One of the clearest examples of the triumph of the law of universal gravitation is the discovery of the planet Neptune. In 1781, the English astronomer William Herschel discovered the planet Uranus. Its orbit was calculated and a table of the positions of this planet was compiled for many years to come. However, a check of this table, carried out in 1840, showed that its data differ from reality.
Scientists have suggested that the deviation in the motion of Uranus is caused by the attraction of an unknown planet, located even further from the Sun than Uranus. Knowing the deviations from the calculated trajectory (disturbances in the movement of Uranus), the Englishman Adams and the Frenchman Leverrier, using the law of universal gravitation, calculated the position of this planet in the sky. Adams completed the calculations earlier, but the observers to whom he reported his results were in no hurry to verify. Meanwhile, Leverrier, having completed his calculations, indicated to the German astronomer Halle the place where to look for an unknown planet. On the very first evening, September 28, 1846, Halle, pointing the telescope at the indicated place, discovered new planet. They named her Neptune.
In the same way, on March 14, 1930, the planet Pluto was discovered. The discovery of Neptune, made, in the words of Engels, at the "tip of a pen", is the most convincing proof of the validity of Newton's law of universal gravitation.
Using the law of universal gravitation, you can calculate the mass of the planets and their satellites; explain phenomena such as the ebb and flow of water in the oceans, and much more.
The forces of universal gravitation are the most universal of all the forces of nature. They act between any bodies that have mass, and all bodies have mass. There are no barriers to the forces of gravity. They act through any body.
Determination of the mass of celestial bodies
Newton's law of universal gravitation makes it possible to measure one of the most important physical characteristics of a celestial body - its mass.
The mass of a celestial body can be determined:
a) from measurements of gravity on the surface of a given body (gravimetric method);
b) according to the third (refined) Kepler's law;
c) from an analysis of the observed perturbations produced by a celestial body in the movements of other celestial bodies.
The first method is applicable so far only to the Earth, and is as follows.
Based on the law of gravity, the acceleration of gravity on the surface of the Earth is easily found from formula (1.3.2).
The acceleration of gravity g (more precisely, the acceleration of the component of gravity due only to the force of attraction), as well as the radius of the Earth R, is determined from direct measurements on the surface of the Earth. The gravitational constant G is determined quite accurately from the experiments of Cavendish and Yolli, well known in physics.
With the currently accepted values of g, R and G, formula (1.3.2) yields the mass of the Earth. Knowing the mass of the Earth and its volume, it is easy to find the average density of the Earth. It is equal to 5.52 g / cm 3
The third, refined Kepler's law allows you to determine the ratio between the mass of the Sun and the mass of the planet, if the latter has at least one satellite and its distance from the planet and the period of revolution around it are known.
Indeed, the motion of the satellite around the planet obeys the same laws as the motion of the planet around the Sun and, therefore, the third Kepler equation can be written in this case as follows:
where M is the mass of the Sun, kg;
m is the mass of the planet, kg;
m c - satellite mass, kg;
T is the period of revolution of the planet around the Sun, s;
t c - period of revolution of the satellite around the planet, s;
a is the distance of the planet from the Sun, m;
and c is the distance of the satellite from the planet, m;
Dividing the numerator and denominator of the left side of the fraction of this equation pa m and solving it for the masses, we get
The ratio for all the planets is very great; the ratio, on the contrary, is small (except for the Earth and its satellite, the Moon) and can be neglected. Then in equation (2.2.2) there will be only one unknown relation, which is easily determined from it. For example, for Jupiter, the inverse ratio determined in this way is 1: 1050.
Since the mass of the Moon, the only satellite of the Earth, is quite large compared to the mass of the Earth, the ratio in equation (2.2.2) cannot be neglected. Therefore, to compare the mass of the Sun with the mass of the Earth, it is necessary to first determine the mass of the Moon. The exact determination of the mass of the Moon is a rather difficult task, and it is solved by analyzing those perturbations in the motion of the Earth, which are caused by the Moon.
Under the influence of lunar attraction, the Earth should describe an ellipse around the common center of mass of the Earth-Moon system within a month.
By precise definitions The apparent positions of the Sun in its longitude were found to change with a monthly period, called “lunar inequality”. The presence of “lunar inequality” in the apparent motion of the Sun indicates that the center of the Earth really describes a small ellipse during the month around the common center of mass “Earth - Moon”, located inside the Earth, at a distance of 4650 km from the center of the Earth. This made it possible to determine the ratio of the mass of the Moon to the mass of the Earth, which turned out to be equal. The position of the center of mass of the Earth-Moon system was also found from observations of the minor planet Eros in 1930-1931. These observations gave a value for the ratio of the masses of the Moon and the Earth. Finally, according to the perturbations in the movements of artificial Earth satellites, the ratio of the masses of the Moon and the Earth turned out to be equal. The last value is the most accurate, and in 1964 the International Astronomical Union accepted it as the final one among other astronomical constants. This value was confirmed in 1966 by calculating the mass of the Moon from the orbital parameters of its artificial satellites.
With the known ratio of the masses of the Moon and the Earth, from equation (2.26) it turns out that the mass of the Sun M ? 333,000 times the mass of the Earth, i.e.
Mz \u003d 2 10 33 g.
Knowing the mass of the Sun and the ratio of this mass to the mass of any other planet that has a satellite, it is easy to determine the mass of this planet.
The masses of planets that do not have satellites (Mercury, Venus, Pluto) are determined from the analysis of the perturbations they produce in the motion of other planets or comets. So, for example, the masses of Venus and Mercury are determined by the perturbations that they cause in the motion of the Earth, Mars, some minor planets (asteroids) and the Encke-Backlund comet, as well as by the perturbations they produce on each other.
earth planet universe gravity
DISCOVERY AND APPLICATION OF THE LAW OF UNIVERSAL GRAVITY Grade 10-11
UMK B.A. Vorontsov-Velyaminov
Razumov Viktor Nikolaevich,
teacher MOU "Bolsheyelkhovskaya secondary school"
Lyambirsky municipal district of the Republic of Mordovia
Law of gravity
Law of gravityAll bodies in the universe are attracted to each other
with a force directly proportional to the product of their
masses and inversely proportional to the square
distances between them.
Isaac Newton (1643–1727)
where m1 and m2 are the masses of the bodies;
r is the distance between the bodies;
G - gravitational constant
The discovery of the law of universal gravitation was largely facilitated by
Kepler's laws of planetary motion
and other achievements of astronomy of the XVII century. Knowing the distance to the moon allowed Isaac Newton to prove
the identity of the force that holds the moon as it moves around the earth, and
the force that causes bodies to fall to the ground.
Since gravity varies inversely with the square of distance,
as follows from the law of universal gravitation, the moon,
located at a distance of about 60 of its radii from the Earth,
should experience an acceleration 3600 times smaller,
than the acceleration of gravity on the surface of the Earth, equal to 9.8 m/s.
Therefore, the acceleration of the Moon must be 0.0027 m/s2. At the same time, the Moon, like any body, uniformly
moving in a circle has an acceleration
where ω is its angular velocity, r is the radius of its orbit.
Isaac Newton (1643–1727)
If we assume that the radius of the Earth is 6400 km,
then the radius of the lunar orbit will be
r \u003d 60 6 400 000 m \u003d 3.84 10 m.
The sidereal period of the Moon's revolution is T = 27.32 days,
in seconds is 2.36 10 s.
Then the acceleration of the moon's orbital motion
The equality of these two accelerations proves that the force holding
the moon in orbit, there is the force of the earth's gravity, weakened by 3600 times
compared to those on the Earth's surface. When the planets move, according to the third
Kepler's law, their acceleration and acting on
them the gravitational force of the sun back
proportional to the square of the distance, like this
follows from the law of gravity.
Indeed, according to Kepler's third law
the ratio of the cubes of the semi-major axes of the orbits d and the squares
circulation periods T is a constant value:
Isaac Newton (1643–1727)
The acceleration of the planet is
From Kepler's third law it follows
so the acceleration of the planet is
So, the force of interaction between the planets and the Sun satisfies the law of universal gravitation.
Perturbations in the motions of the bodies of the solar system
planetary motion solar system does not follow the law exactlyKepler because of their interaction not only with the Sun, but also among themselves.
Deviations of bodies from moving along ellipses are called perturbations.
The perturbations are small, since the mass of the Sun is much greater than the mass, not only
individual planet, but all planets as a whole.
Deviations of asteroids and comets during their passage are especially noticeable.
near Jupiter, whose mass is 300 times the mass of the Earth. In the 19th century the calculation of perturbations made it possible to discover the planet Neptune.
William Herschel
John Adams
Urbain Le Verrier
William Herschel in 1781 discovered the planet Uranus.
Even taking into account the perturbations from all
known planets observed motion
Uranus was not consistent with the calculated.
Based on the assumption that there are
one "transuranium" planet John Adams in
England and Urbain Le Verrier in France
independently made calculations
its orbits and position in the sky.
Based on Le Verrier German calculations
astronomer Johann Galle 23 September 1846
discovered in the constellation Aquarius unknown
formerly the planet Neptune.
According to the perturbations of Uranus and Neptune,
predicted and discovered in 1930
dwarf planet Pluto.
The discovery of Neptune was a triumph
heliocentric system,
the most important confirmation of justice
the law of universal gravitation.
Uranus
Neptune
Pluto
Johann Galle