Multiple Choice The smaller terrestrial planets have cooler interiors than the l

Question

Multiple Choice

The smaller terrestrial planets have cooler interiors than the larger terrestrial planets because they were cooler when they formed the smaller ones are farther from the Sun they have relatively fewer radioactive elements they have relatively more surface area compared to their volume they had more volcanic eruptions in the past, which released their internal heat A one Solar Mass star is found to have a planet in circular orbit around it with a period of 8 years. What is the size (radius)of the planet's orbit? 8 AU 4AU 1 AU 0.25 AU 0.125 AU

Explanation / Answer

14) d

15) b) 4 AU

we know, T = 2*pi*r^(3/2)/sqrt(G/M)

T2/T1 = (r2/r1)^(3/2)

(T2/T1)^(2/3) = r2/r1

==> r2 = r1*(T2/T1)^(2/3)

= 1 AU*(8years/1 year)^(2/3)

= 1 AU*8)^(2/3)

= 4 AU

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