🚀Learn Astronomy in the largest Astronomy Course in Brazil: https://academyspace.com.br/bigbang Link to buy the NASA Kit: https://mailchi.mp/4267cd1b4f52/kitnasa What is the closest planet to Earth? You must have answered Venus. Anyone, in any table you look at, will come to the conclusion that Venus is the closest planet to Earth. But everyone can be wrong, and in fact, Mercury is the closest planet to Earth. Let's try to understand all this. First of all, Venus is the planet that comes closest to Earth, during the orbit of both around the Sun, when they are at their closest approach the distance between the two is 0.28 AU, this continues to be the smallest distance between Earth and a planet in the Solar System. Now, on average, over the course of the orbits, the planet Mercury is the closest to Earth. The method used to calculate this average orbit used the following calculation: subtract the average radius of an inner orbit from the average radius of an outer orbit. Although this calculation is intuitive, this average distance between each point of two concentric ellipses would be the difference in their radii, and in reality, this difference would only determine the average distance of the closest points of the ellipses. It is possible to improve this calculation a little, calculating the average distance of the closest point between the two orbits and the farthest point between them, and thus the average distance between Earth and Venus would be 1 AU. But the correct calculation is a little more complicated. The most accurate way to capture the average distance between planets is using the method known as the Point-Circle Method, or PCM. The PCM treats the orbits of two objects as being circular, concentric and coplanar. For the Solar System, this is a good premise. The eight planets have an average inclination of 2.6 degrees, plus or minus 2.2 degrees, to the ecliptic, and the average eccentricity of their orbits is 0.06 plus or minus 0.06. An object in a circular orbit maintains a constant velocity. The researchers assumed the position of the planet at a given time to be a uniform probability distribution around the circle defined by the mean orbital radius, as shown in Figure A. The average distance between two planets can be described as the average distance from each point on the circle c2, defined by r2, to each point on the circle c1, defined by r1. Because of rotational symmetry, the average distance d from a particular point on c2 to each point on c1 is the same for any chosen point on c2. The mean distance d is also equivalent to the mean distance from a single point on c2 to each point on c1, as shown in Figure b. Thus, the mean distance d can be determined by integrating the point-to-point distance around c1, and the above equation defines the PCM method. In this equation, E(x) is a second-order elliptic integral. And so, doing the math for Mercury and Venus, we have the following. The mean distance between Earth and Venus is 1.14 AU, and between Earth and Mercury is 1.04 AU. From the PCM, it was possible to see that the distance between two orbiting bodies is minimum when the inner orbit is at its minimum. This created a corollary, called the Whirly-Dirly Corollary, after an episode of Rick and Morty. For two bodies with approximately coplanar, concentric, and circular orbits, the mean distance between them decreases as the radius of the inner orbit decreases. Mercury has an average orbital radius of 0.39 AU, Venus 0.72, so Mercury is closer to Earth on average. In fact, this works for all the other planets in the solar system, and Mercury is the closest to Neptune. It just doesn't work for Pluto, for example, which has an inclination of 17 degrees and an eccentricity of 0.25, which means it escapes the premises proposed by the corollary. To validate all this, the researchers ran a simulation in Python, using a library called PyEphem. You can see the result of the simulation there. Pay attention to the graphs at the bottom, where you have a green and blue bar. The green one oscillates, because it shows the variation in the distance between the planets. And the blue one is the average distance. There is also a line connecting the planets, so we can clearly see the distance between them. The point is that since Mercury is closer to the Sun and orbits our star faster, it spends more time, closer to Earth, than Venus, which has a slower orbit. Although, again, the planet that comes closest to Earth is still Venus, but on average Mercury is the closest planet to us. And how can this change anything? It can help apply the PCM method to bodies in orbits and improve the planning of data relay satellites. So, what do you think of this? Source: https://physicstoday.scitation.org/do...