as Venus orbits the sun, its semi -major axis length is 0.72 AU. How long does it take Venus to orbit the sun in years?
A) 0.61 years
B) 0.37 years
C) 0.80 years
D) 0.72 years
Pls help me somebody
To find the answer, we can use Kepler's third law of planetary motion, which states that the square of a planet's orbital period is proportional to the cube of its semi-major axis.
First, let's convert the semi-major axis length of Venus from astronomical units (AU) to kilometers (km). One astronomical unit (AU) is approximately 149.6 million kilometers (km).
Given that the semi-major axis length of Venus is 0.72 AU, we can calculate the semi-major axis length in kilometers:
Semi-major axis length = 0.72 AU * 149.6 million km/AU
Semi-major axis length = 107.712 million km
Next, we need to convert the semi-major axis length of Venus from kilometers to meters, because the formula requires the distance to be in meters. There are 1,000 meters in one kilometer, so:
Semi-major axis length = 107.712 million km * 1,000 m/km
Semi-major axis length = 107.712 billion m
Now, let's calculate the orbital period of Venus using Kepler's third law.
Orbital period^2 = (Semi-major axis length)^3
Orbital period^2 = (107.712 billion m)^3
Orbital period^2 = 1.2887 x 10^27 m^3
Orbital period ≈ √(1.2887 x 10^27) m
Orbital period ≈ 1.135 x 10^13 m
Finally, let's convert the orbital period of Venus from meters to years. One year is approximately 31,557,600 seconds.
Orbital period in years = 1.135 x 10^13 m / (31,557,600 s/year)
Orbital period in years ≈ 3.597 years
Therefore, the closest answer choice to how long it takes Venus to orbit the sun is:
A) 0.61 years
However, it is important to note that the calculated value is an approximation, and the actual orbital period of Venus is approximately 0.62 years or about 225 Earth days.