Question

An undiscovered planet, many lightyears from Earth, has one moon in a periodic orbit. This moon takes 2010 × 103 seconds (about 23 days) on average to complete one nearly circular revolution around the unnamed planet. If the distance from the center of the moon to the surface of the planet is 225.0 × 106 m and the planet has a radius of 3.80 × 106 m, calculate the moon's radial acceleration a c .

Answer 1

Answer:

Radial acceleration of moon is $a_{r} = 2.246\times 10^{-3}$$\frac{m}{s^{2} }$

Explanation:

Given :

Time period $T = 1.987 \times 10^{6}$ sec

Distance from center of moon to planet $r = 225 \times 10^{6}$ m

From the equation of radial acceleration,

  $a_{r} = r\omega ^{2}$

Where $\omega = 2\pi f = \frac{2\pi }{T}$

So   $\omega = 3.16 \times 10^{-6} \frac{rad}{s}$

Now moon's radial acceleration,

 $a_{r} = 225 \times 10^{6} \times (3.16 \times 10^{-6} )^{2}$

 $a_{r} = 2246.76 \times 10^{-6}$

 $a_{r} = 2.246\times 10^{-3}$ $\frac{m}{s^{2} }$