I understand that lighter satellites orbits decay faster. There is 2 satellites that weigh the same but 1 is huge and the other tiny in comparison. Would the size of the satellite make a difference on the orbit?

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    $\begingroup$ A larger satellite experiences a larger atmospheric drag and has more area from which to absorb solar radiation. For this reason, a sheet of paper would probably decay faster than the same paper crumpled in a ball. $\endgroup$
    – Dragongeek
    May 6 '18 at 16:23
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    $\begingroup$ For LEO satellites, drag would be different. But for GEO satellites, drag would be very, very small. $\endgroup$
    – Uwe
    May 6 '18 at 19:21

Absolutely! The parameter that applies is the ballistic coefficient, the object's mass divided by its projected area modified by the drag coefficient. The drag force is given by$$ F_{\text{drag}}=-\frac{1}{2} C_{\text{drag}} A \rho V^2 \,,$$where:

  • $C_{\text{drag}}$ is the drag coefficient (at orbital speeds and atmospheric densities this is usually very close to $2$);

  • $A$ is the projected area;

  • $\rho$ is the atmospheric mass density; and

  • $V$ is the velocity relative to the surrounding atmosphere.

The minus sign out front says the drag force is in the direction opposite the velocity direction. Acceleration, in this case deceleration, is $a_{\text{drag}}=\frac{F_{\text{drag}}}{m}$, where $m$ is the object's mass, so divide the expression for $F_{\text{drag}}$ by $m$ and you get acceleration. Within this new expression is $\frac{C_{\text{drag}}A}{m}$, the inverse of the ballistic coefficient,$$ \text{BC} = \frac{m}{C_{\text{drag}}A} \,.$$The higher that number, i.e. the more massive the object per unit area, the lower the deceleration will be, and the longer it will take its orbit to decay.

Interestingly, the very small vertical gradient in atmospheric density shows up in decaying objects, if they aren't gravity-gradient stabilized (paper).

The slightly increased density on the lower side of the spacecraft produces more drag force per unit area there, and the spacecraft starts to rotate!


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