Question

What would be the duration of the year if the distance between the sun and earth becomes half the present distance? (working)

Answer 1

Hello Friend,

Here, we will use Kepler's Third Law.

→Kepler's Third Law states that the square of time period of revolution of a planet is proportional to the cube of the semi-major axis of that planet.

That is , T² is proportional to a³

The orbit of Earth around the Sun is almost circular. So, the radius can directly be taken as semi-major axis.

→ Let initial distance between Sun and Earth be R.

Finally, it becomes R/2.

→ Also, initial time period of revolution is 365 days . Finally it becomes, say, T days

→ Now ,T² is proportional to R³
So, (365²)/T² = (R³) ÷ (R/2)³
So, (365²)/T² = 8
So, T² = 365²/8
So, T = 365/√8
(which is 365 divided by square root of 8)

So, T ≈ 129.04 days
So, T ≈ 129 days

→ Thus, if distance between Sun and Earth becomes half, then the length of the year would reduce to 129 days

Hope it helps.

Purva
@Purvaparmar1405
Brainly.in