Determining the orbit of the two stars of Kepler-34, also called A and B. These two stars together are called a binary. A) Assume that star A has a mass of 1 solar mass and star B also has a mass of 1 solar mass. The semi major axis is 0.23 AU and the eccentricty is 0.53. What is the orbital period of the stellar A-B binary in days? Ignore the (much less massive) planet and focus on the orbit of the binary. B) Now let's consider the orbit of the planet, called "b". Since the planet orbits some distance away from the stars, it is an acceptable approximation to pretend like the stellar binary is like a single star with a mass that is the sum of the masses of stars A and B and that the mass of planet "b" is very small, calculate the semi-major axis in AU of the planet's orbit with a period of 289 days. (note: I think for this problem you are supposed to use Newton's version of Kepler's third law P2= 4π2/G(M1-M2)x a3 but, I'm not sure if that's the right thing to do). 1 solar mass= 2 x 1030kg ### Diagram Explanation: Kepler-34 SystemThis diagram represents the Kepler-34 star system, highlighting its orbital dynamics. #### Key Features:1. **Stars A and B**: - Two stars are depicted in the center with overlapping elliptical orbits. - Star A is labeled with an orange circle, while Star B is labeled with a red circle. - Their orbits are closely intertwined, indicating a binary star system.2. **Planet b**: - The position of planet "b" is labeled with a small red circle and a blue label. - Its orbit is shown as a large circle encompassing both stars A and B.3. **Orbital Scale**: - An indicator in the upper right corner notes "0.5 AU" (Astronomical Units), giving a sense of scale for the system's dimensions.4. **Perspective**: - The direction labeled "To Earth" with an arrow shows the viewing angle relative to Earth.5. **Shaded Region**: - A grey vertical band passes through part of the orbits, possibly marking a significant observational area or eclipsing zone.This diagram provides a simplified view of the Kepler-34 binary star system with its orbiting planet, illustrating the relative positions and scales of their orbits.

For a binary system, the period T is T=4π2a3Gm1+m2 Where a is the semi-major axis, m represents the…

Determining the orbit of the two stars of Kepler-34, also called A and B. These two stars together are called a binary. A) Assume that star A has a mass of 1 solar mass and star B also has a mass of 1 solar mass. The semi major axis is 0.23 AU and the eccentricty is 0.53. What is the orbital period of the stellar A-B binary in days? Ignore the (much less massive) planet and focus on the orbit of the binary. B) Now let's consider the orbit of the planet, called "b". Since the planet orbits some distance away from the stars, it is an acceptable approximation to pretend like the stellar binary is like a single star with a mass that is the sum of the masses of stars A and B and that the mass of planet "b" is very small, calculate the semi-major axis in AU of the planet's orbit with a period of 289 days. (note: I think for this problem you are supposed to use Newton's version of Kepler's third law P2= 4π2/G(M1-M2)x a3 but, I'm not sure if that's the right thing to do). 1 solar mass= 2 x 1030kg

Determining the orbit of the two stars of Kepler-34, also called A and B. These two stars together are called a binary. A) Assume that star A has a mass of 1 solar mass and star B also has a mass of 1 solar mass. The semi major axis is 0.23 AU and the eccentricty is 0.53. What is the orbital period of the stellar A-B binary in days? Ignore the (much less massive) planet and focus on the orbit of the binary. B) Now let's consider the orbit of the planet, called "b". Since the planet orbits some distance away from the stars, it is an acceptable approximation to pretend like the stellar binary is like a single star with a mass that is the sum of the masses of stars A and B and that the mass of planet "b" is very small, calculate the semi-major axis in AU of the planet's orbit with a period of 289 days. (note: I think for this problem you are supposed to use Newton's version of Kepler's third law P2= 4π2/G(M1-M2)x a3 but, I'm not sure if that's the right thing to do). 1 solar mass= 2 x 1030kg

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