Arthur Ernest Hodgson was educated at the Royal College of Science, South Kensington, London, and became a demonstrator in astrophysics at the same institution. Subsequently, in June 1902, he was appointed as a computer and astronomical assistant at the Solar Physics Observatory in South Kensington, under Sir Norman Lockyer. In 1903 he published a paper on "Stellar classifications" in the Journal of the Astronomical Society (Leeds).
In April 1903 Hodgson received an appointment as junior astronomical assistant at the Natal Observatory, Durban, under the Government Astronomer, Edmund N. Nevill*, and the senior assistant, R.F. Rendell*. Arriving on 12 May that year, his duties included routine clock star observations and their reduction, comparing clocks and chronometers and working out daily corrections for the standard mean time clock, searching for and observing comets and asteroids, and assisting meteorological assistant F.A. Hammond* with meteorological observations and their reduction. In 1907 he made a series of observations of Comet D (1907) with the observatory's 200 mm equatorial telescope, the results of which were sent to the Royal Astronomical Society for publication. The next year he made a series of lunar photographs for a determination of the physical libration of the moon [slight variations in the moon's rotation on its axis, caused by minor irregularities in its shape and amounting to less than two minutes of arc]. He was promoted to senior assistant from 1 January 1910, but the Natal Observatory was closed soon thereafter.
Hodgson was an enthusiastic worker with an interest in various branches of science relating to his profession. He was elected a Fellow of the Royal Astronomical Society (FRAS) in November 1903 and was a member of the Physical Society. Colleagues and friends remembered him as a companionable and friendly person. He was a member of the Durban Rowing Club.