The average distance between the Earth and the Sun is called the astronomical unit
(AU), which is about 150 million km (1.5 x 108 km). Jupiter is 780 million km from the
sun.
a) How far is Jupiter from the sun in astronomical units (AU)?
b) Based on your calculation in part a, how many Earth years does it take for
Jupiter to orbit the sun in years?
(Hint: remember, when using years and AU, a3 = P2 for all planets)
As I said in my answer to your other question, you must insert a ^ before exponents. you are not going to learn much astronomy with sloppy equation writing.
(a) Divide the Jupiter-sun distance (in km) by the length of 1 a.u. (also in km). That will give you the number of au's
(b) Use the formula you were given,
P^2 = 1/a^3
with 'a' measured in a.u., from part (a)
P^2 = a^3
P = sqrt(a^3)
How fast is this CME moving in comparison to a jetliner
a) To find the distance from Jupiter to the Sun in astronomical units (AU), we can divide the distance in kilometers by the average distance between the Earth and the Sun in kilometers.
Distance from Jupiter to the Sun = 780 million km.
Average distance between Earth and Sun = 150 million km.
Distance from Jupiter to the Sun in AU = (780 million km) / (150 million km/AU)
Simplifying, we get:
Distance from Jupiter to the Sun in AU = 780 / 150 AU
Distance from Jupiter to the Sun in AU = 5.2 AU
Therefore, Jupiter is approximately 5.2 astronomical units (AU) away from the Sun.
b) To calculate the orbital period of Jupiter (time taken to complete one orbit around the Sun), we can use the relationship "a^3 = P^2," where 'a' is the average distance in astronomical units and 'P' is the orbital period in Earth years.
In part a, we found that the distance from Jupiter to the Sun is approximately 5.2 AU. So, we can substitute this in the equation.
5.2^3 = P^2
Simplifying, we get:
140.608 = P^2
To find the orbital period, P, we take the square root of both sides:
P = √140.608
P ≈ 11.85 Earth years
Therefore, it takes approximately 11.85 Earth years for Jupiter to orbit the Sun.