I have to make a paper for scientific work in the second year. I chose the sun as my subject. We had to adjust sub-questions 1 of my sub-questions is how it is that the planets revolve around the sun. The plants do revolve around the sun, but why and how come?
Answer
First let’s do this: at the equator we fire a bullet horizontally in a westerly direction so that it flies over the equator. We assume that there is no air resistance to slow the bullet, and that there is nothing on Earth to get in the way. So the Earth’s surface is a perfectly smooth sphere.
What is that bullet doing? After a certain distance it will of course fall to the ground, due to gravity. The greater the bullet’s initial velocity, the farther it travels before it falls to the ground. However, the Earth’s surface also bends downwards, because the Earth is a sphere. Well, if the initial velocity of a super-fast bullet were 8 km/s, the curvature of its trajectory would exactly match the curvature of the Earth’s surface. (You can prove this mathematically.) So this means that, although the bullet falls permanently due to the Earth’s gravity, it keeps flying at the same height above the Earth’s surface, or in other words, always at the same distance from the center of the Earth. the earth, the center of the gravitational field. The bullet therefore falls permanently. This is only possible if he always maintains the same constant correct speed. That is why we have also stated that there is no air resistance.
Similarly, a planet “flies” in orbit around the sun (let’s assume for the sake of simplicity that this is a circle first). Also, the planet has a constant speed that is not slowed down by anything (space = vacuum), and it therefore falls constantly towards the sun, but in such a way that its distance from the sun remains the same. Just like that super-fast bullet flies around the earth at a constant height. The constant speed ensures that this balance is not disturbed.
In reality, the orbit is not a perfect circle, but an ellipse. As a result, the planet’s distance from the sun changes a little as it orbits the sun, and its speed also changes a little bit all the time. When the planet gets a little closer to the sun, its speed increases slightly, so that it eventually moves a little further from the sun. As a result, the speed decreases slightly and she will come a little closer to the sun again. For Earth, the distance from the sun varies between 147 million and 152 million kilometers. The variation is therefore less than two percent more or less compared to the average.
Answered by
prof.dr. Paul Hellings
Department of Mathematics, Fac. IIW, KU Leuven
Old Market 13 3000 Leuven
https://www.kuleuven.be/
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