Question

if the distance between earth and sun were half of its present value the number of days in an year would have been?

Answer 1

According to Kepler’s law
T² ∝ r³

(T₁ / T₂)² = (r₁ / r₂)³
(365 / T₂)² = (2r₁ / r₁)³
(365 / T₂)² = 8
365 / T₂) = 2√2
T₂ = 365 / (2√2)
T₂ = 129 days

There will be 129 days in an year.

Answer 2

The distance between the earth and the sun was part of the current number and the number of days in a year would be:

The distance between the earth and the sun was part of the current number and the number of days in a year would be:

T1 and R1 should be the starting point and the orbits of the planet Earth and T2 and R2 should be the time and radius after the reduction of the distance between the Sun and the Earth.

Thus, if the distance between the extremities of the earth and the sun were to be equals, our total number of days in the year would be$129$ days.

If T is the transition period and r is the orbit radius.

So the new time is$129$ days = the number of days in a year.

We know that $T 1 = 365 days.$

From the formula, $= 365 × 0.3536$

$= 129.1 T 2 = 129.1 days.$

The time of year can be $129.1 days.$