Question

Show that the , escape velocity = √2 ×
critical velocity.​

Answer 1

To escape Earth's gravity, an object's kinetic energy must be greater than or equal to its gravitational potential energy:

(1/2)mv2 = GMm/R

M = the object's mass.

v = the object's velocity (escape velocity).

G = gravitational constant.

M = Earth's mass.

R = Earth's radius.

Solving for v2.

v2 = 2GM/R

v = √(2GM/R)

Now for an object orbiting right at the Earths surface, its centripetal force (mv2/R) will exactly equal the gravitational force:

mvc2/R = GMm/R2

vc2 = GM/R

So the escape velocity is:

v = √(2GM/R) = √(2vc2) = √(2)·vc

Answer 2

Explanation:

answer is :

( i don' know the answer besause i. not read this chapter properly no t t