Question

A space probe is orbiting a planet on a circular orbit of radius R and a speed v. The acceleration of the probe is a. Suppose rockets on the probe are fired causing the probe to move to another circular orbit of radius 0.5R and speed 2v. What is the magnitude of the probe’s acceleration in the new orbit?

Answer 1

Answer:

acceleration in the new orbit is 8 time of acceleration of planet in old orbit

$a_{new} = 8a.$

Explanation:

given data:

radius of orbit = R

Speed pf planet = v

new radius = 0.5R

new speed = 2v

we know that acce;ration is given as

$a = \frac{v^{2}}{R},$

$a_{new} =\frac{(2v)^{2}}{0.5R},$

           $= \frac{4v^{2}}{0.5R}$

          $= \frac{8 v^{2}}{R}$

$a_{new} = 8a.$

acceleration in the new orbit is 8 time of acceleration of planet in old orbit