Task id11941

A spacecraft weighing 400 kg moved around the Earth with a radius of 6370 km in a circular orbit at an altitude h1=200 km from its surface. As a result of turning on the rocket engine for a short time Δt, the speed of the spacecraft increased by Δv=10 m/s, and the motion trajectory became an ellipse with a minimum distance from the Earth's surface h1=200 km and a maximum distance from the Earth's surface h2=234 km. At what speed v2 is the spacecraft moving at the point of maximum distance from the Earth's surface? What is the thrust force F of a rocket engine, the time dt of its operation, and the mass of consumed fuel Δm? Neglect the change in the mass of the ship. The mass of the Earth M should be considered equal to 6 1024 kg, the gravitational constant G=6.67•10-11 N•m2/kg2, the second fuel consumption mс=Δm/Δt=1 kg/s, the gas flow velocity u=4000 m/s, specific heat of combustion of fuel and oxidizer q=1.2 10 J/kg.