please help me, thank you, will rate! (a) Use the above information to find the
ID: 1384450 • Letter: P
Question
please help me, thank you, will rate!
(a) Use the above information to find the orbital speeds of the Moon around the Earth and of Pluto around the Sun.
vMoon
vPluto
(b) What is the expression for the mass M of the parent in terms of the orbital speed v of the satellite, the orbital period 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 Sun to that of the Earth.
=
vMoon
= m/svPluto
= m/sExplanation / Answer
a) We know, Orbital speed, vo = 2*pi*r/T
r ---> aradius of the orbit
T ---> time period
so,
Vmoon = 2*pi*3.84*10^8/(0.07481*365*24*60*60)
= 1023 m/s or 1.023 km/s <<<<<<------Answer
Vpluto = 2*pi*5.9*10^12/(248.3*365*24*60*60)
= 4734 m/s or 4.734 km/s <<<<<<------Answer
b) orbital speed, Vo = sqrt(G*M/r)
==> M = vo^2*r/G
so, Ms/ME = (4734)^2*5.90*10^12/(1023^2*3.84*10^8)
= 329022 <<<<<<------Answer
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