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Author Question: How big is Earth on the 1-to-10 billion scale described in Section 1.2? What will be an ideal ... (Read 35 times)

mydiamond

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on: Jul 27, 2018
How big is Earth on the 1-to-10 billion scale described in Section 1.2?
 
  What will be an ideal response?

Question 2

Use the information in Table 6.1 to compare the angular momentum in Earth's orbital motion, Jupiter's orbital motion and Pluto's orbital motion.
 
  Which factor seems to be most significant to the orbital angular momentum of these bodies: radius, mass or angular speed? Why?


kaylee05

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Reply #1 on: Jul 27, 2018
Answer to Question 1

Scaled radius of Earth = actual radius / 1010
= 6,378 km / 1010
= 6,378  105 cm / 1010
= 6.378  108 cm / 1010
= 6.378  10-2 cm
= 0.6 mm
This is about the size of the tip of a (fine tip) ballpoint pen.

Answer to Question 2

Since looking at the ratios of the angular momentums of these bodies will suffice, we can leave the units alone. So angular momentum is proportional to mass  angular speed  radius of the orbit2.
For Earth, this is 1 Earth mass  1/(1 Earth year)  (1 AU)2 = 1
Jupiter: 318  1/11.9  (11.2)2 = 3350 times Earth's orbital angular momentum
Pluto: 0.002  1/248  (39.5)2 = 0.013 times Earth's orbital angular momentum
The radius of the orbit (approximated by the semi-major axis) is most significant because it is squared in the relationship. We can see this by comparing Pluto and Earth. Even though Pluto is only 0.2 of the Earth's mass, it has more than 1 of the Earth's orbital angular momentum.


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