How do Astronomers measure the mass of the Sun (about 2x1030kg!)?

Question

How do Astronomers measure the mass of the Sun (about  2x1030kg!)?

BlackTom AI · Accepted Answer

Question restatement: How do Astronomers measure the mass of the Sun (about 2 x 10^30 kg)?

Given answer: By observing the motion of the Sun and applying Newton's version of Kepler's law.

Reasoning steps:
- The mass of the Sun can be inferred from the gravitational influence it exerts on bodies that orbit it, such as planets and spacecraft. By carefully tracking the orbital motions (periods, semi-major axes, etc.) we can relate these quantities to the solar mass via gravitational laws.
- Newton's version of Kepler's third law states that for objects orbiting the Sun, the cube of the semi-major axis (a^3) divided by the square of the orbital period (P^2) is proportional to the solar mass (specifically, a^3 / P^2 = G M_sun / (4π^2) for two-body orbits, where G is the gravitational constant). Therefore, precise measurements of orbital dynamics yield M_sun when combined with G.
- This method does not rely on direct weighing or ambiguous proxies; it uses celestial mechanics and observed motions to deduce the Sun's mass from fundamental gravitational relationships.
- Why this is a strong approach: the Sun’s gravitational field governs the planets and many other bodies, and the laws of gravity provide a direct link between orbital motion and central mass. By measuring distances and periods with high precision, astronomers obtain a robust estimate of M_sun.
- If there were alternative methods mentioned (e.g., measuring solar luminosity, surface oscillations, or purely theoretical models without orbital data), they would be less direct or would require additional heavy assumptions. Since the question explicitly references motion and a Newtonian framework, the stated option aligns with the standard and reliable method.
- In summary, using observed orbital dynamics and Newton’s formulation of Kepler's law leverages the fundamental gravitational relationship to deduce the Sun’s mass from celestial motions, which is the cornerstone of solar mass measurements.

Note: The provided data shows the correct answer as a single option and there are no other options given to compare; the explanation above discusses why this approach is scientifically valid and how it connects orbital motion to solar mass.

COS SPR 25 class1 Mar 4 Ch14: Our Star

How do Astronomers measure the mass of the Sun (about 2x1030kg!)?

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