JVH>"If the Earth is going around the Sun, then the speed of its satellite would have to adjust due to the differences of the gravitational pull of the Earth. When the satellite is 'in the back' the Earth, it would have to 'follow' the Earth. When the satellite is 'in front' of the Earth, the Earth would 'follow' its satellite.
Since the Earth is supposed to be going around the Sun with an alleged speed of 107,534 km/hr or there abouts, the speed of its satellite - to account for the change of the gravity pull - would have to drastically change. It doesn't, apparently.
If the Earth does not circle the sun, and "the universe" revolves the Earth, Earth's gravitational pull on its satellite would be the same - regardless of its position on the orbit - which seems to be the case."
What you have stated is false. Gravity follows an inverse square law. That is, its power declines with the square of the distance between the attractors. The distance between the earth and the sun is 93,000,000 miles. The distance between the earth and the moon is approx. 384,000 miles. Even given the immense mass of the sun the distance is so great that the moon barely notices the sun in relation to the earth.
If the sun were a basketball and you put it on the goal line of a football field then take a pin and go to the 30 yard line that would be the earth. The moon is 1/6 the size of the head of the pin. It is barely affected by the basketball's gravity at this distance compared to the pin. However... it's still six inches away.
Just in case you're curious. Saturn would be three football fields away. The nearest star would be in Hawaii if the basketball were on a football field in Baltimore.