General information. Venus is the second closest planet to the Sun, almost the same size as the Earth, and its mass is more than 80% of the Earth's mass. For these reasons, Venus is sometimes referred to as Earth's twin or sister. However, the surface and atmosphere of these two planets are completely different. The Earth has rivers, lakes, oceans and the atmosphere we breathe. Venus is a scalding hot planet with a dense atmosphere that would be fatal to humans. The average distance from Venus to the Sun is 108.2 million km; it is practically constant, since the orbit of Venus is closer to a circle than our planet. Venus receives from the Sun more than twice as much light and heat as the Earth. However, on the shadow side, Venus is dominated by a frost of more than 20 degrees below zero, since the sun's rays do not fall here for a very long time. The planet has a very dense, deep and very cloudy atmosphere, preventing us from seeing the surface of the planet. The atmosphere (gas shell) was discovered by M. V. Lomonosov in 1761, which also showed the similarity of Venus with the Earth. The planet has no satellites.

Traffic

Traffic. Venus has an almost circular orbit (eccentricity 0.007), which it bypasses in 224.7 Earth days at a speed of 35 km/sec. at a distance of 108.2 million km from the Sun. Venus rotates around its axis in 243 Earth days - the maximum time among all the planets. Venus rotates around its axis in the opposite direction, that is, in the opposite direction to its orbit. This slow and reverse rotation means that, as seen from Venus, the Sun rises and sets only twice a year, since a Venusian day is equal to 117 Earth days. The axis of rotation of Venus is almost perpendicular to the orbital plane (tilt 3 °), so there are no seasons of the year - one day is similar to another, has the same duration and the same weather. This weather uniformity is further enhanced by the specificity of the Venusian atmosphere - its strong greenhouse effect. Also, Venus, like the Moon, has its own phases.

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How far is the planet Venus from the Sun? description of the orbit around the star, comparison with the Earth, Mercury and Mars in the photo, retrograde Venus.

Venus is called Earth's sister for a reason. There are many similar characteristics between the planets. Although if you remember the hellish heating of a neighbor, you understand that in the process of its development something did not go according to plan. Somehow, a dense atmosphere has formed and we have the hottest planet in the solar system.

This is interesting if you remember that in terms of distance, Venus is only in second place from the star, but it is ahead of Mercury in terms of temperature. Let's take a closer look at what distance from the Sun to Venus.

Distance from Sun to Venus

perihelion and aphelion

While all solar planets follow an elliptical orbit, Venus ignores this and is considered the most circular. The average distance from Venus to the Sun is 108,208,000 km. Fluctuations from this mark reach 107,477,000 km (perihelion) and 108,939,000 km (aphelion).

If we compare with earthly indicators, then we note that the average distance of the Earth from the Sun is 149,598,020 km and fluctuates between 147,095,000 km and 152,100,000 km.

Mars has an average distance of 227,939,200 km. But due to the high eccentricity (0.0934), the distance varies from 206,700,000 km to 249,200,000 km.

Mercury has the highest eccentricity. While the average distance reaches 57,909,050 km, it can vary from 46,001,200 km to 69,816,900 km.

You may have already noticed that Venus stands out among all the representatives. In addition, it takes 224.7 days for an orbital passage at a speed of 35.02 km / s.

retrograde

This is another surprise. While all solar planets rotate in the direction of the orbital path, retrograde Venus does so in the opposite direction. In addition, the process itself is extremely slow and one axial rotation covers 243 days.

Scientists believe that the situation was influenced by two major collisions in the past. The first created a satellite, and the second changed the direction of rotation.

Each planet has its own zest. Although Venus is our sister, she is still able to incinerate her guests to ashes and pour acid rain on them. Now you have learned more about the distance from Venus to the Sun.

PROJECT

Demo Solutions

exam paper 2007

Part 1

Choice questions

Task 1, part 1.

The distance from Venus, one of the planets of the solar system, to the Sun is 108 million km. How is this value written in standard form?

A. 1.08∙10 6 km B. 1.08∙10 7 km C. 1.08∙10 8 km D. 1.08∙10 9 km

// Answer: B.

// Solution: 108 million km = km =
km.

Task 2, part 1.

The results of the district control work in algebra in the 9th grade were presented in the form of a diagram. How many students received a mark of "2" if a total of 320 ninth graders wrote the paper?

A. 5 students B. 16 students C. 64 students D. 160 students

//Answer: B.

//Decision: (account).

Task 3, part 1.

There is an inscription on the wallpaper roll, which guarantees that its length is 10 ± 0.05 m. What length cannot the roll have under this condition?

A. 10 m B. 9.98 m C. 10.04 m D. 9.92 m

//Answer: G.

//Solution: l - the length of the wallpaper in a roll,
; 9,92

Task 4, part 1.

car expends a liters of gasoline per 100 kilometers. How many liters of gasoline do you need to travel 37 km?

BUT.
l B.
l V.
l G.
l

// Answer: A.

//Solution: Denote the desired value by a letter X. We have a proportion
.

Another way: L of gasoline is consumed per 1 km, which means that l of gasoline is consumed per 37 km.

Task 5, part 1.

Specify an expression that makes sense for any value of the variable m.

BUT.
B.
AT.
G.

//Answer: G.

//Solution. The expression does not contain division by a variable.

Task 6, part 1.

For each expression from the top line, indicate its equal from the bottom one by entering the corresponding letters in the cells of the table:

1)
2) (b 4 b 3) 2 3) b 4 (b 3) 2

a) b 14 b) b 12 c) b 10 G) b 9

//Solution:
;
;
.

Task 9, part 1.

Which equation has two different roots?

BUT.
AT.

B.
G.

// Answer: B.

//Solution: A.
B.
AT. .

Task 11, part 1.

From a rectangular sheet of cardboard, the dimensions of which are 56 cm and 32 cm, it is necessary to make a box without a lid. To do this, identical squares are cut out at the corners of the sheet and the edges are folded up. What should be the side of the square to be cut out so that the bottom of the box has an area of ​​640 cm2?

Let the side of the square to be cut out be X see Which equation corresponds to the condition of the problem?

A. (56 - X)(32 – X) = 640 V. 56∙(32 - 2 X) = 640

B. (56 - 2 X)(32 – 2X) = 640 G. 56∙32 - 4 X 2 = 640

//Answer: B.

//Decision: If X cm is the length of the side of the cut square, then the bottom of the box has dimensions
mass media
cm. The area of ​​the bottom is
cm 2. We have an equation: .

Task 13, part 1.

About numbers a and With it is known that a > c. Which of the following inequalities is incorrect?

A. 3 a > 3c B. -2 a > –2c AT.
G. 1 - a With

//Answer: B.

//Solution: Inequality 3 a > 3c- right, inequality –2 a > –2c is false, because if a > c, then -2 a c.

Task 14, part 1.

The sequences are given by the first few terms. One of them is an arithmetic progression. Specify it.

A. 1; 2; 3; 5; ... IN 1; 3; 5; 7; ...

B. 1; 2; four; eight; ... G. ...

// Answer: B.

//Decision: In case B we have .

Task 15, part 1.

The figure shows a graph of a quadratic function. Which of the following formulas defines this function?

BUT. at =
AT. at =

B. at =
G. at =

// Answer: B.

//Solution. Various ways of reasoning are possible. For example, next.

Since the branches of the parabola are directed upwards, it is a graph of one of two functions - A or B. The graphs of both functions intersect the y-axis at the point (0; -3), so another way of recognition must be found. Find the zeros of the functions. In the case of A, the zeros of the function are the numbers –3 and 1, in the case of B, the numbers 3 and –1. Therefore, the figure shows the graph of the function at = .

You can also choose from these two formulas by directly substituting any points of the graph into the abscissa formula, for example, points of intersection with the axis X.

Task 16, part 1.

The regular bus traveled from city A to city B and after parking came back. The figure shows a graph of its movement: the time is plotted along the horizontal axis (in hours), and the distance from city A (in kilometers) is plotted along the vertical axis. Which of the following statements is incorrect?

A. The distance between cities A and B is 180 km.

B. The speed of the bus on the way from A to B was less than on the way back.

B. Parking in city B lasted 2 hours.

D. The bus spent 1 hour more on the return trip than on the trip from A to B.

//Answer: B.

//Solution:
km/h;
km/h;

but 60 km/h > 45 km/h.

Short answer questions .

Task 7, part 1

Simplify the expression
.

Answer:____________________

//Answer: . Answer options: 0.5.

//Solution:
.

Task 8, part 1

Simplify the expression
.

Answer: __________________

//Answer:
. Answer options: ;
.

//Solution: .

Task 10, part 1

Solve System of Equations
.

Answer: __________________

//Answer: (3;1). Answer options:
;

//Solution:

at = 1; X = 4at – 1 = 3.

Task 12, part 1

Solve the inequality X – 1 ≤ 3X + 2.

Answer: _____________________

//Answer: x≥ -1.5. Answer options: [–1.5; +∞); X [–1,5; +∞).

//Solution: .

Part 2

Questions with a detailed answer .

These tasks are designed to test mastery of the course material at advanced levels. They are performed on a separate sheet with a record of the progress of the decision. Task conditions are not overwritten, drawings are not redrawn.

The requirements for completing tasks of an advanced level are as follows: the solution must be mathematically literate, contain consideration of all possible cases (if any), and the student's reasoning must be clear from it. There are no special requirements for the details of the explanations, the presence of references to theoretical facts, the design of the decision. The student has the right to give explanations with varying degrees of completeness, depending on his ideas about their necessity.

The general criteria for evaluating the tasks of the second part of the examination paper are as follows. For the complete and correct completion of the task, the student is credited with the score indicated in the text of the work for this task. If a mistake or a typo is made in the solution that does not affect the correctness of the overall course of the solution (even with an incorrect answer) and allows, despite its presence, to draw a conclusion about the mastery of the material, then the student is credited with a score that is 1 less than the specified one. Other cases are not covered by the criteria. This is due to the interpretation of qualitative properties, which are measured by the second part of the work: the ability to perform tasks of a complex nature, the ability to integrate knowledge from various topics of the algebra course. These qualities appear only if the student discovers the ability to solve the problem of the proposed level and content.

The description of the criteria for evaluating the performance of specific tasks contains examples of errors / omissions that allow you to count a score that is 1 less than the specified one. These examples, however, do not exhaust all possible errors of this kind. When checking the work of the subject commission, in a number of cases it will be necessary to decide how to qualify this or that student's shortcoming.

Task 1, part 2

Plot the Function
. What values ​​of the argument satisfy the inequality
?

//Answer: The graph is shown in the figure. The inequality holds for
.

Other possible solutions.

The graph can be built on any other points.

The answer to the question can be obtained by solving the double inequality
:
, ,
. (The double inequality can be replaced by a system of two linear inequalities).

	The graph is correctly constructed and the correct answer to the question is given.
	With a correctly constructed graph, an error was made in answering the question, or the answer to the question is missing.
	Incorrectly constructed graph and other cases that do not meet the specified criteria.

Comment.

With a correctly constructed graph, the absence of a reference to the fact that the graph is a straight line, or indications in the figure of the coordinates of the points of the graph should not serve as a basis for lowering the score.

Task 2, part 2

Simplify the expression
.

//Answer: 4.

//Solution.

1) The roots of a square trinomial m 2 + m – 2: m 1 = –2, m 2 = 1. Hence, m 2 + m – 2 = (m + 2)(m – 1). =
.

Other possible solutions.

Division by a fraction is replaced by multiplication by an integer expression, and then the distributive property is used:

=
.

During the simplification, the possibility of simplifying the fraction was not used
:

In addition to the fact that the fraction is not reduced, the possibility of bracketing the multiplier may also not be used m+ 2 when converting the numerator.

	Criteria for assessing the performance of the assignment
	With the chosen solution method, all transformations are performed correctly and the correct answer is received
	A typo or one error was made (for example, the conversion of the expression (2 m- 2) 2 , or the student made a mistake in the sign), but taking into account the result obtained, the solution was completed.

Comment.

An irrational decision with correctly performed transformations cannot serve as a basis for lowering the score.

Task 3, part 2

Is there a geometric progression b 2 = –6, b 5 = 48 and b 7 = 192?

//Answer: exists.

//Solution.

If exponentially b 2 = -6 and b 5 = 48, then
and q= -2. Under this condition b 7 = b 5 ∙ q 2 = 48∙4 = 192, i.e. such a progression exists.

Another possible solution.

From the system of equations
we find that b 1 = 3, q= -2. Further: b 7 = b 1 ∙ q 6 = 3∙(–2) 6 = 192.

There are also some variations of the first and second methods. For example, for the first method, finding q from conditions b 5 = 48 and b 7 = 192 and then condition check b 2 = –6.

	Criteria for assessing the performance of the assignment
	Correctly found a way to solve and get the right answer.
	With the correct course of the solution and the correct use of formulas, a technical error was made in the calculations (for example, a computational error, or an error in the sign), the answer was given taking into account the result obtained.
	Other cases that do not meet the specified criteria

Task 4, part 2.

For what positive values k straight at = kX– 7 crosses the parabola at = X 2 + 2X– 3 at two points?

//Answer: at k> 6.

//Solution.

If straight at = kX– 7 crosses the parabola at = X 2 + 2X– 3 at two points, then the equation kX – 7 = X 2 + 2X– 3 has two roots. After transformations, we obtain the equation X 2 + (2 – k)X+ 4 = 0. Let us find out for what k the inequality D > 0:

D = (2 – k) 2 – 16 = k 2 – 4k – 12; k 1 = –2, k 2 = 6. So D> 0 at k k > 6.

Given the condition k> 0, we find that k > 6.

	Criteria for assessing the performance of the assignment
	The correct solution was found, all its steps were performed correctly, the correct answer was received
	Either one technical error was made (during the transformation of the equation, simplification of the discriminant), but taking into account the result obtained, the solution was completed, or the condition was not taken into account to > 0.
	Other cases that do not meet the specified criteria.

Venus- the second inner planet of the solar system, having a period of revolution of 224.7 Earth days. The planet got its name in honor of the goddess of love Venus from the Roman pantheon.

The planet Venus is often referred to as Earth's "cosmic sister". Indeed, according to its external data, this planet resembles the Earth. Its diameter is only 600 km less than the earth's, and the force of gravity on the surface of Venus is almost the same as on Earth. A weight of 1 kg, being transferred to Venus, would weigh 850 g there.

However, this is where the similarities end - for earthlings, landing on a "sister" planet would be fatal: pressure 90 times higher than Earth's and a temperature of +400 degrees Celsius are only some of the "surprises" that Venus has prepared for us.

The average distance of Venus from the Earth is 41 million km at the nearest point (2 times closer than ) and 259 million km at the far point of the orbit. The distance from Venus to the Sun is 108.2 million km.

Venus has an almost spherical shape, the planet's orbit is almost circular, its eccentricity is 0.0068 - the smallest in the solar system. The speed of movement of Venus in orbit is 35 km / s. The orbital period is 224.7 Earth days, and the rotation period around the axis is 243.02 Earth days.
A feature of rotation around its axis is that Venus rotates in the opposite direction, compared to other planets in the solar system. Such a movement is called retrograde.

Due to this, one day on Venus lasts 116.8 Earth days (i.e. half of the Venusian year). Thus, day and night on Venus last for 58.3 Earth days.

The surface of the planet is constantly covered with dense clouds.

The planet Venus as it can be seen from orbit - the surface of the planet is never visible due to a veil of clouds

The atmosphere of the planet Venus

The cloudy veil on Venus is completely opaque, and if we found ourselves on the surface of this planet, we would be forever deprived of the view of the Sun and the starry sky. Therefore, when viewing Venus through telescopes, we do not see the surface of the planet, but only observe the upper edge of the cloudiness.

As for the chemical composition of the Venusian atmosphere, its only reliably determined component is carbon dioxide, the relative content of which, according to astronomical data, should be about 95%. There is also reliable evidence of the presence of water vapor in the gaseous envelope of Venus. In the upper atmosphere of Venus, the oxygen content does not exceed 0.1% of its content in the same layers of the Earth's atmosphere.

The greenhouse effect also occurs in the atmospheres of other planets. But if in the atmosphere of Mars it raises the average temperature near the surface by 9°, in the atmosphere of the Earth by 35°, then in the atmosphere of Venus this effect reaches 400 degrees. The recorded maximum temperature on the surface is +480°C - above the melting point of lead!

Such a high temperature requires an explanation. Calculations show that it cannot be the result of Venus' proximity to the Sun alone. There must be some additional factors that contribute to warming up. Most likely, such a factor is the extremely strong "greenhouse effect" of the Venusian atmosphere. It is likely that the gaseous envelope of the planet, while transmitting visible sunlight well, almost completely absorbs infrared radiation resulting from the heating of the planet's surface.

On Earth, the greenhouse effect is associated with the presence of carbon dioxide and water vapor in the atmosphere. On Venus, carbon dioxide is also present in large quantities. But carbon dioxide in the infrared region of the spectrum absorbs far from all wavelengths. Water vapor could "fill in" these "windows of transparency". But only very small amounts of water have been found in the atmosphere of Venus. Of course, the possibility is not ruled out that some other gas absorbs the planet's thermal radiation, but which one is completely unclear. In addition, it is noteworthy that the day and night sides of the planet are equally hot.

In this regard, a natural assumption arises about the high internal temperature of a cloudy planet. It is possible that Venus is currently undergoing violent volcanic activity. In this case, the high temperatures found on the surface of Venus are explained by a powerful influx of energy from its depths.

Space exploration of Venus

The space probe "Venera-1" was the first spacecraft from Earth built specifically to study other planets, it was launched on February 12, 1961, but communication with it was soon lost.

Therefore, the first artificial device to "measure" Venus on its own was the American Mariner 2, launched on August 27, 1962 and already in December of the same year transmitted valuable information about the enormous surface temperature and the complete absence of a magnetic field around the planet.

But then the Soviet "Venus" paid off the first failures - 16 Soviet spacecraft transmitted to Earth a colossal amount of information about planet No. 2, and "Venera-7" on December 15, 1970 made a soft landing on Venus and successfully transmitted not only data on atmospheric parameters, but also photographs of the surface - the first photographs of the surface of another planet that earthlings saw. In total, Venera-7 worked for 23 minutes, until the harsh conditions of the “evil sister” of the earth put an end to the mission of the device.

Venera-13 and Venera-14 found that the soil of Venus consists of 50% silica, 16% aluminum alum, and 11% magnesium oxide.

The period of rotation of the planet and the coordinates of its North Pole, obtained as a result of joint processing of onboard radar and Doppler measurements of Magellan and Venera-15, Venera-16 for 20 reference points on the surface of Venus, turned out to be as follows: Rotation period T = 243.0183 Earth days. Right Ascension = 272.57. Declination = 67.14.