What is the relationship of solar system in to the earth and space?
The Earth is a part of the Solar System
I'm not quite sure what your question is asking, but if you want to know the relationship between Earth and the Solar System, to simply put it, the Earth is a part of the solar system.
The Sun is a large powerful celestial being, and therefore it has a large gravitational field. Billions of years ago, space rock fused together with various elements through random collisions to create large rocks which eventually cooled to formed planets (one of these planets happened to be Earth).
Through inertia these planets remained constantly moving until they came into the Sun's gravitational field and became satellites. They began to orbit the Sun and will continue to orbit the Sun until something stops them from doing so, such as a collision with a much larger planet, or the Sun being destroyed.