Question

17. Europa, one of Jupiter's moons, is roughly spherical. The equatorial radius

of Europa is about 1,600,000 meters, and the mass of Europa is about
48,000,000,000,000,000,000,000 kilograms.
a. Find the order of magnitude of the radius r of Europa, and the order of
magnitude of the mass m of Europa.
b. Find the order of magnitude of the volume V of Europa.
c. Use the orders of magnitude of mand V that you found in parts (a) and
(b) to approximate the average density d (in kilograms per cubic meter)
of Europa using the formula d = m.

Answer 1

Given

• r = 1 600 000 m = 1.6×10⁶ m
• m = 48 000 000 000 000 000 000 000 kg = 4.8×10²² kg

a)

• Given above

b)

• V = 4/3 πr³ = 4/3*3.14*(1.6×10⁶)³ = 17.14×10¹⁸ ≈ 1.71×10¹⁹ m³

c)

• d = m / V
• d = 4.8×10²² kg / 1.71×10¹⁹ m³ ≈ 2.8×10³ kg/m³