Q2) Figure 3.5 shows the geometry of a planetary orbit around the sun. The position of the sun is given by S, the position of the planet is given by P. Let a denote the angle defined by PoOA, measured in radians. The dotted line is a circle concentric to the ellipse and having a radius equal to the major axis of the ellipse. Let T be the total period of the planet, and let t be the time required for the planet to go from A to P. Then Kepler's equation from orbital mechanics, relating x and t, is x-esinx= 2nt T Here is the eccentricity of the elliptical orbit (the extent to which it deviates from a circle). For an orbit of eccentricity = 0.01 (roughly equivalent to that of the Earth), what is the value of a corresponding to t= T/4? What is the value of a corresponding to t = T/8? Use Newton's method to solve the required equation. Figure 3.5 Orbital geometry for Problems 4 and 5

Can I get a better explanation on how clockwise and counterclockwise motion of a particle impacts sine and cosine to which variable it should correspond to?

A Moving to the next question prevents changes to this answer. Question 7 Find the length of the Conjugate axis if the length of the semi-transverse axis is 92 and the distance from the focus to the center is 198. Round your answers to two decimal places

Graph each spiral of Archimedes r = Θ (use both positive and nonpositive values)

Steps to Sketching the Sinusoidal Functions: 1. Lightly sketch the midline line y = D. The midline "splits" the graph into upper and lower halves. 2. Lightly sketch the horizontal lines y=D+A and y = D-A. These two lines determine a horizontal strip inside which the graph of the sinusoidal function will oscillate. Notice, the points where the sinusoidal function has a maximum value lie on the line y = D + |A|. Likewise, the points where the sinusoidal function has a minimum value lie on the line y = D-|A|. 3. Lightly sketch the vertical lines at x = C and x=C+B. One cycle of the sinusoidal function will lie between these two lines. 4. Sketch one cycle of the sinusoidal function in the box created by steps 2 & 3. The important points (minimums, maximums, and crossing the midline) will B, C+B. occur when x= C, C+-B, x= C, C+ B, C+ B, C+ B₁C 4 2 4 a. Sine, A > 0: mid-max - mid - min - mid Sine, A 0: max - mid - min - mid - max Cosine A < 0: min - mid-max - mid - min 5. The fact that the…