A newly discovered planet orbits a distant star with the same mass as the Sun at an average distance of 118 million kilometers. Its orbital eccentricity is 0.5.
A.Find the planet's orbital period.
B.Find the planet's nearest orbital distance from its star.
C.Find the planet's farthest orbital distance from its star.
Bruh me too i don't know the answer lemme know when you get it.
To calculate the answers to the questions, 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 star.
A. To find the planet's orbital period (P), we can use the formula:
P^2 = a^3
where P is the orbital period and a is the average distance from the star.
Plugging in the given values:
P^2 = (118 million km)^3
To solve for P, take the square root of both sides:
P = square root of (118 million km)^3
Calculating this value gives us:
P ≈ 46.48 years
Therefore, the planet's orbital period is approximately 46.48 years.
B. To find the planet's nearest orbital distance from its star (periapsis), we can use the formula:
periapsis = a × (1 - eccentricity)
Plugging in the given values:
periapsis = 118 million km × (1 - 0.5)
Calculating this value gives us:
periapsis = 118 million km × 0.5
periapsis ≈ 59 million km
Therefore, the planet's nearest orbital distance from its star is approximately 59 million kilometers.
C. To find the planet's farthest orbital distance from its star (apoapsis), we can use the formula:
apoapsis = a × (1 + eccentricity)
Plugging in the given values:
apoapsis = 118 million km × (1 + 0.5)
Calculating this value gives us:
apoapsis = 118 million km × 1.5
apoapsis ≈ 177 million km
Therefore, the planet's farthest orbital distance from its star is approximately 177 million kilometers.
To find the answers to these questions, we can use Kepler's Laws of Planetary Motion. Kepler's Third Law states that the square of a planet's orbital period is proportional to the cube of its average distance from the star.
A. To find the planet's orbital period:
1. Convert the average distance from kilometers to astronomical units (AU). Since 1 AU is the average distance between the Sun and Earth (about 149.6 million kilometers), we can divide the average distance by 149.6 million to get it in AU.
Average distance in AU = 118 million kilometers / 149.6 million kilometers per AU = 0.788 AU
2. Apply Kepler's Third Law equation: (Period)^2 = (Average Distance)^3
(Period)^2 = (0.788 AU)^3
Period = ∛(0.788 AU)^3
Use a calculator to find the cube root of (0.788 AU)^3 to get the orbital period.
B. To find the planet's nearest orbital distance from its star:
1. Subtract the eccentricity from the average distance to get the nearest distance.
Nearest distance = Average distance - (Eccentricity x Average distance)
Nearest distance = 0.788 AU - (0.5 x 0.788 AU)
Use a calculator to find the product of 0.5 and 0.788 AU, subtract it from 0.788 AU to get the nearest distance.
C. To find the planet's farthest orbital distance from its star:
1. Add the eccentricity to the average distance to get the farthest distance.
Farthest distance = Average distance + (Eccentricity x Average distance)
Farthest distance = 0.788 AU + (0.5 x 0.788 AU)
Use a calculator to find the product of 0.5 and 0.788 AU, add it to 0.788 AU to get the farthest distance.