Magnetopause is a shielding boundary of planetary magnetic field. Many mathematical models have been proposed to describe or to reproduce the magnetopause location, but they are restricted to the real-number functions. In this work, we analytically develop a magnetopause model in the complex-number domain, which is advantageous in deforming the magnetopause shape in a conformal (angle-preserving) way, and is suited to compare different models or map one model onto another.

We propose a new method that combines observations and models to estimate the loss of atmosphere by ion escape from unmagnetized planets. The proposed method allows us to estimate the ionospheric ion escape rate from one bow shock crossing using ion and magnetic field observations. This new technique is applicable to studies on how escape depends on different parameters, work on escape rates during extreme solar wind conditions, and research on escape in the early solar system and at exoplanets.