Final Answer:
To correct his diagram, Brendan should choose options b and d. Changing the Fg = Fc vector label to Fa = Fc (option b) accurately represents the net force acting on the satellite, and adjusting the Fg = Fc vector to be perpendicular to the velocity vector V (option d) aligns with the correct centripetal force direction.
Step-by-step explanation:
Option b is a necessary correction as the label Fg = Fc suggests that gravitational force is equal to centripetal force, which may not be accurate. Renaming it Fa = Fc ensures that it represents the net centripetal force acting on the satellite.
Option d is crucial for accurately illustrating centripetal force. Centripetal force is always directed toward the center of the circular path, which means it should be perpendicular to the velocity vector V. Correcting the Fg = Fc vector to be perpendicular ensures that Brendan accurately depicts the direction of the net force acting on the satellite.
Options a and c are not necessary corrections. Option a suggests drawing the Fg = Fc vector at a 45° angle from the V vector, which does not accurately represent the relationship between centripetal force and velocity. Option c, suggesting the Fg = Fc vector should be longer than the V vector, may misrepresent the magnitude of forces involved, as centripetal force is dependent on the mass and velocity of the satellite rather than being inherently larger.