Final answer:
The most accurate method to determine the chemical composition of a planet's atmosphere is by taking the spectrum of the planet's atmosphere. Spectroscopy allows the detection of specific elements and molecules through their unique absorption lines in the spectrum of the light that the planet reflects or emits.
Step-by-step explanation:
To determine the chemical composition of a planet's atmosphere most accurately, the best method would be (d) Taking the spectrum of the planet's atmosphere. Analyzing the light spectrum that comes from a planet can reveal information on the atmospheric constituents, as light interacts with elements and molecules in the atmosphere, creating absorption lines that indicate their presence.
For example, the spectrum obtained from HR 8799 planet 1 indicated a hydrogen-rich atmosphere, and the presence of methane was detected on planet 4. Spectroscopy is a fundamental tool in astrophysics for determining the chemical composition of celestial objects.
While other methods, such as measuring the overall color of the planet or bouncing radio waves, provide some information, they are less direct and often less precise than spectral analysis. The Doppler effect, although useful for detecting and characterizing planets by observing the wobble of the star caused by planetary gravity, does not yield specific details on the chemical composition of planetary atmospheres.