Question

Planet-X has a mass of 5.46x1024 kg and a radius of 5550 km. What is the First Cosmic Speed i.e. the speed of a satellite on a low lying circular orbit around this planet? (Planet-X doesn't have any atmosphere.) Submit Answer Tries 0/12 What is the Second Cosmic Speed i.e. the minimum speed required for a satellite in order to break free permanently from the planet? Submit Answer Tries 0/12 If the period of rotation of the planet is 14.7 hours, then what is the radius of the synchronous orbit of a satellite? Submit Answer Tries 0/12 Post Discussion Send Feedback

Answer 1

Solution

1) 8099.298 m/s

2) 11454.137 m/s

3) 787552.742 m

Solution R the Givern mass of planet M = 5.46x1024 ug , radies R = 5550410 1 Frost compoppie speed is the orbital velocity at an orbit of radices Itsell (It is the smallest possible or low lying corcular orbit around planet. We have arbital velocity, Universal R M. Mass of planet Ripodies of orbif. 6.674x10 x 5.46x1024 5550x103 GM growtational consland 시 8099.298 m/s 28.099 kn/ 2) Second commic speed is the escape velocity gener escape vebety of planet. We have by, ve 2CM - (M) ve ya N R NZX 8099.298 =) Ve 11454.137 m/s 2 11.454 kro/s Using the orbital velocity forrsula, COM am as Radius of orbit CD R v² a circular orbit radius of orbit R anal vo are connected as, Bat forr Ti Time period 07 ve = 40²R² U = Rw = P20 T2 GIM or (2) in (1) =) R3 40²2/2 GMT 40² 13 Thus radius of arbut R = 16674810" x 5.46x1024 1407* (GM13) 1947- Corol's fun harus Substituting the values R = (667446" 34. Thours = 14.7*60*60) seconds 4 a 2 78,7552.742 m 2 787.552 km