Using Newton's Second Law, the Law of Gravity, and the equation for centripetal acceleration, derive an...

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Using Newton's Second Law, the Law of Gravity, and the equation for centripetal acceleration, derive an expression for the Universal Gravitational Constant, G. Using the values from Body 2's orbit, solve for the value of G used in the simulation. Show ALL your work below. Record your result in the units of the simulation: AU, km, s, and kg x 1028. wwww EFr-mac Fg=m(v^2/r) G= Q7: In metric units, G = 6.67 x 10-11 m/kgs. Given that 1 AU=1.496 X 1011 m, convert your G value to the units of m/kgs. It should be close to 6.67 x 10-11 m/kgs. Show all your work. Q8: Rearrange your equation for G to solve for the speed of an object in a circular orbit. Using this equation, solve for the speed required for Body 2 to be in a circular orbit about Body 1 with a 4 AU radius. Use G = 4.46 AU-km/skgx1028 for the rest of the lab. Show all your work below. I Activity 4: Zoom out all the way by clicking Change the number of bodies to 3 by clicking Bodies arrow in lower left. Input the values shown at right, using your values for Vy from Q5 and Q8. Using your equation from Q8, the fact that speed is the distance over time, and Mass (1028 kg) Position (AU) Velocity (km/s) X y 300.0 0.0 0.0 0.1 2.0 0.0 0.1 4.0 0.0 888 0.0 0.0 0.0 7 0.0 7 the equation for the circumference of a circle, derive an equation for the period of an object in a circular orbit in terms of G, M, and r. Simplify your equation and show all your work below. Using Newton's Second Law, the Law of Gravity, and the equation for centripetal acceleration, derive an expression for the Universal Gravitational Constant, G. Using the values from Body 2's orbit, solve for the value of G used in the simulation. Show ALL your work below. Record your result in the units of the simulation: AU, km, s, and kg x 1028. wwww EFr-mac Fg=m(v^2/r) G= Q7: In metric units, G = 6.67 x 10-11 m/kgs. Given that 1 AU=1.496 X 1011 m, convert your G value to the units of m/kgs. It should be close to 6.67 x 10-11 m/kgs. Show all your work. Q8: Rearrange your equation for G to solve for the speed of an object in a circular orbit. Using this equation, solve for the speed required for Body 2 to be in a circular orbit about Body 1 with a 4 AU radius. Use G = 4.46 AU-km/skgx1028 for the rest of the lab. Show all your work below. I Activity 4: Zoom out all the way by clicking Change the number of bodies to 3 by clicking Bodies arrow in lower left. Input the values shown at right, using your values for Vy from Q5 and Q8. Using your equation from Q8, the fact that speed is the distance over time, and Mass (1028 kg) Position (AU) Velocity (km/s) X y 300.0 0.0 0.0 0.1 2.0 0.0 0.1 4.0 0.0 888 0.0 0.0 0.0 7 0.0 7 the equation for the circumference of a circle, derive an equation for the period of an object in a circular orbit in terms of G, M, and r. Simplify your equation and show all your work below.