As a navigation technician for a space research station, you are verifying the orbital data for a satellite. The satellite follows an elliptical path where the closest distance to the central planet is 20 AU and the furthest distance is 50 AU. Match each orbital component below with its correct calculated value based on the standard elliptical model described in your technical manual.

A navigation specialist for a satellite research team is modeling an elliptical orbit where the semi-major axis $a = 35$ AU and the focal distance $c = 15$ AU. According to the relationship $b^2 = a^2 - c^2$, what is the value of $b^2$ that will be used in the standard equation rac{x^2}{a^2} + rac{y^2}{b^2} = 1?

As an aerospace technician, you need to derive the orbital equation for a satellite. Arrange the following steps in the correct order to calculate the value of $b^2$ based on a closest approach (periapsis) of ${}20$ AU and a furthest approach (apoapsis) of ${}50$ AU.

As a mission specialist, you are verifying the orbital equation for a spacecraft. The spacecraft follows an elliptical path centered at the origin with a semi-major axis $a = 35$ AU and a focus located at $c = 15$ AU. True or False: The denominator of the $y^2$ term in the standard equation rac{x^2}{a^2} + rac{y^2}{b^2} = 1 is ${}1000$.

As a data records specialist at an aerospace firm, you are tasked with entering standard orbital equations into the tracking database. For a specific elliptical orbit centered at the origin, the semi-major axis $a$ is 35 AU ($a^2 = 1225$) and the sun is located at a focus distance $c$ of 15 AU. Based on the documented model where $b^2 = a^2 - c^2$, the calculated value that replaces $b^2$ in the standard equation $\frac{x^2}{1225} + \frac{y^2}{b^2} = 1$ is ____.