"Please point your telescope to a point on the ecliptic in the constellation Aquarius at 326° of ecliptic longitude. You will find a round and bright new planet within an area of about 1° from this point..."
This is a letter written by French astronomy enthusiast Le Verrier to the German astronomer Galle. On September 23, 1846, that is, the night when Galle received the letter, a planet that was not on the original star map was indeed discovered at the position pointed out by Le Verrier. This was the eighth planet in the solar system - Neptune , which was later known as the planet discovered under the tip of the pen.
Neptune
Although the German astronomer Galle first discovered it at the Berlin Observatory, this discovery was based on the calculations of the French mathematician Le Verrier, so in a sense, Le Verrier was the real discoverer of Neptune.
Auburn Jean-Joseph Le Verrier
I still remember when I saw this story when I was in junior high school, I was shocked. The knowledge I had at that time made me feel that all this was so incredible, that planets far away in the sky could actually appear on paper so close at hand. While shocking, it also aroused my strong curiosity for knowledge. How did he do it?
In my third year of junior high school, something unexpected happened to me. I'm admitted to high school! ! ! It didn’t take long for me to get to know Kepler , Newton and other big guys. And the problems that had puzzled me for several years were solved afterwards.
Without further ado, let’s get down to business
Although we cannot discover a planet as easily as Le Verrier did, as ordinary people, it is simple for us, as ordinary people, to calculate the moon revolution period based on the knowledge we have learned. Just two formulas
The formula of gravity : (1)
Gravitation is an interaction between objects due to their mass. Its size is related to the mass of the object and the distance between the two objects.
The formula for calculating the centripetal force of circular motion: (2)
The moon revolves around the earth, just like two people holding hands and spinning in circles. So how come the earth and the moon are holding hands when they are so far away? At this time, gravity plays the role of the hand.
In this way we connect the centripetal force and the gravitational force. Now that the theoretical foundation is in place, the next step is the calculation problem.
We require the revolution period of the moon, but the time parameter does not appear in the formula. Don't worry, just make a small deformation of (2), and the parameter time will emerge.
linear speed and motion period in circular motion.
At this time, equation (2) can become like this:. The time constant T appears.
We have explained before that the gravitational force between the earth and the moon acts as the centripetal force for the moon to move in a uniform circular motion around the earth. That is,
moves the required T to the left side of the equation, and the other terms move to the right side of the equation. The expression to get the period T is:
At this point, 90% has been completed, and the next 10% is to substitute the relevant data.
Among them, the mass of the earth
The distance between the earth and the moon
The gravitational constant
Substitute the above data into the periodic expression to obtain T=2370328.6s. After unit conversion, T=27.43 days.
Through a series of calculations, we found that the moon's revolution period around the earth is 27.43 days. Interested friends can verify whether our calculation results are significantly different from the actual revolution period.
Conclusion
Physics seems to many people to be a difficult and boring subject. When we study physics, we mostly memorize formulas. But in fact, as long as we connect the formula with some phenomena in life, it is easy to keep it in mind. You can also enjoy the sense of accomplishment after solving the problem. The author of
is not a physics major, and his physics level is only in high school. Although I studied engineering in college, physics has never been my professional subject. If there are any mistakes, you are welcome to criticize and point them out.
