A spacecraft departing from a 200 km LEO has a total AV of 10 km/s. Determine the following: a) The maximum velocity it can attain upon leaving the solar system and the ejection angle, relative to periapsis, required to achieve this. b) The maximum velocity it can attain using a Jupiter fly-by gravity assist. Assume Jupiter and Earth are in co-planar, circular orbits.
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- A planet with an orbital radius of the sun of R has a velocity of V. The point of planet B has an orbiting speed of the sun of 2V. Determine the orbital radius of planet B!(a) What is the escape speed on a spherical asteroid whose radius is 274 km and whose gravitational acceleration at the surface is 0.444 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 311 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 289.4 km above the surface?9
- (a) What is the escape speed on a spherical asteroid whose radius is 803 km and whose gravitational acceleration at the surface is 1.75 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1330 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1811 km above the surface?Designing an interplanetary mission from Earth to Jupiter. Given the position and velocityvectors for the Earth parking orbit, r = 8228 I +389 J +6888 K (km)v = -0.7 I +6.6 J -0.6 K (km/s) 1.) Assuming that the satellite will enter the Hohmann transfer elliptical orbit from perigee of its current Earth parking orbit, determine the total velocity increment, Δvtotal required for a Hohmann transfer from the Earthparking orbit to 200km altitude Jupiter parking orbit. 2.) Calculate the semi-major axis, period in earth years, and eccentricity of the Hohmann transfer ellipse.Suppose you are in a circular orbit above the moon Rhea with a radius of 824.7 km, and you have 154.4 m/s of delta V. Suppose you put all your delta V to go into an elliptical orbit, what is the semi-major axis of this elliptical orbit assuming the mass of Rhea is 2.3065 ×1021 kg and you can ignore the gravitational effects of Saturn?
- An artificial satellite is going round the earth, close to its surface. Calculate time taken by it to complete one round. Take radius of the earth 6400 km and accleration due to gravity= 9.8m/sA satellite is in circular polar orbit around Earth at an altitude of 450 km – meaning it passes directly overhead of the North and South Poles. What is the magnitude and direction of the displacement vector when it is directly over the North Pole to when it is at 40° latitude? Earth’s radius is 6,370 km.(a) Calculate the orbital inclination required to place a Venus-orbiting spacecraft in a 400 km-by-900 km sun-synchronous orbit. (b) Determine the periapsis and apoapsis for a Mars-orbiting spacecraft whose orbit satisfies all the following conditions: it is sun-synchronous, its argument of perigee is constant, and its period is 7 h.
- 19Let the radius of the Earth be R, and we approximate the Earth as a sphere. In order for an object to glide along the equator of the Earth at sea level, what is the speed at which it needs to be moving? gR gR VgR O (gR)?The eccentricity e of the Moon's orbit is 0.0549 and the mean orbital radius r, = (ab)!2 is 384,100 km. (a) Calculate the lengths of the principal axes a and b of the Moon's orbit. (b) How far is the center of the Earth from the center of the elliptical orbit? (c) Calculate the distances of the Moon from the Earth at perigee and apogee.