A50 kg satellite circles the earth in an orbit with a period of 100 min. what minimum energy e is required to change the orbit to one with a period of 310 min? assume both the initial and final orbits are circular. the earth’s radius is 6.37 × 106 m, its mass is 5.98 × 1024 kg, and the value of the universal gravitational constant is 6.672 × 10? 11 n · m2 /kg2 . answer in units of j.

7.4 x 10⁸ J

Explanation:

= mass of the satellite = 50 kg

= mass of the earth = 5.98 x 10²⁴ kg

= initial radius of the orbit

= initial time period of the orbit = 100 min = 100 (60) = 6000 s

Initial time period of the orbit is given as

= final radius of the orbit

= final time period of the orbit = 310 min = 310 (60) s = 18600 s

Final time period of the orbit is given as

Minimum energy required to change the orbit is given as