 TangentialOrbit ManeuverTangentialorbit maneuver occurs at the point where the velocity vector of spacecraft is tangent to its position vector, typically at perigee point.
Example 91
 Determine the ∆V required to transfer from a circular orbit into elliptic orbit.
 Solution
 The ∆V between two orbit can be shown as follow:
 ( 9‑5)

Figure 96. Single coplanar maneuver.



 Figure 96 shows a typical tangential orbit maneuver at perigee point. Using the equation 95, the ∆V required is,

NonTangential Coplanar Maneuver
The orbit maneuver does not limited only at apogee and perigee point. If condition is allowed, the satellite able to perform the orbit maneuvers at any point.
Figure 9 1 shows the ∆V vector required for a nontangential orbit maneuver, where α is the difference angle between the flight path angle of V_{1} and V_{2}.
 ( 9‑6 )

Hohmann Transfer
The Hohmann’s transfer is the minimum twoimpulse transfer between coplanar circular orbits. It can be used to transfer a satellite between two nonintersecting orbits (Walters Hohmann 1925).
The fundamental of the Hohmann’s transfer is a simple maneuver. This maneuver employs an intermediate elliptic orbit which is tangent to both initial and final orbits at their apsides. To accomplish the transfer, two burns are needed. The first burn will insert the spacecraft into the transfer orbit, where it will coast from periapsis to apoapsis. At apoapsis, the second burn is applied to insert spacecraft into final orbit.
Figure 97 represents a Hohmann’s transfer from a circular orbit into another circular orbit. A tangential ΔV_{1} is applied to the circular orbit velocity. The magnitude of ΔV_{1} is determined by the requirement that the apogee radius of the resulting transfer ellipse must equal the radius of the final circular orbit. When the satellite reaches apogee of the transfer orbit, another ΔV must be added or the satellite will remain in the transfer ellipse. This ΔV is the difference between the apogee velocity in the transfer orbit and the circular orbit velocity in the final orbit. After ΔV_{2} has been applied, the satellite is in the final orbit, and the transfer has been completed.
 (9‑7)

Figure 97. Hohmann transfer.


Example 92
 Determine the total ∆V required for Hohmann transfer to transfer from a LEO with h_{initial} = 191.344 km into GEO.
 Solution
 The initial and final radius is,
r_{initial} = 191.344 + 6378.145 = 6569.489 km
r_{final} = 42164.215 km
At first impulse, the deltav required is,
where,
Thus,
For the second impulse, the deltav required is,
The total deltav require is,
km/sec
 Example 9‑3
 Two geocentric elliptical orbits have common apse lines and their perigees are on the same side of the Earth. The first orbit has a perigee radius of km and , whereas for the second orbit km and .
 Find the minimum total deltav and the time of flight for a transfer from the perigee of the inner orbit to the apogee of the outer orbit.
 Do part (a) for a transfer from the apogee of the inner orbit to the perigee of the outer orbit.
 Solution
  For 1^{st} orbit:
km
km
km/sec
For 2^{nd} orbit:
km & km
km
km/sec
For transient orbit:
km & km
km
km/sec
km/sec
km/sec
km/sec
km/sec
sec
Time of flight, TOF:
sec hr
 For 1^{st} orbit:
km
km/sec
For 2^{nd} orbit:
km/sec
For transient orbit:
km & km
km
km/sec
km/sec
km/sec
km/sec
km/sec
sec
Time of flight, TOF:
hr

Date: 20160422; view: 726
