(Originais Teachy 2023) - Question Medium of Physics

An astronaut travels in a spaceship at a constant speed of 0.8c, where c is the speed of light in a vacuum. He intends to conduct an experiment involving the emission of a light signal to a satellite in orbit. According to the special theory of relativity, the time for an observer at rest on Earth between the emission and reception of the light signal would be different from the time recorded by the astronaut in the spaceship. Considering the time dilation given by the Lorentz factor, where γ = 1 / sqrt(1 - (v^2 / c^2)), and that c = 3 x 10^8 m/s, calculate: 1) The γ factor for the astronaut's speed. 2) The time dilation, that is, the relationship between the time measured by the astronaut and the time that an observer on Earth would measure for the light signal to travel the round trip distance of 4.8 x 10^8 meters. Consider the speed of light as c = 3 x 10^8 m/s and respond in terms of c and the exact value of the γ factor, without rounding.