The more massive a star, the closer it will lie to the center of mass. If you keep the same two stars but double their separation, d, will also double. If you keep the same two stars and double their separation, d, will stay the same. If you keep the same two stars but double their separation, the distance ratio 을 will also double. (Hint: at least two of the statements are true.) If you keep the same two stars and double their separation, the distance ratio will stay the same. de = d2 = AU AU (e) What is the ratio of d, to d, this time? = (f) Select any of the following statements that you agree with. This online calculator you can use for computing the average molecular weight (MW) of molecules by entering the chemical formulas (for example C3H4OH (COOH)3 ). It then produces a screen with the numeric data and a graphical presentation of the calculated masses and their relative occurrences. (One AU is Earth's average distance from the Sun.) (a) What is the distance, d, (in AU) from Star 1 to the center of mass? AU (b) What is the distance, d2, (in AU) from Star 2 to the center of mass? AU (c) What is the ratio of d, to di? d1 (d) Now change the separation, R, to 40 AU and find d, and dz (in AU) under this new condition. The program calculates the exact molecular formula and molecular weights and the isotopic distributions of the molecules. Assume that Star 1 has m = 2.7 solar masses, Star 2 has m2 = 1.6 solar masses, and the total separation of the two (R) is 80 AU. Using the center-of-mass equations or the Center of Mass Calculator (under Binary-Star Basics, above), you will investigate a specific binary-star system. Use the M(1) slider to set up the first 10 mass in Solar Units. Use the Distance slider to set up the distance 3 between the objects. Use the 10 drop down list to select the units (AU, pc, or ly). d = 150.0 AU Distance 1 d1 = 50.0 AU M (1) in Solar Units 0.5 150 Instructions 300 Use the Center of Mass Calculator to evaluate the 6 distances from the two objects to the center of mass. Note: if you click on the dot at the end of each slider, you then can increase or decrease the variable of interest with the left and right arrow keys on your computer keyboard. Practice using the Calculator, then use it to complete the following activity. Note that the illustration is not to scale: if it were, the stars would appear smaller than the period at the end of this sentence. Center of Mass Calculator The following Calculator allows you to visualize the relationships between masses and distances in a range of wide binary-star systems (systems where the separation dwarfs the sizes of the stars themselves).
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