The minimum speed required for a satellite in order to break free permanently from the planet and the radius of the synchronous orbit of a satellite are 7.3 Km/s and 3.1 × 10⁴ km respectively.
To find the answer, we need to know about the escape velocity and time period of revolving satellite.
What's the expression of escape velocity of a satellite?
- Mathematically, escape velocity= √(2GM/R)
- G = gravitational constant, M = mass of planet, R= radius of the planet
- Here, M = 4.74×10²⁴kg, R = 5870 km
- Escape velocity= √(6.67×10^(-11)×4.74×10²⁴/5.870×10⁶)
= 7.3 Km/s
What's the expression of time period of a circularly orbiting satellite?
- T= {2π×r^(3/2)}/√(GM)
- r= (T/2π)⅔× (GM)^(1/3)
- r is the radius of the orbit
What's the radius of the circular orbit, if the time period of the satellite is 16.6 hours?
- T = 16.6 hours = 16.6×3600 second = 59760s
- r = (59760/2π)^⅔× (6.67×10^(-11)×4.74×10²⁴)^(1/3)
= 3.1 × 10⁴ km
Thus, we can conclude that the escape velocity and the radius of the synchronous orbit of a satellite are 7.3 Km/s and 3.1 × 10⁴ km respectively.
Learn more about the escape velocity here:
brainly.com/question/8057108
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