if a comet is 125 years from sun and has a perihelion distance of 1. AU..What is the aphelion distance?
I formulated it this way, is this right?
125years^2/1.AU^3= 15,625
my book tells me the answer is 49 AU. I am just not getting the calculation. Please help
I explained this yesterday. The distance that gets used in the Kepler equation is the semimajor axis, a, NOT the perihelion distance. Therefore
125^2/a^3 = 1
a^3 = 125^2 = 15625
a = cube root of 15625 = 25 AU
(Aphelion + Perihelion)/2 = a
(Aphelion + Perihelion) = 50
Aphelion = 50 - 1 = 49 AU
yes this is explained much better thank you for your time
To find the aphelion distance of a comet given its perihelion distance and the time it takes to complete one orbit, you can use Kepler's third law of planetary motion.
Kepler's third law states that the square of the orbital period (in years) is proportional to the cube of the semi-major axis length (in astronomical units, AU) of the ellipse.
Let's denote the perihelion distance as r1 (1 AU in this case), the aphelion distance as r2, and the orbital period as T (125 years in this case).
Using Kepler's third law, we have:
(r1 + r2) / 2 = (T^2)^(1/3)
Now we can substitute the known values and solve for r2:
(1 AU + r2) / 2 = (125^2)^(1/3)
To find r2, we can rearrange the equation and solve for it:
r2 = 2 * (125^2)^(1/3) - 1 AU
Evaluating the expression using a calculator, we get:
r2 ≈ 17.47 AU
Therefore, the aphelion distance of the comet is approximately 17.47 astronomical units.