Concept explainers
A spacecraft of mass mdescribes a circular orbit of radius r1 around the earth, (a) Show that the additional energy ΔE that must be imparted to the spacecraft to transfer it to a circular orbit of larger radius
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Vector Mechanics For Engineers
- How much energy per pound should be imparted to a satellite in order to place it in a circular orbit at an altitude of (a) 400 mi, (b) 4000 mi?arrow_forwardA space probe is to be placed in a circular orbit of 5600-mi radius about the planet Venus in a specified plane. As the probe reaches A, the point of its original trajectory closest to Venus, it is inserted in a first elliptic transfer orbit by reducing its speed by ΔvA. This orbit brings it to point B with a much reduced velocity. There the probe is inserted in a second transfer orbit located in the specified plane by changing the direction of its velocity and further reducing its speed by ΔvB. Finally, as the probe reaches point C, it is inserted in the desired circular orbit by reducing its speed by ΔvC. Knowing that the mass of Venus is 0.82 times the mass of the earth, that rA = 9.3 × 103 mi and rB = 190 × 103 mi, and that the probe approaches A on a parabolic trajectory, determine by how much the velocity of the probe should be reduced (a) at A, (b) at B, (c) at C.arrow_forwardA 500-kg spacecraft first is placed into a circular orbit about the earth at an altitude of 4500 km and then is transferred to a circular orbit about the moon. Knowing that the mass of the moon is 0.01230 times the mass of the earth and that the radius of the moon is 1737 km, determine (a) the gravitational force exerted on the spacecraft as it was orbiting the earth, (b) the required radius of the orbit of the spacecraft about the moon if the periodic times (the periodic time of a satellite is the time it requires to complete one full revolution about the planet) of the two orbits are to be equal, (c) the acceleration of gravity at the surface of the moon.arrow_forward
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