All the related formulas of gravitation in higher physics

All the related formulas of gravitation in higher physics

Here are two sets of summaries
1、 Gravitation
1. Kepler's third law: T2 / R3 = K (= 4 π 2 / GM) {R: orbital radius, t: period, K: constant (independent of the mass of the planet, depends on the mass of the central celestial body)}
2. Law of universal gravitation: F = gm1m2 / R2, g = 6.67 × 10-11n? M2 / kg2, direction on their connecting line)
3. Gravity and acceleration of gravity on celestial bodies: GMM / r2 = mg; g = GM / r2 {R: radius (m), M: mass (kg)}
4. Orbit velocity, angular velocity and period: v = (GM / R) 1 / 2; ω = (GM / R3) 1 / 2; t = 2 π (R3 / GM) 1 / 2 {M: mass of central celestial body}
5. The first (second and third) cosmic velocity V1 = (g land r land) 1 / 2 = (GM / R land) 1 / 2 = 7.9km/s; V2 = 11.2km/s;
V3＝16.7km/s
6. Geostationary satellite GMM / (r earth + H) 2 = M4 π 2 (r earth + H) / T2 {h ≈ 36000km, H: height from the earth surface, R earth: radius of the earth}
Note:
(1) The centripetal force of celestial body motion is provided by gravitation, f direction = f ten thousand;
(2) The mass density of celestial bodies can be estimated by using the law of universal gravitation;
(3) The geostationary satellite can only run over the equator, and its cycle is the same as the earth's rotation cycle;
(4) When the orbit radius becomes smaller, the potential energy becomes smaller, the kinetic energy becomes larger, the velocity becomes larger, and the period becomes smaller;
(5) The maximum orbit speed and minimum launch speed of the earth satellite are 7.9km/s
2、 Gravitation
13. The content of Kepler's first law is that the orbits of all planets around the sun are ellipses, and the sun is in a focus of the ellipse orbit
The content of the third law is that the ratio of the third power of the semimajor axis of all planets to the square of the revolution period is equal
14. If the mass of the earth is m, the radius is r, the constant of gravitation is g, and the acceleration of gravity on the earth's surface is g, then a common relationship exists between them
15. The expression of the first cosmic velocity (the orbit velocity of the near earth satellite) is, which is the minimum velocity of the launching satellite and the maximum orbit velocity of the earth satellite. With the increase of the satellite height h, V decreases, a decreases and t increases
16. The second cosmic velocity (escape velocity), which is the minimum emission velocity to free an object from gravity
17. The third cosmic velocity (escape velocity), which is the minimum emission velocity to free an object from the solar gravity
18. For a binary star in space, its orbit radius is inversely proportional to its mass, and its orbit velocity is inversely proportional to its mass

The formula of pulling force
The formula of pulling force in physics is as follows~
The length of a spring without any tension is 3cm. When it is pulled by 2n force, the length of the spring is 7cm. When the length of the spring is 8cm, what is the tension on the spring?

Let the stiffness coefficient of spring be K (n / cm)
The original spring length is 3cm
According to the meaning of the question, the equation 2 = k × (7-3) can be given
5 (n / cm)
Required force F = k × (8-3) = 0.5 × 5 = 2.5 (n)

Let f be the pulling force and f be the friction force, then the mechanical efficiency of the inclined plane = (f-f) / F. how is this formula derived

 
Mechanical efficiency = w useful & nbsp; / & nbsp; W total = (W total - W useless) / & nbsp; W total & nbsp; = & nbsp; (fs-fs) / & nbsp; FS & nbsp; = (f-f) / F
 
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