Does anybody know how R³/3.98x10^14 = (2360448/2π)² equal to 1.411332x10^11
I don't have the foggiest idea.
my calculator says:
(2360448/(2π))² = 1.4113318 x 10^11 , (notice the change in the division by 2π)
don't know how the R³/3.98x10^14 fits in
Looks like Kepler's 3rd law, where you are trying to find the semi-major axis of the orbit.
R = 3.83*10^8
Looks like 1 AU in km
To understand how R³/3.98x10^14 = (2360448/2π)² equals 1.411332x10^11, let's break it down step by step:
1. Start with the equation: R³/3.98x10^14 = (2360448/2π)²
2. Divide both sides of the equation by (2360448/2π)²:
R³/3.98x10^14 / (2360448/2π)² = (2360448/2π)² / (2360448/2π)²
Simplifying the right side of the equation: (2360448/2π)² cancels out with (2360448/2π)², leaving us with:
R³/3.98x10^14 = 1
3. Multiply both sides of the equation by 3.98x10^14:
R³ = 1 * 3.98x10^14
Simplifying the right side of the equation: 1 multiplied by any number equals that number, so we're left with:
R³ = 3.98x10^14
4. Take the cube root of both sides of the equation to solve for R:
R = ∛(3.98x10^14)
5. Calculate the cube root of 3.98x10^14:
R = 145749.066
6. Now we can verify if the value of R is approximately equal to 145749.066:
(145749.066)³ / (3.98x10^14) should be approximately equal to 1.
Evaluating the expression:
(145749.066)³ = 3.960835x10^21
(3.960835x10^21) / (3.98x10^14) ≈ 9.959689
The answer is approximately equal to 9.959689, which is close to 1 but not exactly.
Therefore, the given equation R³/3.98x10^14 = (2360448/2π)² does not exactly equal 1.411332x10^11. There may be an error or some approximation made during calculations.