Celestial Mechanics and Orbital Period Composition

AE-641 Challenges Set No . 1

1 ) The orbital period of a great Earth satellite is 106 min. Get the apogee altitude if the perigee hohe is 200 km. 2 . Find the orbital amount of a satellite tv if the perigee and apogee altitudes are 250 kilometres and 300 km, respectively. 3. Get the maximum and minimum orbital speed with the Earth in case the eccentricity from the Earth's orbit around Sunshine is 1/60. What is the mean speed if the indicate radius is 1 AU? (Sun's Gm1=1. 327x10 11 km3/s installment payments on your ) 5. Given the orbital length of Mars about Sun as 687 Globe mean solar days, find the semi-major axis of Mars orbit in AU. 5. Estimation solar gravitational constant using Kepler's third law. six. A spacecraft in a two hundred km excessive circular Earth orbit fire its retro-rocket, reducing speed instantly by simply 600 m/s. What is the speed of the spacecraft when it actually reaches an altitude of 100km? (Assume no atmospheric move. ) six. What is the parabolic escape velocity by a geosynchronous orbit? What extra speed will be required for a geosynchronous satellite to escape Earth's the law of gravity? 8. A hyperbolic Earth departure flight has a perigee speed of 15 km/s at an eminence 300 km. Calculate (a) hyperbolic surplus speed, (b) radius and speed when true anomaly is 100o. 9. Voyager-I's closest method to Saturn just visited a periapsis radius of 124000 kilometers and the hyperbolic excess acceleration was several. 51 km/s. What was the angle through which the spacecraft's velocity vector was converted by Saturn? (Saturn's meters = 37. 931x10 6th km3/s2. ) 10. Derive expressions intended for the position and velocity vectors of a spacecraft in a coordinate system fixed to the orbital plane in a way that the unit vectors of the responsable are along the eccentricity vector, e, the direction of parameter, p, and the slanted momentum vector, h. Communicate the answers in terms of semi-major axis, a, eccentricity, e, and accurate anomaly, queen. 11. Halley's comet last passed perihelion on Feb . 9, 1986. Its orbit has a semi-major axis, a=17. 9564 AU and disposition, e=0. 967298. Predict the date of next...

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