Senior 1 Physics Compulsory 2 Answers to questions about gravitational force are answered by masters

Question 1: It can be obtained: g=(2*h) (t*t) and the analysis shows that the gravitational force provides the centripetal force, m*g=(m*v*v) r

It can be seen that v = g*h. under the root number

If the mass of an object on the surface of the planet is m, then the gravitational force of the object can be approximated as the gravitational force between the object and the planet, mg=(gmm) (r*r).

Therefore, the density of the planet = (3*h) (2*

Question 2: From the analysis, it can be seen that g=g*m (r*r), then m=(g*r*r) g;

Then m*a=(g*m*m) pushes out a=(g*r*r) in the same way we know m*v*v (r+h)=(g*m*m) pushable speed.

1. The object falls freely from h (h is much less than r) and falls back to the surface of the planet after time t, so the gravitational acceleration of the planet is g1 = 2h t under the root number and the centripetal force is provided according to gravity to obtain mg1=mv 2 r to find v

2. From the gravitational force equal to the gravitational force, mg=gmm r 2 can be solved m According to the radius of the planet r, the volume v of the planet can be obtained, so the average density = m v

1. mg=gmm r 2 gmm (r+h) 2=ma is solved to obtain the acceleration a2, gmm (r+h) 2=mv 2 (r+h) to solve v

1.It is obtained from g = mg, m = g g = 16 10n = .

From Newton's second law, the acceleration due to gravity of an object at high altitude is g1, then.

f-mg1=ma

g1=(f-ma) m=(, derived from the law of gravitation, g=gmm r---1).

g1=gmm (r+h) square ---2).

Obtained from (1) and (2).

g g1=(r+h) square r square.

Then h r = g under the root number g1-1=10 (5 8)-1=3

2.First, calculate the mass of the planet (including the relationship between the mass of the earth, the radius of the earth and the radius of the planet) by mass = volume * density, and then use the law of gravitation to calculate the relationship between the earth and the radius (note that the height of the earth satellite is 7 times the radius of the earth), and bring each relation into the gravitational relationship between the planetary period and the radius (the height of the planetary satellite is times the radius of the planet) to obtain the ratio of the rotation period of the planet to the earth is, so b is chosen.

3.According to the gravitational force formula.

gmm/r^2=mrω^2=mr(2π/t)^2

Simplification has m r 3=4 2 (g*t 2).

Density =m v=3m (4 r 3)=3 (g*t 2).

4.The first cosmic velocity refers to the lowest velocity of the object moving in a circle around the surface of the earth, at this time, the gravitational force provides the centripetal force of the circular motion of the object: gmm r2=mv2 r g=(2 3) 10 (-10)n(m kg)2 is the gravitational constant, m is the mass of the earth, m is the mass of the object moving in a circle, r is the radius of the earth, v is the speed of the object in a circular motion, that is, the first cosmic velocity.

The calculation shows that v1= (gm r).

The second cosmic velocity refers to the lowest velocity at which an object breaks free from the gravitational constraints of the earth and becomes a planet in the solar system, at which time all kinetic energy is converted into potential energy:, and the calculation shows that v2= (2gm r).

When the Earth mass and the Earth's radius in the second cosmic velocity are replaced with the mass of the Sun and the radius of the solar system, respectively, the third cosmic velocity, which is the minimum velocity at which an object breaks away from the solar system and becomes an interstellar traveler.

Radius of the Earth: , mass of the Earth: 6 10 24kg, radius of the Solar System: about 1 light year, mass of the Sun: 2 10 30kg.

Calculated: v1=, v2=, v3=.

Let the masses of the two stars be m1 and m2 respectively, the radii of the circular motion are r1 and r2 respectively, and the angular velocities are w1 and w2 respectively. There is it according to the title.

w1=w2 ①

r1+r2=r ②

According to the laws of gravitation and Newton's laws, there are

Lianli can solve all of the above problems.

It is known according to the relationship between angular velocity and period.

Simultaneous solution.

(g*m1*m2)/r²=(2π/t)²*m1*r1=(2π/t)²*m2*(r-r1)

The first two formulas are equal, and we get gm2 r = (2 t) and the first and last formulas of r1 are equal, and we get gm1 r =(2 t) (r-r1) together, what do you see? g(m1+m2) r =(2 t) r got it, m1+m2==(2 t) r g typing is not good for typing, you sort it out.

The historical significance of geocentrism.

Geocentrism is the world's first model of a planetary system. Although it is wrong to regard the Earth as the center of the universe, its historical merits should not be erased. Geocentrism, which acknowledges that the Earth is "round" and distinguishes planets from stars, with an eye toward exploring and revealing the laws of planetary motion, marks a great advance in human understanding of the universe.

The most important achievement of geocentrism was the use of mathematics to calculate the orbit of the planets, and Ptolemy also proposed the concept of "orbit" for the first time, designing a model of the current round and the average wheel. According to this model, people were able to quantitatively calculate the motion of the planets and speculate on the location of the planets, which was a remarkable creation. In a certain period of time, according to this model, the first celestial phenomenon can be correct to a certain extent, so it has also played a certain role in production practice.

Although Ptolemy's geocentric system was later replaced by heliocentrism, it has brought far more to Westerners than Copernicus's heliocentric theory in the more than 1,500 years since its birth. Geocentrism is the world's first model of planetary systems and the world's earliest hypothesis-deductive system. In the process of building theories, mathematical tools were used to study and prove from beginning to end, creating a precedent for constructing accurate theories.

During the millennium, due to the dominance and widespread influence of geocentrism, it shaped the analytical way of thinking of Westerners, the physical view of nature that does not contain ethics, and the habit of applying mathematical tools in the study of nature.

The relativity of motion and geocentrism.

From the understanding of the principle of relativity of the motion of objects, geocentrism is no longer wrong, because the earth where we are located is stationary relative to ourselves relative to the desolate universe, so we can think about the right and wrong of geocentrism from the point of view of relativity. Moreover, China has been studying the stars since ancient times, and they all believe that the stars are moving according to a mysterious trajectory, so can this be regarded as the ancient China has studied the theory of relativity, but neither China nor the Holy See has made corresponding research on the theory of relativity. If it is said that the relationship between the theory of relativity and the geocentric theory has been studied in ancient times, then it is still worth pondering whether the current cosmological theory should be rewritten.

The reason why it has lasted so long is also because the people who believe in geocentrism do not realize that this is due to the error of geocentrism itself, but they use the method of increasing this round to remedy geocentrism. At first, this method could barely cope, but later the small round increased to more than 80, but it was still not satisfactory to calculate the exact position of the traveling star. This cannot but cast doubt on the correctness of the geocentric theory.

In the 16th century, Copernicus finally founded the "heliocentric theory" on the basis of his ancient Greek ancestors and contemporaries who held a heliocentric view. Since then, geocentrism has gradually been eliminated. The reason why geocentrism has been broken through is that the founders and proponents of geocentrism have not infinitely expanded the meaning and connotation of geocentrism (after all, there is still room for non-geocentric theory to survive in the elaboration of celestial movements, that is, geocentric theory can be "falsified").

Because they can be stupid.

Kepler's third law (periodic law, harmony law): t2 r3 k (4 2 gm).

r: orbital radius, t: period, k: constant (independent of the mass of the planet, depending on the mass of the central object)}

2.Law of gravitation: f gm1m2 r2

g, the direction is on their line).

3.Gravity and gravitational acceleration on and near the surface of a celestial body (planet):

gmm/r2＝mg；g＝gm/r2

r: celestial radius (m), m: celestial mass (kg)}

4.Satellite orbit velocity, angular velocity, period:

v＝(gm/r)1/2；ω＝gm/r3)1/2；t＝2π(r3/gm)1/2

m: central celestial mass}

5.1 (2, 3) cosmic velocity v1 (g r ) 1 2 (gm r ) 1 2 ;

v2＝；v3＝

6.Geosynchronous satellites GMM (R+H)2 M4 2(R+H) T2

h 36000km, h: height from the earth's surface, r: radius of the earth}

Note: (1) The centripetal force required for the motion of celestial bodies is provided by gravitational force, f to f thousand;

2) the law of gravitation can be applied to estimate the mass density of celestial bodies;

3) Geosynchronous satellites can only operate over the equator, and the period of operation is the same as that of the Earth's rotation;

4) The orbital radius of the satellite becomes smaller, the potential energy becomes smaller, the kinetic energy becomes larger, the velocity becomes larger, and the period becomes smaller (together with three antis);

5) The maximum orbital velocity and the minimum launch velocity of the Earth satellite are both.

Law of gravitation: f gm1m2 r2

g, the direction is on their line).

Synonymous with this and Newton's second law, all the formulas come out.

g Hong's (G1+A) = 32 18;

g1=5 8 m s ;

by (gm1m2) (r1) = mg1

G1 G2 = (Gm1M2 R1 ) Gm1M2 Shirt Luck R ) or Beam R1 = 4R = 25600km

is powered).

g (g1+a)=32 Shen Min 18;

g1=5 8 m s ;

From the reputation of blind (gm1m2) (r1 ) = mg1 to get g1 g2 g2 = (gm1m2 r1 ) gm1m2 r ) to get r1 = 4r land = 25600km

h=25600km-64ookm= Qingming to the 7th power) enenen

The mass of 1 Earth and the linear velocity of the spacecraft can be obtained.

1. The mass of the earth on the surface of the earth has gmm r2=mv2 r to get gm=gr2 to get m

2. The linear velocity of the spaceship gmm R2=MV2 r R=R+h can obtain the centripetal force required by the spaceship for v, which cannot be found.

f=gmm r2 and r=r+h has no spacecraft mass m, so the centripetal force f required for the spacecraft cannot be found

The mass of the earth can be found as follows: method 1, m=4(pai) 2*(h+r) 3 gt 2;Method 2: m=g(h+r) 2 g The linear velocity of the spacecraft can be found: v=2(pai)*(h+r) t The centripetal force cannot be found because the mass of the spacecraft is not known.

Note:''''''&2 denotes''''''Because gr&2 equal gm m equal gr&2 divided g two: v equal root number (gm divided by r + h) m substituted in:

V and other root numbers (gr&2 divided by r+h) three: A and other v&2 divided by (r+h) obtained: (gr&2) divided by (r+h)&2 Note:

''''&2 denotes''''''of the squared.

The mass of the earth can be obtained by substituting ** (gmm) r = mg m by v=2 [pi] r+h t or by (gmm) (r+h) =mv (r+h) v (r+h) v can be obtained by f=mv (r+h)=(gmm) (r+h) centripetal force f can be obtained

f gravitational force = g * m sun * m planet r 2 f gravity = m planet r r t planet 2

f gravitational force = g * m sun * m earth r 2 f gravity = m earth * r t earth 2

Lianli 4 formulas are out.

b Eight years.

You list an equation based on the centripetal force provided by gravity, reduce the mass of the asteroid, and deform it, and you can get that the square of the period is proportional to the cubic of the radius of motion.

The radius of motion of the planet is four times that of the earth and sixty-four times that of the three, and after the opening of the root, the period of motion is eight times that of the earth.

Hope it helps. o(∩_o~

Simple, there are two methods, the first is that the gravitational force and the centripetal force formula are equal: the gravitational force acts as a centripetal force, and then the linear velocity term of the centripetal force formula is substituted with the definition of linear velocity, so that the periodic term appears, the specific formula is t = (4 2r 3 gm), and the period of the earth is t to the earth = (4 2r 3 gm) because the radius of the asteroid's uniform circular motion around the sun is 4 times the radius of the earth's revolution, so its period is t star = (4 2(4r) 3 gm).

So t star = 4 3* (4 2(4r) 3 gm) = 4 3 * t = 8 * t .

The cycle of an asteroid is 8 years.