Question

Ganymede's orbit around Jupiter is nearly circular and has a period of 7.155 days. Assume Ganymede is moving in uniform circular motion.

Answer 1

what I have to find radius or angular speed or angular acceleration???

from the given data U did'nt mention what I have to find so Am finding all the three...

The period is the time for Ganymede's to make one orbit around Jupiter. Let’s convert it to seconds.

t = 7.155 days * 24 hr/day * 60 min/hr * 60 s/min = 6.18*10⁵ seconds

We can use the following equation to determine the radius of the orbit.
T² = [4π² / (G*M)]*r³

Mass of Saturn = 1.898*10²⁷ kg
G * M = 6.67*10^-11 * 1.898*10²⁷ = 1.26*10¹⁷
4π² / (G*M)] = 3.11*10^-16
r^3 = (6.18*10⁵)² / 3.11*10^-16
r^3 = 1.22*10²⁷ m³ =>

r = 1.07*10⁹ m

Orbital speed can be calculated as follows:

V₀ = √(GM/r) = sqrt[1.26*10¹⁷ / 1.07*10⁹] = 1.08*10⁴ m/s

Centripetal acceleration = v²/r = 0.110 m/s²