I could theorize that according to R. Firrer, the 'halakhic Earth' would be defined as anywhere that one is still subject to the Earth's gravitational field. Actually reading the article, however, implies that either 1. as soon as something is not touching Earth, it is no longer governed by its halachos (which, as you point out, is ridiculous) or 2. anything that has left Earth would still be Earth-bound material until it touches the moon, at which point "halakhic Earth" status gives way to "halakhic moon" status (maybe you could make kiddush levana upon seeing a person who walked on the moon, until he walks upon Earth...)
Honestly, though, R. Firrer's opinion is quoted by R. J. David Bliech as being 'extreme', and I'm sure that no posek would agree to his "radical point of view", including R. Goren, who R. Firrer quotes as saying that time bound commandments are not applicable outside of earth, where there is no measurable time.
That being said, regarding serious discussion of the "halakhic Earth" (or "hashkafic Earth"), both R. Soloveitchik and R. Yaakov Kamenetsky (Emes L'Yaakov Beraishis 1:1, 5761 edition) have been reported as saying that it includes any reachable part of the physical universe. R. Schachter tells the story that some students came to R. Soloveitchik who were very bothered by the fact that someone could leave Earth and touch the moon, due to the pasuk השמים שמים לה' והארץ נתן לבני אדם - the Heavens belong to Hashem. As this story is quoted in Beis Yitzchak 5754 (translated here), R. Soloveitchik responded
The term "heavens" can be explained in two ways — as something high and/or distant, as it says "It is not in the heavens" (Deut. 30:12), according to which the moon is considered a part of the "heavens." Alternatively, the term can be defined as including everything that is beyond human understanding, including the entire spiritual realm. According to this second understanding, the stars and most distant galaxies — and certainly the moon — are considered part of "earth." Therefore, [according to this latter interpretation,] there is no contradiction between traveling in space or scientific studies of the cosmos and the verse "The heavens are for the Lord and the land for mankind."
The way that I heard this story from R. Schachter, he connected it to the words of the Ramban on the first pasuk of the Torah, who says that "שמים" in the Torah refers to heavenly beings, but anything that is physical, including everything that is discussed in detail in the first chapter of Beraishis, is included in ארץ. This is what R. Kamenetsky is said to have believed as well:
We learn from these words of the Ramban [on Gen. 1:1], and in particular from what he concluded in the continuation of his words on verse 8, that everything that exists in the creation in the entire world, including the sun, the moon and all the heavenly hosts, are not called "heavens." The "heavens" are only things that have no physical bodies, such as angels, hayos and the merkavah. However, anything that has a physical body is included in the name "earth" in verse 1 (translated here too)