Planetary problem

Algebra Level 2

In a solar system far, far away there are two planets. The first P l a n e t 1 Planet_{1} has radius of 7000 kilometres, the other P l a n e t 2 Planet_{2} has radius of only 3500 kilometres and it is also two times lighter than the P l a n e t 1 Planet_{1} .

What is ratio of density of P l a n e t 2 Planet_{2} and P l a n e t 1 Planet_{1} ?

ρ 2 ρ 1 \frac{ρ_{2}}{ρ_{1}} = ?

Note: Assume that both planets are spheres.


The answer is 4.

Bernhard Folprecht by Bernhard Folprecht , 20, Czech Republic

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1 solution

X X
Jul 28, 2018

Mass ratio is M 1 : M 2 = 2 : 1 M_1:M_2=2:1

Volume ratio is V 1 : V 2 = 700 0 3 : 350 0 3 = 8 : 1 V_1:V_2=7000^3:3500^3=8:1

So the density ratio is ρ 1 : ρ 2 = 2 8 : 1 1 = 1 : 4 ρ_1:ρ_2=\dfrac28:\dfrac11=1:4 , ρ 2 ρ 1 = 4 \frac{ρ_{2}}{ρ_{1}}=4

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Oh, you are right, I put there inverted value... My bad sorry, thank you for poiting it out!

Bernhard Folprecht - 2 years, 10 months ago

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It's okay.

X X - 2 years, 10 months ago

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