The tension exerted in the cable amounts to T = 16653.32 N.
Parameters:
Cross section area A = 1.3 m²
Drag coefficient CD = 1.2
Velocity V = 4.3 m/s
The angle formed by the cable with the horizontal is 30 degrees.
Density defined as follows:
The drag force FD is determined by the equation:
FD = (1/2) * ρ * V² * A * CD
Calculating the drag force yields 14422.2 N acting opposite to motion.
Given the cable's angle of 30 degrees with horizontal, the horizontal component contributes to the drag force calculation:
T * cos(30) = F_D
Thus, T = 16653.32 N.
The height is h = 17 10⁶ meters above the surface of Mars. To determine this, we apply Newton's second law according to the universal law of gravitation, represented by F = m a. The centripetal acceleration a is expressed as v² / r. Applying the gravitational force we have G m M / r² = m v² / r. Given that the speed of the object remains constant, we derive v from d / t, where d is the circumference and t is the orbital period. Substituting gives us d = 2π r and v = 2π r / T. Replacing these values leads to the equation G M / r² = (4π² r² / T) / r, so r³ = G M T² / 4π². Converting time into SI units, T = 24.66 h converts to 88776 seconds. Ultimately, the computed value of r is 2,045 10⁶ m, and after subtracting Mars’ radius of 3.39 10⁶ m, we find the height h to be 17 10⁶ m.
I do not concur with her stance. The concept of planetary motion emerges from a collaborative effort involving Johannes Kepler and Sir Isaac Newton. I believe Tycho Brahe's role was minimal since it was really Kepler who made the significant discoveries.
(this is my original response that was accepted)
