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Force on a Satellite Due to Drag

See the attached files.
Calculate the force on a satellite due to drag and the mass of propellant needed to overcome the drag force.

Sun synchronous orbit alt = 700 km
Mass of satellite = 800 kg
Assume Cd = 2
Thruster Isp = 80 s
Propellant = N2 (Molecular Weight = 28, etc)
Propellant temperature = 280 K
Length of satellite = 4 m
Width (diameter) of satellite = 1 m

F = (1/2*m)*Cd*A*density*V^2 but how would you calculate the mass of propellant needed.

Please show all steps.

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Solution Preview

The drag force is

F =(Cd/2)*rho*A*V^2,

where

Cd = 2 (given),

and we address the values of A, rho, and V below.

The momentum "eaten up" by the drag over lifetime T is

P_lost = F*T = (Cd/2)*rho*A*V^2 *T.

The momentum added by emitting the propellant over the lifetime is

P_added = Isp * g * M,

where

Isp = 80 s

is the given thruster specific impulse (e.g. see definitions at http://en.wikipedia.org/wiki/Specific_impulse),

g = 9.8 m/s^2

is the free fall ...

Solution Summary

This solution calculates the force on a satellite due to drag and the mass of the propellant needed to overcome the drag force.

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