We know since the Coulomb experiment in 1784 that point-like behaving charges adiabatically increase their energy as they get closer to each other according to 1/d.
Consequently electrons and the charged subcomponents of which the internal structures of protons and neutrons are made, which are the only carriers of charge and mass in the universe, will increase their energy when they get closer to each other.
As all charged particles making up the nuclei of all atoms of which the plane and atomic clock are made increase their altitude up to 10 km from the surface of the Earth, they are progressively pulled less strongly outwards due to the diminishing intensity of the outward pulling gravitational gradient of the elementary charges making up the Earth.
Consequently, the charged subcomponent triad of each proton and neutron of the atoms making up the plane and the clock will draw closer together, increasing their energy and thus their measurable mass, which will in turn draw all electronic orbitals closer to each atomic nucleus, in turn increasing the energy of all electrons of all electronic escorts of the plane and clock, and consequently their frequencies.
The only possible outcome is that the cesium reference photons emitted at the 10 km altitude will have a higher frequency than those emitted by the atomic clock that remained at the surface of the Earth.
When the plane moves in the eastern direction (contrary to the direction of rotation of the Earth), at the same altitude, the energy induced in all charges of which the atoms of the plane is made due to its motion will be equal to that corresponding to the velocity of the plane minus that due to the opposite velocity of the Earth rotation, causing the frequency of the cesium reference photons to diminish.
Contrariwise, when the plane moves in the western direction, the energy of all charges making up the plane and the clock will increase by being induced by the velocity of the plane plus the velocity of the Earth rotation, causing the frequency of the cesium reference photons to increase.
Analyzed in this paper published in 2013:
Article Inside Planets and Stars Masses
This paper is part of the synchronization project initiated by Wilhelm Wien in 1901 between classical kinematic mechanics and electromagnetic mechanics, summarized in this paper published in 2023:
Article Electromagnetic and Kinematic Mechanics Synchronized in thei...
Direct links to the complete sequence of papers analyzing all aspects of electromagnetic mechanics published since year 2000 are available from this resourse:
Article INDEX -Electromagnetic Mechanics (The 3-Spaces Model)
Understanding the relation between the trispatial vector geometry and Hamilton's quaternion can be reached from the presentation published in the following paper published in 2024:
Article Evolution From the Complex Plane to the Quaternion Coordinat...
Links to all formal historical papers of the initiators of electromagnetic mechanics from Heavisde to Marmet, including Searle, Lorentz Wien, Kaufmann, Abraham, Einstein and de Broglie are directly linked for confirmation of their contribution in the Reference section of each paper.
For readers unfamiliar with electromagnetic mechanics, the best way to insure clear understanding of each paper is to personally numerically resolve each equation along the way to confirm the validity of the numerical values provided, by means of a pocket scientific calculator.
This numerical validation process has been made easy by all equations involving only known physical constants and a single variable.
Other discussions on issues raised by electromagnetic mechanics
https://www.researchgate.net/post/The_adiabatic_nature_of_the_energy_induced_in_charged_elementary_particles_as_a_function_of_the_inverse_of_the_distances_separating_them
https://www.researchgate.net/post/How_to_calculate_the_energy_of_any_photon_from_ist_wavelength_without_any_need_of_using_Plancks_quantizing_constant
https://www.researchgate.net/post/Why-did-the-Lorenz-interpretation-prevail-over-Maxwells-in-defining-Electrodynamics
See also discussion: