Estimate the parameters of the orbit of a spacecraft flying from Earth to the Moon

We assume that the orbit of the ship will be an ellipse, at which the perigee is located near the Earth, and the apogee is near the orbit of the Moon. Let the geocentric distance at perigee be determined by the auxiliary orbit of an artificial Earth satellite. The major axis of the elliptical orbit is equal to the distance from the Earth to the Moon – 400 thousand km, then the semi-major axis is a = 200 thousand km. From the formula for the ship’s distance at perigee rn = a (1-e), we conclude that the eccentricity e is close to unity. Hence it follows that near the Earth the orbit differs little from the parabola and the velocity at perigee should be equal to the parabolic one, and, given the low altitude, this velocity is close to the second cosmic velocity — 11.2 km / s. The flight time is equal to half the period of revolution of the body in a given elliptical orbit. Using Kepler’s third law, we can estimate this time to be about 5 days.

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