Question

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? Please explain how your got your answer. "g"

Answer 1

T= 6.78 10⁷ s

Step-by-step 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
`M_(s)`) 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

`T_(e)`² = (4π² / G
`M_(s)`) ae³

T² = (4pi2 / G
`M_(s)`) a³

Let's solve with these equations

T² /
`T_(e)`²2 = a³ /
`a_(e)`³

T² =
`T_(e)`² (a /
`a_(e)`)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