Which of the following statements cannot be supported by kepler's laws of planetary motion?
a) a planet's distance from the sun will not be the same in six months.
b) a planet's speed as it moves around the sun will not be the same in six months.
c) the rotational speed of the four smallest planets can be determined using the rotational speeds of the four largest planets and their orbital periods.
d) the average distance of saturn can be calculated using the average distance of neptune and the orbital period of both planets.

B) A planet's speed as it moves around the sun will not be the same in six months.

Explanation:

A planet's speed as it moves around the sun will not be the same in six months, is a  statement that CANNOT be supported by Kepler's laws of planetary motion.

The statement ‘A planet's speed as it moves around the sun will not be the same in six months’ cannot be supported by Kepler’s law of planetary motion.

Option B

Explanation:

Johannes Kepler stated three significant laws related to planetary motion. The option A statement is true. Because, the first law defines that the distance between the planet and the sun will not be same as they are rotating around the sun in elliptical orbits.

The third law states that the ratio of square of time taken to complete one orbital rotation by two planets will be equal to the ratio of cube of the distances of the two planets from the sun.

So, according to third law, the statements (c) and (d) can also be supported by Kepler's law. Hence, option (b) is not supported by Kepler's law.

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day