We can imagine creating a new planet with twice the mass of the earth, and an orbital radius of 2.5 ⨯ 1011 m (earth's orbital radius is 1.5 ⨯ 1011 m). how long will a year last on this new planet? explain how your got your answer. "g"

   T= 6.78 10⁷ s

Explanation:

One way to accomplish this problem is to use Kepler's third law, which relates the order of the planets to their orbital distance.

      T² = (4π² / G ) a³

Where T and a are the period and orbital radius, respectively

Let's start by writing the data for Earth and the new planet

    ² = (4π² / G ) ae³

    T² = (4pi2 / G ) a³

Let's solve with these equations

    T² /  ²2 = a³ /  ³

    T² =  ² (a /  )³

The land period is 1 year

     Te = 1 year (365 days / 1 year) (24h / 1 day) (3600s / 1h)

    Te = 3.15 10⁷ s

Let's calculate

      T² = (3.15 107)² (2.5 1011 / 1.5 1011) 3

     T = RA 45.94 10¹⁴ s

     T= 6.78 10⁷ s

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