaches the speed of light (c), the denominator of the equation approaches zero, causing the relativistic mass (m') to increase. However, it's crucial to understand that this increase in relativistic mass does not have a direct impact on the weight experienced by an object.
Weight is determined by the gravitational force acting on an object, and it depends on the mass of the object and the strength of the gravitational field it is in. The gravitational force experienced by an object does not change due to its velocity. Therefore, the weight of an object traveling close to the speed of light would remain the same as it would at rest in a gravitational field.
It's also worth noting that the effects of traveling at such high speeds, such as time dilation and relativistic mass, are more pronounced as the speed approaches the speed of light. These effects are significant for objects with mass, but they do not imply an immediate threat to human life. The challenges and dangers associated with traveling at relativistic speeds are primarily related to the enormous amounts of energy required and the technical difficulties in achieving and maintaining such velocities.