Question

to determine the mass of the central object, we must apply newton's version of kepler's third law, which requires knowing the orbital period and average orbital distance (semimajor axis) for at least one star. we could consider any of the stars shown in the figure, so let's consider the star with the highlighted orbit (chosen because its dots are relatively easy to distinguish). what is the approximate orbital period of this star?

Answer 1

The approximate orbital period of this star is 13 years.

What is Kepler's third law?

The square of a planet's period of revolution around the sun in an elliptical orbit is directly proportional to the cube of its semi-major axis, states Kepler's law of periods.

T² ∝ a³

The time it takes for one rotation to complete depends on how closely the planet orbits the sun. With the use of the equations for Newton's theories of motion and gravitation, Kepler's third law assumes a more comprehensive shape:

P² = 4π² /[G(M₁+ M₂)] × a³

where M₁ and M₂ are the two circling objects' respective masses in solar masses.

Learn more about Kepler's third law here:

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