Use Kepler's third law to find the planet's average distance (semimajor axis) from its star. (Hint: Because the mass of the star is about the same as the mass of our Sun, you can use Kepler's third law in its original form, p2)

Explanation: The planet average distance = 42300km

Kepler's 3rd Law also known as the Harmonic Law states that;

for each planet orbitting the sun, its side real period squared divided by the cube of the semi-major axis of the orbit is a constant.

A planet, mass m, orbits the sun, mass M, in a circle of radius r and a period t. The net force on the planet is a centripetal force, and is caused the force of gravity between the sun and the planet.

Please find the attached file for the solution

answer: at 24 february, 2014 the population gets twice of its initial population.

explanation:

since we have given that

the population for alpha city, t years after january 1, 2004 is given as

first we find out the initial population, i.e. t=0,

so, our quadratic equation becomes,

according to question, we have said that if the population has twice its initial population, then it becomes

so, time taken to reach this above mentioned population is given by

now, we know that time can't be negative so, we take t=9.149 years.

hence, at 24 february, 2014 the population gets twice of its initial population.