Rocket Propulsion/Boost From A Planet

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[edit] 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

\int_0^{t_{orbit}} a\,dt = \int_0^{t_{orbit}} {T \over m}-{D \over m} - g\,dt

where a is the acceleration, D is the drag, and g is the planets gravitational pull.

[edit] Boost From Rotating Planet

[edit] 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

Wi = Pwi

where wi is a normalized weight for the stage. The total stack weight is thus

W = P \left (1+ \sum_{n=1}^N w_i \right )

The change of velocity per unit mass for each stage is

\Delta v_i = I_{sp_i}\ln \mu_i

where μi is the ratio of the weight before the burn of the ith stage to the weight after the burn of that stage. Thus, μi will always have a value greater than 1. The total change in velocity per unit mass for each stage is

\Delta v = \sum_{n=1}^N I_{sp_i}\ln \mu_i
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