Q1: Write
out and breifly explain in your own words the equations for centripetal
froce and Newton's Law of Universal Gravitation. Include a sketch
for each explanation.
F_{c} = (mv^{2})/r 
F_{G} = (GM1m)/r^{2}(M1
is the primary body) 
image 
image 
In both equations we are describing a force between the same
two objects F_{c} always acts inward F_{G} acts
between both objects, so one can say F_{c} = F_{G}.
Jupiter's four moons were discovered by Galileo in 1610. The innermost
moon called Io is about half the size of the Earth. Io orbits an
average distance of 422,000 from the center of Jupiter and has an
orbital period of 1.769 days.
Q2: The
Keplerian Ratio is defined as K = T^{2}/r^{3} for
any satellite orbiting a planet or moon. It depends only on the
mass (M) of that planet. Calculate the Keplerian Ratio K_{Jupiter}
for any satellite of Jupiter.
The Keplerian Ratio for Jupiter with respect to Io is:K=(152841.6)^{2}
/ (422,000,000)^{3} = 3.1 x 10^{16}
Q3: Use
the above information to find an equation for the mass of Jupiter.
Solve it.
Q4:What
is the Keplerian Ratio KSun for any object
orbiting our sun? (Hint: You can use T and r for Earth, as it orbits
the sun.) The Earth's average orbital radius about the sun is 150,000,000,000m.
