Number 4 Thank you very much An unmanned satellite orbits th

Number 4? Thank you very much!

An unmanned satellite orbits the earth with a perigee radius of 7000 km and an apogee radius of 70, 000 km. Calculate a) The eccentricity of the orbit b) The semi major axis of the orbit (km) c) The period of the orbit (hours) d) The specific energy of the orbit (km^2/sec^2) e) The true anomaly at which the altitude is 1000 km (degrees) f) V_r and V_theta at the points found in part (e) (km/sec) g) The speed at perigee and apogee A meteoroid is first observed approaching the earth when it is 402,000 km from the center of the earth with a true anomaly of 150degree. If the speed of the meteoroid at that time is 2.23 km/sec, calculate a) The eccentricity of the trajectory b) The altitude at closest approach (km) c) The speed at closest approach (km/sec)

Solution

a) e = (Ra - Rp) / (Ra + Rp)

= (70000 - 7000) / (70000 + 7000)

= 0.818

b) a = Ra + Rp / 2

= (70000 + 7000) /2

= 38500 km

c) T = 2 pi sqrt[ a^3 / GM]

= 2pi sqrt[ (38500 x 10^3)^3 / (6.67 x 10^-11 x 5.972 x 10^24)]

= 75205.25 sec

d) Speific energy of orbit = - G M / 2a

= (6.67 x 10^-11 x 5.972 x 10^24) / (2 x 38500x 10^3)

= - 5173148 J