How does the Earth orbit the Sun? We often think about the Earth orbiting the Sun in an elliptical orbit as shown here. But in this view, we are misinterpreting how the gravitational field of the Sun sees the Earth. The Earth is not orbiting alone. The Moon is also present and orbiting the Sun with the Earth. However, in astronomical scales, the gravitational field of the Sun doesn't really differentiate between the Earth and the Moon, resulting in the two bodies acting as a single point mass orbiting the Sun. This begs the question, what is the center of mass of the Earth and Moon together orbiting the Sun? In order to answer this, we need to gather some information about the Earth and the Moon. The Earth shown here has an average radius of 6,378 kilometers, and a total mass of 5.98 times 10 to the power of 24 kilograms. Conversely, the Moon is quite a bit smaller, having a total mass of 7.35 times 10 to the power of 22 kilograms. The distance between the centers of mass of the Earth and the Moon is about 385,000 kilometers. Finally, the Moon has an average radius of 1,737 kilometers. Needless to say, the diagram is also not drawn to scale here, as the radii of the Earth and Moon are on the order of about 1% of the distance between the two bodies. So we can safely treat them as point masses with respect to each other. If we define a coordinate system as shown here, we can use the formula for the center of mass in summation form, as our bodies are being treated as point masses. Expanding this out, we get the location of the center of mass of the Earth multiplied by the mass of the Earth, plus the location of the center of mass of the Moon multiplied by the mass of the Moon, all divided by the total mass of the system. Since our coordinate frame is centered on the Earth, its contribution to the numerator becomes zero, and we can fill in the appropriate masses and distances from above. If we evaluate this expression, we obtain that the location of the center of mass x bar is equal to 4,675 kilometers. Looking back at our problem, we can clearly see this value is less than the radius of the Earth. So the center of mass of the Earth Moon system is located within the Earth, but closer to the Earth's surface than the center of the Earth. What does this practically mean? Well, that elliptical orbit that we believe the Earth follows is actually the orbit of the center of mass of the Earth Moon system. So in actuality, the center of the Earth follows a wobbly orbit around the Sun, which is exaggerated here for clarity, but is still significant to know and to take into account if you wanted to say launch a probe that explored the solar system, and that you wanted it to be able to return back to Earth and be in the Earth's orbit accurately.