Astronomers can calculate the mass of a planet by using the orbital parameters o

Question

Astronomers can calculate the mass of a planet by using the orbital parameters of one of its moons. Consider a hypothetical planet, which has a hypothetical moon that orbits the planet in a roughly circular orbit with a radius of 3.2108 m. The moon takes 16 Earth days to orbit the planet. What is the mass of the planet?

While at the county fair, you decide to ride the Ferris wheel. Having eaten too many candy apples and elephant ears, you find the motion somewhat unpleasant. To take your mind off your stomach, you wonder about the motion of the ride. You estimate the radius of the big wheel to be 22 m, and you use your watch to find that each loop around takes 22 s. Note that your mass is 60 kg.

(b) What is your "apparent weight" at the bottom of the ride?

Explanation / Answer

: r3/T2 = (GM)/(42)

( 3.2 x 10^8)^3/ ( 16 x 24 x 3600)^2 = (6.674 x 10^-11) (M) / ( 4 x 3.14 ^2)

( 32.768 x 10^ 24 )/ ( 19.11x 10^11) = (0.169 x 10^-11) M

m = 10.1354 x 10^ 24 kg apprx

b) Apparenr weight at bottom = mv^2/ r + mg

v = 2pir / T = 2(3.14) ( 22)/22 = 6.28 m/s

Wieght = 695.559 N apprx

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