Answer to Question #102696 in Astronomy | Astrophysics for sakshi

Question

On Jupiter a day lasts for 9.9 earth hours and the circumference at the equator is 448600 km. If the measured value of gravitational acceleration at the equator is 24.6mls² , what is the true gravitational acceleration and the centrifugal acceleration. b) A ball of mass 50g is hit due south with a speed of 70 ms-1 at latitude 60 ºN. Calculate the magnitude and direction of the coriolis force on the ball.

Answer 1

1)

$$\omega=\frac{2\pi}{9.9\cdot 3600}=0.0001762\frac{rad}{s}$$

The centrifugal acceleration

$$g_c=\omega^2r=(0.0001762)^2\frac{448600000}{2\pi}=2.22\frac{m}{s^2}$$

The true gravitational acceleration:

$$g_t=g+g_c=24.6+2.22=26.82\frac{m}{s^2}$$

2)

$$F_c=2mv\Omega \sin{\lambda}$$

$$F_c=2(0.05)(70)(7.3\cdot 10^{-5}) \sin{60}=4.4\cdot 10^{-5}\ N$$

The missile with a south-pointing velocity is deflected to the right of its motion in the Northern Hemisphere, which is toward the west.