if earth is one astronomical unit from the sun and has a period of 1 year, approximately how far is planet X form the sun if it has a period of 26 yearS

Question

if earth is one astronomical unit from the sun and has a period of 1 year, approximately how far is planet X form the sun if it has a period of 26 yearS

Answer 1

Kepler's third law says that R^3/P^2 = constant.

http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

We can choose to measure P in years and the orbital radius R in a.u.

In your case, the ratio (R^3/26^2) = 1^3/1^2 = 1
R^3 = 676
R = 8.8 a.u.

Answer 2

To determine the approximate distance of planet X from the sun, we can use Kepler's Third Law of planetary motion, which states that the square of the orbital period of a planet is proportional to the cube of its average distance from the sun.

Let's denote the average distance of planet X from the sun as "d" (in astronomical units, AU). We can set up the following equation:

(Period of Earth / Period of Planet X)^2 = (Average Distance of Earth / Average Distance of Planet X)^3

We can plug in the values:

(1 year / 26 years)^2 = (1 AU / d)^3

Simplifying, we have:

(1/26)^2 = 1/d^3

1/676 = 1/d^3

To isolate "d^3", we can take the reciprocal of both sides:

d^3 = 676

Taking the cube root of both sides, we find:

d ≈ ∛676

Calculating the cube root of 676, we get:

d ≈ 8.42

Therefore, the average distance of planet X from the sun is approximately 8.42 astronomical units (AU).

Answer 3

To determine the approximate distance of planet X from the sun, you can make use of Kepler's Third Law of Planetary Motion, which states that the square of the orbital period of a planet is directly proportional to the cube of its average distance from the sun.

Let's denote the distance of planet X from the sun as "d". Since the orbital period of planet X is 26 years and the Earth's orbital period is 1 year, we can set up the following proportion:

(26 years)^2 / d^3 = (1 year)^2 / (1 AU)^3

Before solving for "d," let's simplify the equation by plugging in the values:

(26^2) / d^3 = (1^2) / (1 AU)^3

Simplifying further:

26^2 = d^3

676 = d^3

To find the cube root of 676, we get:

d ≈ ∛676

Using a calculator, you'll find that the approximate value of ∛676 is 8.38. Therefore, the approximate distance of planet X from the sun would be around 8.38 astronomical units (AU).