Question

A probe from earth, with a mass of 106 kg, is in orbit around planet Pud in another solar system. Pud has a radius of 106 m and the probe has an orbital radius of 107 m (its orbit is circular). If the speed of the probe in orbit is 1 km/s, what is the acceleration due to g

Answer 1

Answer:

The acceleration due to gravity in planet Pud is of 9345.7m/s²

Explanation:

Since the probe is describing a circular motion around planet Pud, its centripetal acceleration is given by the formula:

$a_c=\frac{v^{2}}{R}$

Assuming there is no other external forces acting on the probe in the centripetal direction, we have that

$a_c=g_{Pud}=\frac{v^{2}}{R}$

Before we plug in the values, we have to convert the speed from km/s to m/s:

$1\frac{km}{s} =1000\frac{m}{s}$

Finally, using the given values, we can compute g_{Pud}:

$g_{Pud}=\frac{(1000\frac{m}{s}) ^{2} }{107m}= 9345.7\frac{m}{s^{2}}$

In words, the acceleration due to gravity in planet Pud is of 9345.7m/s²