No, it doesn't take special relativity or general relativity into account. It's purely Newtonian physics.
How do you mean?
The force of gravity is not instantaneous. It "travels" at the speed of light. The Earth is not attracted to where the Sun is "now", it is attracted to where the Sun was approx. 8 minutes ago (the length of time it takes for light to travel from the Sun to the Earth), and vice versa.
The Earth is not attracted to where the Sun is "now", it is attracted to where the Sun was approx. 8 minutes ago
That's not entirely true as there are higher order effects in GR canceling this lag "to second order".