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Understanding Orbital Mechanics: Velocity, Radius, and Period Calculations

This guide explores the fundamental concepts of orbital mechanics, including how to calculate orbital velocity and radius for objects in various orbits. We will analyze examples such as finding the velocity of an object 250 miles above Earth and determining the radius of a geosynchronous orbit. Detailed algebraic steps and formulas used in these calculations, like ( v^2 = frac{GM}{r} ) and ( T^2 = frac{4pi^2r^3}{GM} ), are explained for clarity. Perfect for students and enthusiasts looking to grasp orbital dynamics.

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Understanding Orbital Mechanics: Velocity, Radius, and Period Calculations

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  1. Orbit • Orbit condition • Example • Whiteboards

  2. Orbit msv2 r or ms42r T2 ms = Gmsmc r2 mc Example 1 - What is the velocity of orbit 250 miles above the earth? r = 6.38x106 m + (250 mi)(1609 m/mi) = 6782250 m mc = 5.97 x 1024 kg, use mv2/r = Gmm/r2 Do algebra first!!!!!!!! How to enter on calculator TOC

  3. Orbit msv2 r or ms42r T2 ms = Gmsmc r2 mc Example 2 - What is the radius of a geosynchronous orbit? T = 23:56:04 = 23(3600) + 56(60) + 4 = 86164 s mc = 5.97 x 1024 kg, use m42r/T2 = Gmm/r2 Algebra TOC

  4. Whiteboards: Orbit 1 | 2 | 3 | 4 TOC

  5. msv2 r • = Gmsmc • r2 What is the velocity of orbit 7.2 x 106 m from the earth’s center for a 23.5 kg object? Me = 5.97 x 1024 kg 7436 m/s W 7400 m/s

  6. msv2 r • = Gmsmc • r2 At what distance from the moon’s center is the orbital velocity 52.5 m/s? Mm = 7.36 x 1022 kg • r = Gmc • v2 1781086621 m W 1.78 x 109 m

  7. ms42r T2 • = Gmsmc • r2 You are orbiting 2.3 km from the center of an asteroid in a 24,600 kg spacecraft with a period of 2500 seconds. What must be the mass of the asteroid? mc = 42r3 GT2 1.15223E+15 kg W 1.2 x 1015 kg

  8. ms42r T2 • = Gmsmc • r2  42r3 Gmc T = You are orbiting 8.5 x 106 m from the center of a planet with a mass of 4.5 x 1024 kg. Your spaceship has a mass of 45,120 kg. What is your period of motion? 8987.5 s W 9.0 x 103 s

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