Example 13.2 The Density of the Earth Using the known radius of the Earth and th

Question

Example 13.2 The Density of the Earth Using the known radius of the Earth and that g = 9.80 m/s2 at the Earth's surface, find the average density of the Earth. SOLVE IT Conceptualize Assume the Earth is a perfect sphere. The density of material in the Earth varies, but let's adopt a simplified model in which we assume the density to be uniform throughout the Earth. The resulting density is the average density of the Earth. Categorize This example is a relatively simple substitution problem. Using the equation mg = G MEm RE2 , solve for the mass of the Earth: ME = gRE2 G Substitute this mass and the volume of a sphere into the definition of density: E = ME VE = gRE2/G 4 3 RE3 = 3 4 g GRE = 3 4 9.80 m/s2 (6.674 1011 N · m2/kg2)(6.37 106 m) = kg/m3 MASTER IT HINTS: GETTING STARTED We found that a planet has gravity at its surface 7.8 times that on Earth's surface, while its radius is 5.00 107 m. Determine the average density of the planet. kg/m3

Explanation / Answer

for the earth average density is given by

rho)avg = 3*g/(4*pi*G*Re)

rho)avg = 3*9.81/(4*3.14*6.67*10^-11*6.37*10^6) = 5514.87 kg/m^3

now for other planet

rhoE/rhoP = (gE/Re)/(gP/Rp) = gE*Rp/(gP*Re)

rhoP = rhoE*gP*Re/(gE*Rp)

rhoP = 5514.87*7.8*gE*6.37*10^6/(gE*5*10^7)

rhoP = 5480.23 kg/m^3

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.