3. There are two SageMath apps below, similar to the ones for Exercise 2. The first app plots the graph of the distance between Earth and Mars and its derivative in the interval \( [t_{min}, t_{max}] \), where distance is measured in AU (astromonical units; 1 AU = 149,597,870,000 meters) and time is measured in days since January 1, 2000. It also evaluates the distance function at day \( t \). The second app is used to find the roots of the derivative. When searching for a particular root, put a lower bound into “Left” and an upper bound into “Right”. In other words, make sure your desired root is the only one in the interval [Left, Right].
(a) Use the first SageMath app below to find the distance between Earth and Mars on the first and last day of your given interval.
(b) Use the second SageMath app below to find the critial points of the distance function on your given interval.
(c) For each critical point found in part (b), compute the distance at that point using the first SageMath app.
(d) When were the two planets closest on your given interval? How close were they? When were they furthest? How far were they?
(b) Use the second SageMath app below to find the critial points of the distance function on your given interval.
(c) For each critical point found in part (b), compute the distance at that point using the first SageMath app.
(d) When were the two planets closest on your given interval? How close were they? When were they furthest? How far were they?