You realize none of this was actually proved, until we launched spacecraft so we could have a 2nd viewpoint removed from the surface of the earth. Prior to that, the spacecraft, all we had was a theoretical model of the solar system that fit all the facts we had observed, such as the retrograde motion, and the "wobble" of the sun. The moon does NOT orbit the earth. What? You say, it certainly DOES! Well, yes and no. It orbits, yes, but it orbits the center of mass of the earth-moon pair. That point is inside the earth, close to but not at the center of mass of the earth alone. So, the earth wobbles opposite to the moon. The sun wobbles exactly like the earth does in response to the planets in orbit. Einstein came along in 1906 and proposed a "gravity lens", that light would "bend" a little as it passed close by a large gravity field, warping the fabric of space-time. In 1918 this was proved finally, during precise measurements made during a total solar eclipse. Not only did light bend but the sun wobbled. It took several more measurements to verify the wobble. And THAT is how we found over 600 planets around distant stars, because THEY wobble like ours does, and planets eclipse stars just our moon eclipses ours. It boggles the mind...
EDIT: seasons are NOT caused by the distance of the earth to the sun, but by the tilt of the axis. The winter solstice in the northern hemisphere is actually a few days from when we are closest to the sun. It is the angle of the sun's rays hitting the earth which makes the seasons. The lower in the sky as the north pole faces away from the sun, the less heat warms the surface, making winter. Look up perigee and apogee, perihelion and aphelion, and solstice and equinox...