1 15 pts A satellite is in a Tundra orbit with semimajor axi

1. (15 pts) A satellite is in a Tundra orbit with semimajor axis 42,164 km, eccentricity 0.2684, and inclination 63.4 . The apogee of the Tundra orbit is in the northern hemisphere, so the argument of perigee, , is 270 . At perigee, the satellite performs a pure plane change maneuver of 1.5 km/s. (a) What is the orbital velocity at the location of the maneuver? (b) What is the total angle of the plane change, ? (c) What is the argument of latitude, u, at the location of the maneuver? (d) What is the new inclination, i2, and change in RAAN, , after the maneuver? 2. (15 pts) Repeat problem #1 if the maneuver is performed at the ascending node.

Solution

1) a) orbital velocity at the location of the maneuver = 1.5 * cos63.4/0.2684²

                                                                                                                            = 9.323 km/sec

    b)    total angle of the plane change, = 270 - 63.4

                                                                = 206.6 degree

c)    the argument of latitude, u =    135 degree

d)   new inclination, i2, and change in RAAN, , after the maneuver = 52 degree and   0.907571 radians

2) a) orbital velocity at the location of the maneuver = 1.5 * sin63.4/0.2684²

                                                                                                                            = 18.618 km/sec

    b)    total angle of the plane change, = 270 - 63.4 - 90

                                                                = 116.6 degree

c)    the argument of latitude, u =    135 degree

d)   new inclination, i2, and change in RAAN, , after the maneuver = 60 degree and   1.0472 radians