Question

Jupiter's satellite Europa orbits Jupiter with a period of 3.55 d at an orbital radius of 6.71 108 m (assume the orbit to be circular). G = 6.67 x 10-11 Nm2 /kg2 (a) Determine the mass of Jupiter from the data given. (b) What is the orbital velocity of Europa? (c) What is the gravitational field’s magnitude at Europa?

Answer 1

(a)

M = 1.898 x 10^27 kg

(b)

v = 13.74 km/s

(c) E = 0.28 N/kg

Step-by-step explanation:

Time period, T = 3.55 days = 3.55 x 24 x 3600 second = 306720 s

Radius, r = 6.71 x 10^8 m

G = 6.67 x 10^-11 Nm^2/kg^2

(a)
`T=2\pi \sqrt{(r^(3))/(GM)}`

`M=(4\pi ^(2)r^(3))/(GT^(2))`

`M=(4*3.14^(2)* 6.71^(3)* 10^(24))/(6.67* 10^(-11)* 306720^(2))`

M = 1.898 x 10^27 kg

(b) Let v be the orbital velocity

`v=(2\pi r)/(T)`

`v=(2* 3.14* 6.71* 10^(8))/(306720)`

v = 13739.5 m/s

v = 13.74 km/s

(b) The gravitational field E is given by

`E = (GM)/(r^(2))`

`E = (6.67*10^(-11)* 1.898* 10^(27))/(6.71^(2)* 10^(16))`

E = 0.28 N/kg