If a planet had a semi major axis length of 2.3 AU as it orbits the sun,what would be its period in years
To find the period of a planet in years, you can use Kepler's Third Law of Planetary Motion, which states that the square of the period of a planet is directly proportional to the cube of its semi-major axis.
The equation is as follows:
T^2 = (4π^2 / GM) * a^3
Where:
T is the period of the planet in years
a is the semi-major axis length in astronomical units (AU)
G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
M is the mass of the sun (1.989 × 10^30 kg)
Let's plug in the values into the equation and calculate the period.
First, let's convert the semi-major axis from AU to meters:
1 AU is approximately equal to 1.496 × 10^11 meters.
a = 2.3 AU * 1.496 × 10^11 meters/AU
a = 3.4448 × 10^11 meters
Now, we can calculate the period using the equation:
T^2 = (4π^2 / GM) * a^3
T^2 = (4 * π^2 / (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 1.989 × 10^30 kg)) * (3.4448 × 10^11 meters)^3
Now, we can solve for T by taking the square root of both sides of the equation:
T = √[(4 * π^2 / (6.67430 × 10^-11 m^3 kg^-1 s^-2 * 1.989 × 10^30 kg)) * (3.4448 × 10^11 meters)^3]
Calculating this equation will give us the period of the planet.