Answer to Question #57201 in Mechanics | Relativity for cpyadav

Question

Explain what happens when a body is raised to a height from the surface of earth and then given a horizontal velocity v such that:
i) 0 < v < 8.0 km/s
ii) v = 8.0 km/s
iii) 8.0 < v < 11.2 km/s
iv) v = 11.2 km/s

Answer 1

Significant speed values:
a) 8.0 km/s (circular velocity, first cosmic velocity) is a minimum speed required to orbit around the Earth;
b) 11.2 km/s (escape velocity, second cosmic velocity) is a minimum speed required to overcome Earth gravity and escape to interplanetary space
Thus, in specified cases:
i) 0 < v < 8.0 km/s
- the body will fall back to Earth
ii) v = 8.0 km/s
- the body will orbit around the Earth
iii) 8.0 < v < 11.2 km/s
- the body will orbit around the Earth, with different orbit radiuses
iv) v = 11.2 km/s
- the body will escape Earth gravity and travel to interplanetary space