the distance fro jupiter to sun is about 800 million kilometers. Its mass is abo
ID: 1486857 • Letter: T
Question
the distance fro jupiter to sun is about 800 million kilometers. Its mass is about 2 x10^27 kg, the mass of the sun is 2x10^33g and the speed of light is 3x10^10 cm/s. assuming Jupiter has a circular orbit, calculate the following No results found for the distance fro jupiter to sun is about 800 million kilometers. Its mass is about2x10^27 kg, the mass of the sun is 2x10^33g and the speed of light is 3x10^10 cm/s. assuming Jupiter has a circular orbit, calculate the following
1- the time it takes in minutes for the sun's light to reach Jupiter
2- the magnitude of gravitational force between the sun and Jupiter
3-the magnitude of centripetal accelerstion of Jupiter, assuming Sun's gravitational force is the only force acting 4- the speed of Jupiter as it revolves around the sun
5- the orbital period of jupiter in years
Explanation / Answer
Given data
distance between Jupiter and sun, r = 800 millian km = 8*10^11 m
mass of jupiter, Mj = 2*10^27 kg
mass of sun, Ms = 2*10^33 g = 2*10^30 kg
speed of light, c = 3*10^10 cm/s = 3*10^8 m/s
1) time taken to reach light from sun to jupiter, t = r/c
= 8*10^11/(3*10^8)
= 2667 s
= 2667/60
= 44.44 minutes
2) the magnitude of gravitational force between the sun and Jupiter, F = G*Mj*Ms/r^2
= 6.67*10^-11*2*10^27*2*10^30/(8*10^11)^2
= 4.17*10^28 N
3) the magnitude of centripetal accelerstion of Jupiter, a_rad = (G*Mj*Ms/r^2)/Mj
= G*Ms/r^2
= 6.67*10^-11*2*10^30/(8*10^11)^2
= 2.08*10^-4 m/s^2
4) a_rad = v^2/r
v = sqrt(a_rad*r)
= sqrt(2.08*10^-4*8*10^11)
= 12900 m/s 12.9 km/s
5) Orbital period, T = 2*pi*r/v
= 2*pi*8*10^11/(12900)
= 389654903 s
= 389654903/(365*24*60*60)
= 12.36 years
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