Hey, is there a title?

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 this cute little girl and said, "What topic?" Mathematics or Physics? ”

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

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

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

It's not the physics teacher's usual papers, and Fang Chao has never seen this paper, obviously Zhang Lanlan's excellence is not unreasonable, in addition to the normal homework assigned by the teacher, she also bought exercises after class, in order to consolidate her shortcomings in all aspects, the more exercises she does, the more knowledge she will be exposed to, and the fewer and fewer shortcomings will naturally be.

Fang Chao didn't expect that Zhang Lanlan, who was usually well-behaved and lovely, would have this unexpected side, which somewhat made Fang Chao look down on her.

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

Zhang Lanlan's eyes suddenly became a little flustered.

Fang Chao was a little strange, what was Zhang Lanlan looking at just now? How strange is that......

However, he didn't think much of it, and his eyes were locked on the test paper.

[What is being discussed and studied is two launch schemes for a certain space research plan to launch a spacecraft out of the solar system.] The first option is to launch the spacecraft at a speed high enough that it can escape directly into the solar system. The second option is to make the spacecraft approach an outer planet and rely on its help to change the direction of the spacecraft to achieve the speed necessary to escape from the solar system. Assuming that the spacecraft is moving only in the gravitational field of the sun or planet, whether it is moving in the gravitational field of the sun or in the gravitational field of the planet depends on which field strength is at that point.

According to Scheme 1, determine the minimum velocity Va and its direction required to launch the spacecraft with respect to the Earth.

Assuming that the spacecraft has been launched in the direction determined in , but has another velocity Vb with respect to the Earth, find the velocity of the spacecraft as it passes through the orbit of Mars, i.e., the parallel and vertical components relative to this orbit. When the spacecraft passes through the orbit of Mars, Mars is not near this node.

Let the spacecraft enter the gravitational field of Mars, and try to find the minimum velocity required to launch the spacecraft from Earth to escape from the solar system.

Hint: From the results, you can know the magnitude and direction of the optimal velocity required for the spacecraft to escape from the solar system after escaping from the Martian gravitational field. Find the relationship between this optimal velocity and the velocity component of the spacecraft before it entered the gravitational field of Mars, i.e., the velocity component you determined in . What is the conservation of energy in the spacecraft?

Estimate the maximum percentage of energy savings that the second option could achieve over the first.

Note: Assuming that all planets are in the same plane and the energy expended to escape from the Earth's gravitational field.

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

Data: The speed at which the Earth revolves around the Sun is 30km/s, and the ratio of the distance from the Earth to the Sun and Mars to the Sun is 2/3. 】

Fang Chao only thought for a moment before saying, "Isn't this first question very simple?" It can be deduced using the third cosmic velocity. ”

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

V3^2-V0^2=GM

"You use this formula to substitute it, then there will be an answer to the first question immediately, as for the angle, it must be 0 °, this is not to think about it, of course, the calculation formula still has to have ......"

Zhang Lanlan blushed and said, "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 question and the fourth question, because the third question can't be calculated, so I don't know the answer to the fourth question, people...... Talent is not so stupid. ”

Fang Chao: "......"

Slightly awkward.

But in fact, it is understandable that such a topic may be a bit problematic for ordinary high school students, but although Zhang Lanlan is not particularly talented in physics, he is indeed not stupid, after all, he can enter this school and be in the same class as Fang Chao, which in itself says a lot.

And at this time, the boy next to Zhang Lanlan couldn't stand Fang Chao and Zhang Lanlan's appearance of 'eyebrows', and coughed dryly, "Squad leader, you are tired of standing, I just went out to move my muscles, you sit." ”

So under the gaze of a group of people, Fang Chao sat next to Zhang Lanlan, there was a faint fragrance on the little man's body, and it smelled quite good, Fang Chao couldn't help but take two more sips.

Other people's words, Zhang Lanlan was definitely angry, but Fang Chao's words were so shy~

Is the squad leader taking a fancy to me?

But she can't say it clearly, girls need face, and if you like me, class leader, you will boldly pursue me, I'm very good at chasing, I like Xueba, and the class leader, you don't look bad, very sunny, the most important thing is that your head is also quite tall, although there is no one meter eight, but one meter seven five is not bad.

Zhang Lanlan still has requirements for finding a boyfriend, that is, the boyfriend cannot be less than 1.75 meters, otherwise, what should I do if my future baby is not high?

I am not tall anymore, but I must not let my children inherit their genes.

So Fang Chao just met Zhang Lanlan's minimum requirements for her boyfriend's height.

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

Indeed, in terms of Zhang Lanlan's IQ, the first two questions should not be difficult, and in the case of the second question, the average velocity is calculated by Kepler's law, and then the absolute velocity is calculated by the law of conservation of mechanical energy, and the radial velocity is obtained by orthogonal decomposition, everything is perfect.

Zhang Lanlan is still okay, and he is not too stupid.

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

Then, Fang Chao opened his mouth and said, "Since Lan Lan, your first and second questions have been solved, then the third question, because you have calculated the third cosmic velocity, and when the spacecraft enters the gravitational circle with a relative velocity greater than the escape, the orbit is a hyperbolic orbit, and the relative velocity of entering and flying out remains the same, and the direction changes, so first find the escape velocity of the sun in the orbit of Mars, Lan Lan, do you understand?" ”