Fractal Growth on the Surface of a Planet and in Orbit around it

TL;DR

This paper investigates the properties of fractal aggregates in microgravity environments around Earth and Mars, modeling gravitational effects including oblateness and orbital parameters, and finds minimal impact on aggregate size at typical orbital altitudes.

Contribution

It provides a comprehensive gravitational model for fractal aggregate behavior in orbit, incorporating Earth's oblateness and rotation effects, and assesses their influence on aggregate size.

Findings

Aggregate monomer number is unaffected by latitude differences.

Orbital parameters do not significantly influence aggregate size at 300 km altitude.

Gravitational effects have negligible impact on fractal growth in orbit.

Abstract

Fractals are defined as geometric shapes that exhibit symmetry of scale. This simply implies that fractal is a shape that it would still look the same even if somebody could zoom in on one of its parts an infinite number of times. This property is also called self-similarity with several applications including nano pharmacology and drug nano carriers. We are interested in the study of the properties of fractal aggregates in a microgravity environment above an orbiting spacecraft. To model the effect we use a complete expression for the gravitational acceleration. In particular on the surface of the Earth the acceleration is corrected for the effect of oblateness and rotation. In the gravitational acceleration the effect of oblateness can be modeled with the inclusion of a term that contains the J2 harmonic coefficient, as well as a term that depends on the square of angular velocity of the Earth. In orbit the acceleration of gravity at the point of the spacecraft is a function of the orbital elements and includes only in our case the J2 harmonic since no coriolis force is felt by the spacecraft. Using the fitting parameter d = 3.0 we have found that the aggregate monomer number N is not significantly affected and exhibits a minute 0.0001% difference between the geocentric and areocentric latitudes of 90 degrees and 0 degrees. Finally for circular and elliptical orbits around Earth and Mars of various inclinations and eccentricities the aggregate monomer number is not affected at all at the orbital altitude of 300 km.