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Io orbits Jupiter at an average distance of 4.22 105 km with an orbital period of 0.00485 yr. The Moon, which is one of the satellites of the Earth, orbits its parent at an average distance of 3.84 105 km with an orbital period of 0.07481 yr. (a) Use the above information to find the orbital speeds of Io around Jupiter and of the Moon around the Earth. vMoon = m/s vIo = m/s (b) What is the expression for the mass M of the parent in terms of the orbital speed v of the satellite, the orbital radius R of the satellite and the gravitational constant G? (Do not substitute numerical values; use variables only.) M =   (c) Now use your answers from parts (a) and (b) to find the ratio of the mass of the Earth to that of Jupiter.   ME MJ

Io orbits Jupiter at an average distance of 4.22 105 km with an orbital period of 0.00485 yr. The Moon, which is one of the satellites of the Earth, orbits its parent at an average distance of 3.84 105 km with an orbital period of 0.07481 yr. (a) Use the above information to find the orbital speeds of Io around Jupiter and of the Moon around the Earth. vMoon = m/s vIo = m/s (b) What is the expression for the mass M of the parent in terms of the orbital speed v of the satellite, the orbital radius R of the satellite and the gravitational constant G? (Do not substitute numerical values; use variables only.) M =   (c) Now use your answers from parts (a) and (b) to find the ratio of the mass of the Earth to that of Jupiter.   ME MJ

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter7: Rotational Motion And Gravitation
Section: Chapter Questions
Problem 47AP: (a) One of the moons of Jupiter, named Io, has an orbital radius of 4.22 108 m and a period of 1.77...
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Io orbits Jupiter at an average distance of 4.22 105 km with an orbital period of 0.00485 yr. The Moon, which is one of the satellites of the Earth, orbits its parent at an average distance of 3.84 105 km with an orbital period of 0.07481 yr.

(a) Use the above information to find the orbital speeds of Io around Jupiter and of the Moon around the Earth.

vMoon
=		 m/s
vIo
=		 m/s

(b) What is the expression for the mass M of the parent in terms of the orbital speed v of the satellite, the orbital radius R of the satellite and the gravitational constant G? (Do not substitute numerical values; use variables only.)

M =  

(c) Now use your answers from parts (a) and (b) to find the ratio of the mass of the Earth to that of Jupiter.
 
ME
MJ

 

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