MAE 4410: Fundamentals of Astrodynamics
Homework # 6
Due: 7 April 2008
Hohmann Transfer
Radius of orbit 1 = 6828 km
Radius of orbit 2 = 26562 km
1. What is velocity of the first orbit?
2. What is the semi-major axis of the transfer orbit?
3. What is the specific mechanical energy of this transfer orbit?
4. What is the perigee velocity of this elliptic transfer orbit?
5. What is the apogee velocity of this elliptic transfer orbit?
6. What is the velocity of the final orbit?
7. What is ΔVHT_1?
8. What is ΔVHT_2?
9. What is ΔVTot?
10. What is Time of Flight (TOF) for this maneuver?
Simple Plane Change Maneuver
A. Radius of orbit = 6828 km
Current inclination = 28.5°
Desired inclination = 55.0°
1. What is velocity of the orbit (Vi)?
2. What is the inclination change (Δθ= Δi)?
3. What is ΔVs?
4. What is velocity of the orbit after the maneuver (Vf)?
B. Radius of orbit = 26562 km
Current inclination = 28.5°
Desired inclination = 55.0°
- What is velocity of the orbit (Vi)?
- What is the inclination change (Δθ= Δi)?
- What is ΔVs?
- What is velocity of the orbit after the maneuver (Vf)?
C. Compare the two the ΔVs and make a conclusion.
Three Burn Maneuvers
Radius of orbit 1 = 6828 km (i1= 28.5°) Radius of orbit 2 = 26562 km (i2 = 55.0°)
A. Simple Plane Change (1-burn) followed by Hohmann Transfer (2-burns)
ΔV1 = ΔVS
ΔV2 = ΔVHT_1
ΔV3 = ΔVHT_2
(i = deg) (i = deg) (i = deg) (i = deg)
What is the total ΔVtot?
B. Hohmann Transfer (2-burns) followed by Simple Plane change (1-burn)
ΔV1 = ΔVHT_1
ΔV2 = ΔVHT_2
ΔV3 = ΔVS
(i = deg) (i = deg) (i = deg) (i = deg)
What is the total ΔVtot?
C. Compare the two the ΔVtot and make a conclusion.
Combined Plane Changes
Radius of orbit 1 = 6828 km (i1= 28.5°) Radius of orbit 2 = 26562 km (i2 = 55.0°)
A. Combined Plane Change (1-burn) followed by Second Hohmann Transfer burn (1-burn)
ΔV1 = ΔVC
ΔV2 = ΔVHT_2
(i = deg) (i = deg) (i = deg) (i = deg)
1. What is ΔVC?
2. What is ΔVHT_2?
What is ΔVTot?
B. First Hohmann Transfer burn (1-burn) followed by a Combined Plane Change (1-burn)
ΔV1 = ΔVHT_1
ΔV2 = ΔVC
(i = deg) (i = deg) (i = deg) (i = deg)
1. What is ΔVHT_1?
2. What is ΔVC?
3. What is ΔVTot?
C. Compare the two the ΔVtot and make a conclusion.
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