istance of a planet from sun is four times the distance of the planet frpm earth.How many years will the planet take to complete one revolution of sun?

recall Kepler's 3rd law:

P^2/a^3 is constant

Now we have to interpret your statement. As it is, it is rather ambiguous. Read it carefully.

Assuming the most convenient meaning, I'll say that if we substitute 4a for a, we have to find P' such that

P'^2/(4a)^3 = P^2/a^3
P' = 8P

so, the period is 8 times as long.

To find out how many years it takes for the planet to complete one revolution around the sun, we need to know the time it takes for Earth to complete one revolution.

The Earth takes approximately 365.25 days (or 1 year) to complete one revolution around the Sun. Since the distance of the planet from the Sun is four times the distance from Earth to the planet, we can assume that the planet's orbit is four times larger than Earth's orbit.

To calculate the planet's orbital period, we can use Kepler's Third Law of Planetary Motion, which states that the square of the orbital period is proportional to the cube of the semi-major axis of the orbit.

Let's represent the time it takes for the planet to complete one revolution as P (in years) and the distance of the planet from the Sun as R (in astronomical units).

According to Kepler's Third Law:
(P_planet^2 / P_earth^2) = (R_planet^3 / R_earth^3)

Since the planet's distance from the Sun is four times the distance from Earth to the planet, we can rewrite the equation as:
(P_planet^2 / 1^2) = (4^3 / 1^3)

Simplifying the equation:
P_planet^2 = (4^3)
P_planet^2 = 64

Taking the square root of both sides:
P_planet = √64
P_planet = 8

Therefore, the planet takes 8 years to complete one revolution around the Sun.