Seeing as how we humans live on earth, I am not sure what you mean.
all human and animal activity would die
The human race would not be far from extinction.
Well Earth is part of the Universe and one can travel round Earth by walking. To travel to parts of our own solar system one would need a space ship. As far as we know it would take more than a human lifetime to travel to the nearest star to the Sun.
If the sun's radiation could not travel through space, then the Earth would be a cold, dark, frozen rock, and nothing would have ever happened on it.
No one really knows what would happen because humans have never seen that first hand in reality. But I would imagine that the Earth would look similar to Mars.
It is highly unlikely that human travel to Mercury will happen in the near future. Mercury's extreme temperatures, lack of atmosphere, and proximity to the Sun make it a challenging and inhospitable environment for human exploration. Additionally, the cost and technological requirements for such a mission would be enormous.
then it would hardly have vegetation and human life would not exist
The temperature on Earth will become so hot that no living animal, human or plant could survive.
In reality, the interior of the Earth is slowly cooling. In human time perspective, however, this cooling has no impact.
300 billlion years
Saturn has a solid surface so if you land on Saturn you would sink into hotter and deeper surface so you would die.
Without boys and girls on Earth, reproduction through sexual reproduction would not be possible, and the human species would not be able to continue through natural means. This would have severe consequences for the survival and evolution of the human race.