152k views
2 votes
"Opportunity" and "Phoenix" are two of the robotic explorers on Mars. Opportunity landed at 2° south latitude, where Mars’ radius is about 2110 miles. Phoenix landed at 68° north latitude, where Mars’ radius is about 790 miles. Mars rotates on its axis once every 24.6 Earth-hours. How far does each explorer travel as Mars rotates by 1 radian? How many hours does it take Mars to rotate 1 radian? Using this answer, how fast is each explorer traveling around Mars’ axis in miles per hour?

1 Answer

2 votes

Answer:

(a)Distance traveled by each explorer travel as Mars rotates by 1 radian

  • Opportunity=2108.71 miles
  • Phoenix =295.94 miles

(b)Number of hours it takes Mars to rotate 1 radian=3.9152 hours

(c)Speed of each explorer around Mars.

  • Opportunity=538.59 miles per hour
  • Phoenix =75.59 miles per hour

Explanation:

Part A

For any given parallel of latitude
\text{Circumference}=2\pi R \cos \beta$ where \beta$ is the angle of latitude.

Opportunity landed at 2° south latitude, where Mars’ radius is about 2110 miles.


\text{Circumference at 2\°S latitude}=2\pi*2110* \cos 2^\circ\\=13249.44$ miles

Phoenix landed at 68° north latitude, where Mars’ radius is about 790 miles.


\text{Circumference at 68\°N latitude}=2\pi*790* \cos 68^\circ\\=1859.44$ miles

Part B

Next, we determine the distance (Length of arc) covered by each explorer as Mars rotates by 1 radian.


\text{Length of arc (in radian)}=(\theta)/(2\pi) * $Circumference

Opportunity's Distance


=(1)/(2\pi) * 13249.44\\\\ =2108.71$ miles

Phoenix's Distance


=(1)/(2\pi) * 1859.44\\\\ =295.94$ miles

Part C

Mars rotates on its axis once every 24.6 Earth-hours.

Therefore:


(24.6)/(2\pi) \approx $ 3.9152 hour per radian

Part D:Speed of each explorer


\text{Speed}=\frac{\text{Distance}}{\text{Time}}


\text{Speed of Opportunity = }(2108.71)/(3.9152)\\$=538.59 miles per hour\\\\Speed of Phoenix =(295.94)/(3.9154)\\=75.59$ miles per hour

User Stefan Neubig
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories