1 escape velocity is equal to km s. Life of wonderful names

First cosmic velocity (circular velocity)- the minimum speed that must be given to an object in order to launch it into a geocentric orbit. In other words, the first escape velocity is the minimum speed at which a body moving horizontally above the surface of the planet will not fall on it, but will move in a circular orbit.

Computation and Comprehension

In an inertial reference frame, an object moving in a circular orbit around the Earth will be subject to only one force - the Earth's gravitational force. In this case, the movement of the object will be neither uniform nor uniformly accelerated. This happens because speed and acceleration (not scalar, but vector quantities) in this case do not satisfy the conditions of uniformity/uniform acceleration of movement - that is, movement with a constant (in magnitude and direction) speed/acceleration. Indeed, the velocity vector will be constantly directed tangentially to the surface of the Earth, and the acceleration vector will be perpendicular to it to the center of the Earth, while as they move along the orbit, these vectors will constantly change their direction. Therefore, in an inertial reference frame, such motion is often called “motion in a circular orbit with a constant modulo speed."

Often, for convenience, calculations of the first cosmic velocity proceed to consider this movement in a non-inertial reference frame - relative to the Earth. In this case, the object in orbit will be at rest, since two forces will act on it: centrifugal force and gravitational force. Accordingly, to calculate the first escape velocity, it is necessary to consider the equality of these forces.

More precisely, one force acts on the body - the force of gravity. Centrifugal force acts on the Earth. The centripetal force, calculated from the condition of rotational motion, is equal to the gravitational force. The speed is calculated based on the equality of these forces.

$m\backslash frac(v\_1^2)(R)=G\backslash frac(Mm)(R^2)$, $v\_1=\backslash sqrt(G\backslash frac(M)(R))$,

Where m- mass of the object, M- mass of the planet, G- gravitational constant, $v\_1$- first escape velocity, R- radius of the planet. Substituting numerical values ​​(for Earth M= 5.97 10 24 kg, R= 6,371 km), we find

The first escape velocity can be determined through the acceleration of gravity. Because the $g\; =\; \backslash frac(GM)(R^2)$, That

$v\_1=\backslash sqrt(gR)$.

see also

Write a review about the article "First cosmic speed"

Links

An excerpt characterizing the first cosmic velocity

Since ancient times, people have been interested in the problem of the structure of the world. Back in the 3rd century BC Greek philosopher Aristarchus of Samos expressed the idea that the Earth revolves around the Sun, and tried to calculate the distances and sizes of the Sun and Earth from the position of the Moon. Since the evidential apparatus of Aristarchus of Samos was imperfect, the majority remained supporters of the Pythagorean geocentric system of the world.
Almost two millennia passed, and the Polish astronomer Nicolaus Copernicus became interested in the idea of ​​a heliocentric structure of the world. He died in 1543, and soon his life's work was published by his students. Model and position tables celestial bodies Copernicus, based on the heliocentric system, reflected the state of affairs much more accurately.
Half a century later, the German mathematician Johannes Kepler, using the meticulous notes of the Danish astronomer Tycho Brahe on observations of celestial bodies, derived the laws of planetary motion that eliminated the inaccuracies of the Copernican model.
The end of the 17th century was marked by the works of the great English scientist Isaac Newton. Laws of mechanics and universal gravity Newton was expanded and given theoretical basis formulas derived from Kepler's observations.
Finally, in 1921, Albert Einstein proposed general theory relativity, which most accurately describes the mechanics of celestial bodies at the present time. Newton's formulas of classical mechanics and the theory of gravity can still be used for some calculations that do not require great accuracy, and where relativistic effects can be neglected.

Thanks to Newton and his predecessors, we can calculate:

• what speed must the body have to maintain a given orbit ( first escape velocity)
• at what speed must a body move in order for it to overcome the gravity of the planet and become a satellite of the star ( second escape velocity)
• the minimum required speed for leaving the planetary system ( third escape velocity)

“Uniform and uneven movement” - t 2. Uneven movement. Yablonevka. L 1. Uniform and. L2. t 1. L3. Chistoozernoe. t 3. Uniform movement. =.

“Curvilinear motion” - Centripetal acceleration. UNIFORM CIRCULAR MOTION OF A BODY Distinguished: - curvilinear movement with a constant modulus speed; - movement with acceleration, because speed changes direction. Direction of centripetal acceleration and velocity. Motion of a point in a circle. Movement of a body in a circle with a constant absolute speed.

“Motion of bodies on a plane” - Evaluate the obtained values ​​of unknown quantities. Substitute numerical data into the solution general view, make calculations. Make a drawing, depicting interacting bodies on it. Perform an analysis of the interaction of bodies. Ftr. Body movement inclined plane without friction. Study of the movement of a body on an inclined plane.

“Support and movement” - Contact us ambulance brought the patient. Slender, stooped, strong, strong, fat, clumsy, dexterous, pale. Game situation“Concilium of Doctors”. Sleep on a hard bed with a low pillow. “Body support and movement. Rules for maintaining correct posture. Correct posture when standing. Children's bones are soft and elastic.

"Space Speed" - V1. THE USSR. That's why. April 12, 1961 Message to extraterrestrial civilizations. Third escape velocity. On board Voyager 2 is a disk with scientific information. Calculation of the first escape velocity at the Earth's surface. The first manned flight into space. Voyager 1 trajectory. The trajectory of bodies moving at low speed.

“Body dynamics” - What underlies dynamics? Dynamics is a branch of mechanics that examines the causes of the movement of bodies (material points). Newton's laws apply only to inertial systems countdown. Frames of reference in which Newton's first law is satisfied are called inertial. Dynamics. In what frames of reference do Newton's laws apply?

There are a total of 20 presentations in the topic

« Physics - 10th grade"

To solve problems, you need to know the law of universal gravitation, Newton's law, as well as the relationship between the linear speed of bodies and the period of their revolution around the planets. Please note that the radius of the satellite's trajectory is always measured from the center of the planet.

Task 1.

Calculate the first escape velocity for the Sun. The mass of the Sun is 2 10 30 kg, the diameter of the Sun is 1.4 10 9 m.

Solution.

The satellite moves around the Sun under the influence of a single force - gravity. According to Newton's second law, we write:

From this equation we determine the first escape velocity, i.e. the minimum speed with which a body must be launched from the surface of the Sun in order for it to become its satellite:

Task 2.

A satellite is moving around a planet at a distance of 200 km from its surface at a speed of 4 km/s. Determine the density of the planet if its radius is equal to two radii of the Earth (Rpl = 2R 3).

Solution.

Planets have the shape of a ball, the volume of which can be calculated using the formula then the density of the planet

Determine the average distance from Saturn to the Sun if the period of Saturn's revolution around the Sun is 29.5 years. The mass of the Sun is 2 10 30 kg.

Solution.

We believe that Saturn moves around the Sun in a circular orbit. Then, according to Newton’s second law, we write:

where m is the mass of Saturn, r is the distance from Saturn to the Sun, M c is the mass of the Sun.

Saturn's orbital period from here

Substituting the expression for speed υ into equation (4), we obtain

From the last equation we determine the required distance from Saturn to the Sun:

Comparing with the tabular data, we will make sure that the found value is correct.

Source: “Physics - 10th grade”, 2014, textbook Myakishev, Bukhovtsev, Sotsky

Dynamics - Physics, textbook for grade 10 - Cool physics

Trapped by Gravity

The earth is the home of humanity, its cradle. But until recently it was also his prison. The force that shaped his appearance, the force of gravity, kept the man on the planet and did not give him the opportunity to go to the worlds that shone above his head. The first escape velocity was unattainable for him until very recently.

If you throw a stone hard, its speed will not be sufficient to overcome the earth's gravity, and it will eventually pull it towards itself. However, the harder you throw an imaginary stone, the greater its speed will be, and the more it will balance the force of gravity. Finally, the moment will come when the stone begins to fall endlessly to the Earth - it will reach the first cosmic speed. This can be explained by attaching a weight to a rope and spinning it in a circle. The rope will act as gravity, keeping the load from moving in a straight line and uniformly, and causing it to instead move in a circle centered on the hand holding the rope.

In an endless fall

Since celestial bodies have different masses and densities, the first escape velocity at the surface of each of them will be different. It is simply calculated as the square root of the product of the acceleration of gravity and the radius of the celestial body. For the Earth, the minimum speed at which a body begins to move in orbit around it is earth's surface is 7.9 km/s. How more height above the Earth, the lower this speed. During an endless fall, the weight of the body and all objects on or in it equal to zero; they say that a state of weightlessness sets in. At the same time, however, the mass of objects remains unchanged.

Liberation by rocket

Until the mid-50s of the 20th century, neither human muscular power nor the energy of animals, steam or engines internal combustion could not accelerate the vehicles they were moving to the appropriate speed. However, back at the end of the 19th century, the Russian inventor and self-taught scientist Konstantin Tsiolkovsky mathematically proved that the first cosmic speed of orbital flight can be achieved by an aircraft using jet propulsion for propulsion, that is, a rocket. The more powerful its engine is, the better fuel and the lighter the design, the higher speeds can be achieved.

For the first time in the history of mankind, the first escape velocity was communicated to the simplest intercontinental satellite ballistic missile R-7, created in the USSR. The day of the launch of the first satellite - October 4, 1957 - is considered the first day Space Age humanity. Today, there are more than 10 thousand operating and non-operating spacecraft, rocket stages, components and parts, as well as space debris in low-Earth orbit. The weight of the smallest satellite barely reaches 10 kg, the weight of the largest - International space station- exceeds 417 tons.

...and in distant space

If you increase the orbital speed until the closed ellipse of the near-Earth orbit turns into a parabola or hyperbola with respect to the Earth, then spacecraft will acquire a second cosmic speed, identical to that with which the movement of planets and other celestial bodies around the Sun occurs. In this case, the spacecraft will go into orbit artificial satellite Sun. A further increase in speed will exceed the gravitational attraction of our star, and the spacecraft, having acquired the third cosmic speed, will embark on an interstellar journey, orbiting the center of our Milky Way galaxy.