1. Kepler's third law: t2/r3 = k (= 4π 2/gm) {r: orbital radius, t: period, k: constant (independent of the mass of the planet, depending on the mass of the central celestial body)}.
2. Law of gravitation: f = GM1m2/R2 (g = 6.67×10-1n? M2/kg2, the direction is on their connection)
3. Gravity and gravity acceleration on celestial bodies: GMM/R2 = mg; G = GM/R2 {R: celestial radius (m), m: celestial mass (kg)}
4. Orbital velocity, angular velocity and period of the satellite: v = (GM/R)1/2; ω=(GM/R3) 1/2； T = 2π (R3/GM) 1/2 {m: mass of central celestial body}
5. The first (second and third) cosmic velocity V 1 = (G and r)1/2 = (GM/r)1/2 = 7.9 km/s; V2 = 1 1.2km/s； V3
= 16.7 km/s
6. Geosynchronous satellite GMM/(R+H) 2 = M4 π 2 (R+H)/T2 {H ≈ 36,000 km, H: height from the earth's surface, R: radius of the earth}
note:
(1) The centripetal force required for celestial motion is provided by gravity, and the F direction = F million;
(2) The mass density of celestial bodies can be estimated by applying the law of universal gravitation.
(3) Geosynchronous satellites can only run over the equator, and the running period is the same as the earth's rotation period;
(4) When the orbit radius of the satellite decreases, the potential energy decreases, the kinetic energy increases, the speed increases and the period decreases.
(5) The maximum circling speed and minimum launching speed of the Earth satellite are 7.9 km/s. ..