View source for Rocket Propulsion:Boost From A Planet

=Boost From Nonrotating Planet=

To go from a nonrotating planetary surface orbit requires that a rocket change its velocity from a rest velocity (zero) to a velocity that will keep the payload in orbit.  If our rocket maintains a constant thrust during its ascent, then the total velocity change is

<center><math>\int_0^{t_{orbit}} a\,dt = \int_0^{t_{orbit}} {T \over m}-{D \over m} - g\,dt</math></center>

where <math>a</math> is the acceleration, <math>D</math> is the drag, and <math>g</math> is the planets gravitational pull.

=Boost From Rotating Planet=


=Staging=

Many rockets do not have the capability to reach the required orbital trajectory using a single stage.  Also, the mass efficiency (ratio of useful payload to total mass) increases with staging.  In the end, we desire a rocket with a number of stages that optimizes the economic efficiency (cost per payload unit mass).  The economic efficiency depends on a number of factors, the mass efficiency being only one factor.

Let us assume that we desire to launch a payload of weight ''P''.  The weight of each stage in the stack is
: <math>W_i = Pw_i</math>
where <math>w_i</math> is a normalized weight for the stage.  The total stack weight is thus
: <math>W = P \left (1+ \sum_{n=1}^N w_i \right )</math>
The change of velocity per unit mass for each stage is 
:<math>\Delta v_i = I_{sp_i}\ln \mu_i</math>
where <math>\mu_i</math> is the ratio of the weight before the burn of the  ''i''th stage to the weight after the burn of that stage.  Thus, <math>\mu_i</math> will always have a value greater than 1.  The total change in velocity per unit mass for each stage is
:<math>\Delta v = \sum_{n=1}^N I_{sp_i}\ln \mu_i</math>

[[Category:Rocket Propulsion]]