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# 9.6 FE/EIT Review - Momentum, energy, and orbital mechanics.maF The following figure shows a sate... 9.6 FE/EIT Review - Momentum, energy, and orbital mechanics.maF The following figure shows a satellite Q (modalnd s particke of mase m) in an ellptical orbit around Earth. Earth is modeled as a particle O fixed in a Newtonian reference frame N Draw right-handed orthogonal unit vectors i, i,, і, fixed in N with fix horizontally-... right and parallel to the ellipse's major diam- eter, i, vertically-upward and parallel to the ellipse's minor diameter, and fi, perpendicu lar to the ellipse's plane. Draw right-handed orthogonal unit vectors e, Ge, , with &, from O to Q and e,-n Value Symbol Type Quantity Universal gravitational constant Mass of Earth O Mass of Angle between line OQ and long axis of the ellipse | G Constant 6.67 x 10-11 Nom/kg 5.97x 10M kg 200 kg Initial value Initial value Constant m Constant θ variable Distance between O and Q (a) Form Q's linear momentum, angular momentum about O, and kinetic energy in N. Result: (in terms ofymbols in the previous table, their time derivatives, and e.. อ. (10.3) (10.6) 2 (b) Draw Q's free-body diagram and determine the resultant force on Q. r Dot FmMa with "clever" unit vectors and solve for F and a Result rn (c) Form an expression for Q's mechanical energy in N (sum of kinetic energy and potestial energy U). Result: Conservation of mechanical energy KePe m(r)m (d) Optional: Starting with the angular momentum principle in equation (20.4), form an expression that stays constant during Q's motion in N (conservation of angular momentum). ult: HConstan(a0. 0) Draw a line L tangent In general, ('svelocity in N) is parallel to op. True/False perpendicular to f In general, No is paralel to L. Section 20.5) (e) to the ellipse at Q and In general, is parallel to L True/False True/False ) Shown right is a plot of Q's orbital trajectory when the differential equations from part (6b) are solved. Query the Internet (or a textbook, instructor, collesgue, etc.) for the next answers. . Clearly mark Earth's location on the plot. . The Earth is located at (circle one): the center of the ellipse/a focus of the ellipse 225 Homework 9: Particles   #### Earn Coins

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