According to our current understanding of physics, it is not possible for an object with mass to travel at the speed of light. As an object with mass approaches the speed of light, its relativistic mass increases, requiring an infinite amount of energy to reach or exceed the speed of light.
If you were able to travel at a velocity very close to the speed of light for a month (from your perspective), you would experience several interesting effects due to the theory of relativity, specifically time dilation and length contraction.
Time dilation refers to the slowing down of time for a moving object relative to an observer at rest. According to special relativity, as you approach the speed of light, time for you would appear to pass more slowly relative to an observer who is stationary. This means that when you return from your high-speed journey, more time would have passed for the stationary observer than for you. This effect is known as "time dilation."
Length contraction, another consequence of special relativity, states that an object in motion will appear shorter in the direction of its motion when observed by a stationary observer. Therefore, objects and distances in the direction of your motion would appear contracted from your perspective.
From the perspective of an observer on Earth, the effects of time dilation and length contraction would be observed. They would see that the duration of your month-long journey would be significantly shorter than a month according to their clocks, and the length of the spacecraft you are traveling in would appear shorter.
It's important to note that these effects become more pronounced as you approach the speed of light, so they would be relatively small at speeds achievable with current technology. Additionally, the consequences of traveling at such extreme speeds would involve various other factors like the effects of acceleration, energy requirements, and the behavior of matter at those speeds, which are beyond the scope of a simple explanation.
In summary, if it were possible to travel at speeds close to the speed of light, you would experience time dilation and length contraction, and from the perspective of observers on Earth, the duration of your journey would be shorter and distances would appear contracted.