Calculate the first space velocity for a height above the Earth equal to the Earth’s radius

Calculate the first space velocity for a height above the Earth equal to the Earth’s radius. (R = 6400 km) G = 6.67×10 H / kg. The mass of the Earth is 6×10 ^ 24 kg.

For a body to move in a circle, a force must act on it, imparting centripetal acceleration to it. For a satellite, this is the gravitational force of the Earth, and the first cosmic velocity is determined through centripetal acceleration:
V ^ 2 = a * R = F * R / m;
Here F = G * M * m / R ^ 2 is the gravitational force of the Earth, and m is the mass of the satellite.
From here we get:
V = (G * M / R) ^ 0.5;
G = 6.67 * 10 ^ (- 11) N * m ^ 2 / kg ^ 2,
M = 6 * 10 ^ 24 kg;
R = 6400km = 6.4 * 10 ^ 6 m;
V = 7.908 * 10 ^ 3 m / s = 7908 km / s.



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