Kepler's Third Law: Calculations

What is the formula to calculate the orbital period of a planet?

• T = 2π√(GM/a^3)

• T = 2π√(a^3/GM)

• T = 2π√(a/GM)

• T = 2π√(a^2/GM)

What is the value of the constant 'k' in Kepler's Third Law equation?

• k = T^2 / a^3

• k = T / a

• k = T^2 * a^3

• k = T^3 / a^2

If a planet has an orbital period of 1 year, what is its semi-major axis in AU according to Kepler's Third Law?

• 0.5 AU

• 5 AU

• 1 AU

• 2 AU

How is the orbital period of a planet related to its semi-major axis according to Kepler's Third Law?

• The orbital period of a planet is not related to its semi-major axis.

• The orbital period of a planet is related to its semi-major axis by the equation T^2 ∝ a^3.

• The orbital period of a planet is related to its semi-major axis by the equation T = a.

• The orbital period of a planet is related to its semi-major axis by the equation T^2 = a^2.

What are the units of measurement for the constant 'k' in Kepler's Third Law equation?

• (distance)^2/(time)^3

• (time)^3/(distance)^2

• (distance)^3/(time)^2

• (time)^2/(distance)^3

Calculate the semi-major axis of a planet with an orbital period of 2 years using Kepler's Third Law.

• 3.1415

• 2.5874

• 1.5874

• 0.5874

Explain the significance of Kepler's Third Law in understanding planetary motion.

• Kepler's Third Law explains the formation of black holes

• Kepler's Third Law relates the orbital period and distance of a planet from the Sun, aiding in the comprehension of planetary motion.

• Kepler's Third Law only applies to moons, not planets

• Kepler's Third Law is irrelevant to planetary motion

What is the relationship between the orbital period and the size of the orbit of a planet?

• The orbital period of a planet is proportional to the distance from the sun.

• The orbital period of a planet is directly proportional to the size of its orbit.

• The orbital period of a planet is not affected by the size of its orbit.

• The orbital period of a planet is inversely proportional to the size of its orbit.

How does Kepler's Third Law help astronomers study the motion of planets in our solar system?

• Kepler's Third Law allows astronomers to determine the relative distances of planets from the Sun based on their orbital periods.

• Kepler's Third Law allows astronomers to determine the age of planets in our solar system

• Kepler's Third Law helps astronomers predict the weather patterns on planets

• Kepler's Third Law provides information on the geological composition of planets

If a planet has a semi-major axis of 3 AU, what is its orbital period in years according to Kepler's Third Law?

• Approximately 5.196 years

• Approximately 7.891 years

• Approximately 4.567 years

• Approximately 2.345 years