energy required for satellite to escape from earth
Escape velocity The escape velocity from Earth is about 11.186 km/s (6.951 mi/s; 40,270 km/h; 25,020 mph)[1] at the surface. More generally, escape velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero;[nb 1] an object which has achieved escape velocity is neither on the surface, nor in a closed orbit (of any radius). With escape velocity in a direction pointing away from the ground of a massive body, the object will move away from the body, slowing forever and approaching, but never reaching, zero speed. Once escape velocity is achieved, no further impulse need be applied for it to continue in its escape. In other words, if given escape velocity, the object will move away from the other body, continually slowing, and will asymptotically approach zero speed as the object's distance approaches infinity, never to come back.[2] Speeds higher than escape velocity have a positive speed at infinity. Note that the minimum escape velocity assumes that there is no friction (e.g., atmospheric drag), which would increase the required instantaneous velocity to escape the gravitational influence, and that there will be no future sources of additional velocity (e.g., thrust), which would reduce the required instantaneous velocity.
Atmospheric entry For Earth, atmospheric entry occurs above the Kármán line at an altitude of more than 100 km (62 mi.) above the surface, while at Venus atmospheric entry occurs at 250 km (155 mi.) and at Mars atmospheric entry at about 80 km (50 mi.). Uncontrolled, objects accelerate through the atmosphere at extreme velocities under the influence of Earth's gravity. Most controlled objects enter at hypersonic speeds due to their suborbital (e.g., intercontinental ballistic missile reentry vehicles), orbital (e.g., the Space Shuttle), or unbounded (e.g., meteors) trajectories. Various advanced technologies have been developed to enable atmospheric reentry and flight at extreme velocities. An alternative low velocity method of controlled atmospheric entry is buoyancy[1] which is suitable for planetary entry where thick atmospheres, strong gravity or both factors complicate high-velocity hyperbolic entry, such as the atmospheres of Venus, Titan and the gas giants.[2]