Calculations based on escape velocity

What is escape velocity?

Escape velocity is the speed that an object needs to be traveling to break free of a planet or moon's gravity well and leave it without further propulsion. For example, a spacecraft leaving the surface of Earth needs to be going 7 miles per second, or nearly 25,000 miles per hour to leave without falling back to the surface or falling into orbit.

Formula Used :

\[v = \sqrt{\frac{2GM}{R}} \]

where , G = gravitational force 

              M = mass of the object.

              R = distance between the objects

The equation can also be written considering the initial altitude of the escaping object:

\[v = \sqrt{\frac{2GM}{r + h}} \]

where ,r is the radius of the celestial body in km.

             h is the altitude or separation from the surface of the body in km.

             v is escape velocity in km/s

Calculating force required

Formula :v = √(2GM/R)

Input

Reset
⨯ 10


⨯ 10


⨯ 10


Output

Escape velocity {{vvalue}}

Calculating mass of the object

Formula :m = (v2r)/2G

Input

Reset
⨯ 10


⨯ 10


⨯ 10


Output

Mass of the object {{mvalue}}

Calculating gravitational force

Formula :g = (v2r)/2M

Input

Reset
⨯ 10


⨯ 10


⨯ 10


Output

Gravitational force {{gvalue}}

Calculating distance between the object

Formula :r = 2GM/v2

Input

Reset
⨯ 10


⨯ 10


⨯ 10


Output

Distance {{rvalue}}
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