Question
Does the escape speed of a body from the earth depend on
(a) the mass of the body,
(b) the location from where it is projected,
(c) the direction of projection,
(d) the height of the location from where the body is launched?
Solution
Escape velocity is given by,
where,
g is the acceleration due to gravity at the point from where the body is projected,
r is the distance from the centre of the earth from where the body is projected, and
h is the height from the surface of the earth.
(a) Escape velocity, ve does not depend on the mass of the body.
(b) Escape velocity, ve depends on upon g and at different locations g is different (gλ = g - Rω2cos2 λ ), therefore, ve slightly depends on upon the angle of latitude ( ∵ Rω2 cos 2 λ ≤ 3.36 cm/s2).
(c) Escape velocity, ve does not depend on upon the direction of projection.
(d) Escape velocity, ve depends on upon height from the surface of the earth.
where,
g is the acceleration due to gravity at the point from where the body is projected,
r is the distance from the centre of the earth from where the body is projected, and
h is the height from the surface of the earth.
(a) Escape velocity, ve does not depend on the mass of the body.
(b) Escape velocity, ve depends on upon g and at different locations g is different (gλ = g - Rω2cos2 λ ), therefore, ve slightly depends on upon the angle of latitude ( ∵ Rω2 cos 2 λ ≤ 3.36 cm/s2).
(c) Escape velocity, ve does not depend on upon the direction of projection.
(d) Escape velocity, ve depends on upon height from the surface of the earth.
