Calculate the speed of the spacecraft to launch it into the circular orbit of the planet, the atmosphere of the planet

Calculate the speed of the spacecraft to launch it into the circular orbit of the planet, the atmosphere of the planet is rarefied (drag forces can be neglected) The radius of the planet is 6370 km The mass of the planet is 5.976 * 10 to the power of 24 kg

We are talking about calculating the first cosmic velocity, i.e. the speed that the body must gain in order to become an artificial satellite of the planet and not fall on its surface. This speed is calculated by the formula:

v1 = √ (G * M * R), where M is the mass of the planet, R is its radius, G is the gravitational constant.

Thus, we get that:

v1 = √ (G * M / R) = √ (6.67408 * 10 ^ −11 * 5.976 * 10 ^ 24/6 370 000) = 7913 m / s = 7.9 km / s.

Answer: the speed is 7.9 km / s.