The observations that are needed to tell whether an Earth-like planet is geologically alive or dead are: A. Images and spectra of the planet.
A planet can be defined as a large celestial body that has sufficient mass to allow for self-gravity and make it assume a nearly circular shape, which is referred to as hydrostatic equilibrium.
Generally, all planets revolve in an orbit around the Sun in the solar system and has a cleared neighborhood.
Based on Astronomy, the planets of the solar system are broadly grouped into two (2) main types and these include;
Furthermore, planets are classified as being geologically alive or dead. According to astronomical reports, the Moon, Mars, and Mercury are geologically dead planetary bodies.
In conclusion, the observations that are needed to tell whether an Earth-like planet is geologically alive or dead are images and spectra of the planet, because they would be used to view the surface of the planet and check whether impact craters are formed on it.
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Your question is lacking the necessary answer options, so I will be adding them here:
A. Images and spectra of the planet.
B. Spacecraft travel to the actual star system - this is the only way in which we will be able to observe geologic activity on an extrasolar planet.
C. Mass and size, therefore density, from combined Doppler and transit observations.
D. Orbital distance to show if the planet lies in the habitable zone of the star
