Respuesta :
Answer:
Explanation:
To find the orbital speed of Miranda, we can use the formula for orbital speed:
v = √(G * M / r)
where:
v is the orbital speed,
G is the gravitational constant (6.67430 x 10^-11 m^3 kg^-1 s^-2),
M is the mass of Uranus, and
r is the radius of Miranda's orbit.
Let's plug in the values:
v = √((6.67430 x 10^-11 m^3 kg^-1 s^-2) * (8.68 x 10^25 kg) / (1.29 x 10^8 m))
Calculating this, we find:
v ≈ 4.05 x 10^3 m/s
So, the orbital speed of Miranda is approximately 4.05 x 10^3 m/s.
To find the number of Earth days it takes Miranda to complete one orbit, we can use the formula for the orbital period:
T = (2π * r) / v
where:
T is the orbital period,
r is the radius of Miranda's orbit, and
v is the orbital speed.
Let's plug in the values:
T = (2π * (1.29 x 10^8 m)) / (4.05 x 10^3 m/s)
Calculating this, we find:
T ≈ 2.04 x 10^5 s
To convert this to Earth days, we divide by the number of seconds in a day (86,400 seconds):
T ≈ 2.36 Earth days
Therefore, it takes Miranda approximately 2.36 Earth days to complete one orbit around Uranus.
