Become a master from now on

Chapter 233 Lanlan, do you understand? (Ask for a monthly ticket subscription!)
Hey, do you have a question?

It's not easy~
Sure enough, God still favors those who are prepared.

So Fang Chao came to the opposite side of Zhang Lanlan again, looked at the cute little girl and said, "What subject? Math or physics?"

Zhang Lanlan took out a test paper from the drawer, and then said, "It's a physics question, the last question in the test paper, I don't know how to do this question."

"Oh," Fang Chao said with an 'oh', took the test paper in Zhang Lanlan's hand, and said, "Let me take a look."

Soon, Fang Chao's eyes fell on this test paper.

It's not the paper that the physics teacher usually gives, and Fang Chao has never seen this paper before. Obviously Zhang Lanlan's excellence is not unreasonable. In addition to the normal homework assigned by the teacher, she also bought extra-curricular exercises , in order to consolidate their own shortcomings in all aspects, the more exercises you do, the more knowledge you will be exposed to, and naturally the shortcomings will become less and less.

Fang Chao didn't expect that Zhang Lanlan, who is usually well-behaved and pleasant, would have such an unexpected side, which made Fang Chao look at her a little high.

So when Fang Chao glanced over, he found that Zhang Lanlan's eyes were facing his face, and just the next moment, Zhang Lanlan's eyes met Fang Chao's.

Zhang Lanlan's eyes suddenly became a little flustered.

Fang Chao was a little strange, what was Zhang Lanlan looking at just now?very strange……

But he didn't think much about it, and his eyes were fixed on the test paper.

【What is being discussed and researched now is about a certain space research plan, two launch schemes for launching spacecraft to the outside of the solar system.The first option is to launch the spacecraft at a speed high enough that it escapes directly into the solar system.The second option is to bring the spacecraft close to an outer planet and, with its help, change the direction of the spacecraft's motion to achieve the speed necessary to escape the solar system.Assuming that the spaceship only moves in the gravitational field of the sun or the planet, then whether it moves in the gravitational field of the sun or the gravitational field of the planet depends on which field strength is at the point.

(a) According to scheme 1, determine the minimum velocity Va and its direction relative to the earth's motion required to launch the spacecraft.

(b) Assuming that the spacecraft has been launched in the direction determined in (a), but has another velocity Vb relative to the earth, find the velocity of the spacecraft as it passes through the orbit of Mars, that is, the parallel and perpendicular components relative to this orbit.When the spacecraft crosses the orbit of Mars, Mars is not near this node.

(c) Assuming that the spacecraft enters the gravitational field of Mars, try to find the minimum speed required to launch the spacecraft from the earth to escape from the solar system.

Tip: From the result (a), we can know the size and direction of the optimal speed for the spaceship to escape from the solar system after breaking away from the gravitational field of Mars (it is not necessary to consider the precise position of Mars when crossing the orbit of Mars).Find the relationship between this optimal velocity and the velocity component of the spacecraft before it entered the gravitational field of Mars, that is, the velocity component you determined in (b).What about the energy conservation of the spaceship?

(d) Estimate the maximum percentage of possible energy savings for the second alternative over the first.

Note: Suppose all planets are in the same plane and the energy consumed by escaping from the earth's gravitational field.

Neglect air resistance, the rotation of the Earth, and the energy expended to escape from the Earth's gravitational field.

Data: The speed of the earth revolving around the sun is 30km/s, and the ratio of the distance from the earth to the sun and the distance from Mars to the sun is 2/3. 】

Fang Chao just thought for a moment and then said, "Isn't the first question very simple? It can be calculated by using the speed of the third universe."

Fang Chao took a pen and quickly wrote down a formula on the draft paper.

V3^2-V0^2=GM(2/r-2/d)
"If you use this formula to substitute it in, then you will have the answer to the first question immediately. As for the angle, it must be 0°. Don't even think about it. Of course, there is still a calculation formula..."

Zhang Lanlan blushed, "Fang Chao, I'm not stupid. I have already calculated the answers to the first and second questions. What I don't know is the third and fourth questions, because the third question cannot be calculated. So I don't know the answer to the fourth question, people... people are not so stupid."

Fang Chao: "..."

Slightly awkward.

But in fact, it is also understandable that such a topic may be problematic for ordinary high school students, but although Zhang Lanlan does not have a particularly high talent in physics, he is indeed not stupid. Same class, that says a lot in itself.

At this time, the boy next to Zhang Lanlan couldn't stand the way Fang Chao and Zhang Lanlan were flirting with each other. He coughed dryly and said, "Monitor, you're tired of standing. I just went out to stretch my muscles. Please sit down."

So under the eyes of a group of people, Fang Chao sat next to Zhang Lanlan. There was a faint fragrance on the little man's body, which was quite pleasant, and Fang Chao couldn't help taking two more puffs.

Zhang Lanlan would definitely be angry if someone else said it, but Fang Chao was so shy~
Is the squad leader taking a fancy to me?

But she couldn't say clearly, all girls need face, and if you like me, monitor, you can boldly pursue me, I'm easy to chase, I like Xueba, and monitor, you look good It's not bad, it's very sunny, and the most important thing is that it's quite tall, although it's not 1.8 meters, but 1.7 meters five is not bad.

Zhang Lanlan still has requirements in terms of finding a boyfriend, that is, the boyfriend should not be less than 1.7 meters five, otherwise, what should I do if my future baby is not tall?
I am not tall anymore, but I must not let my children inherit my genes.

So Fang Chao just met Zhang Lanlan's minimum requirement for a boyfriend's height.

Of course, our squad leader never cares about this kind of thing.

Indeed, considering Zhang Lanlan's IQ, the first two questions should not be difficult, but for the second question, use Kepler's law to calculate the average speed, and then use the law of conservation of mechanical energy to find the absolute speed. Out radial velocity, everything is perfect.

Zhang Lanlan is still okay, not too stupid.

Fang Chao had a judgment on Zhang Lanlan in his heart.

Later, Fang Chao said, "Since you have solved both the first question and the second question, Lanlan, then the third question, because you have already calculated the third cosmic velocity, and when the spaceship enters at a relative velocity greater than the escape The orbit in the gravitational circle is a hyperbolic orbit, the relative speed of entering and flying out remains the same, but the direction changes, so first find the escape velocity of the sun on the orbit of Mars, Lanlan, do you understand?"

(End of this chapter)