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- Hohmann Transfer
 
 
 
 
 
 

 

     
 
THE HOHMANN TRANSFER
 
 

The transfer that requires the least departure energy but results in the longest travel time is the Hohmann transfer, depicted below.

 
 

Figure 1: The Hohmann Transfer
Figure 1: The Hohmann Transfer
 
 

This transfer, though departure energy efficient, takes approximately 8.5 months to complete. The Hohmann transfer has its transfer velocity (V1) in line with the Earth’s circular velocity (Vcs).  The change in velocity required to make the transfer is ΔV1.

 
 

Figure 2: The Hohmann Transfer Velocity
Figure 2: The Hohmann Transfer Velocity
 
 

Similarly, at Mars there is another ΔV maneuver conducted in order to match the circular velocity of Mars, and put the satellites into orbit about Mars.

To calculate the transfer energy we use the specific energy equation below [3].

 
 

 
 

The specific energy (Et) for this transfer is -351.9104 km2/s2

From this we can calculate the velocities at periapsis and apoapsis

Vp = 32.7171 km/s (at Earth)
Va = 21.4647 km/s (at Mars)

Then using the mean planetary velocities from the table above:

Earth = 29.780 km/s
Mars = 24.130 km/s

So the ΔV for the transfer are:

From Earth an increase from 29.78 km/s to 32.7171 km/s which is a difference of 2.9371 km/s
At Mars an increase from 21.4647 km/s to 24.130 km/s which is a difference of 2.6653 km/s

The total ΔV for this type of transfer is 5.6024 km/s
 
     
   
 


References

[2] "Flight to Mars: How Long? Along what Path?" [Online] Available: http://www-istp.gsfc.nasa.gov/stargaze/Smars1.htm

[3] R. R. Bate, “Fundamentals of Astrodynamics”, Dover Publishing.