Please amswr this very fasst

Dear Student

Solution to your 1st query is given below

​​The minimum velocity with which a projectile has to be projected to escape the earth’s gravitational field is called escape velocity.

Let a body of mass ‘m’ be projected with velocity ‘v’.

At the ground, PE = GMm/R

And the KE = ½ mv²

To overcome earth’s gravitational field,

KE>PE

=> ½ mv² > GMm/R

=> v > (2GM/R)^1/2

We know,

g = GM/R²

Therefore,

v > [2(GM/R²)R]^1/2

=> v > [2gR]^1/2

Thus, to escape the earth’s gravitational field, the minimum velocity must be,

v_e = [2gR]^1/2

Higher is the mass of the planet greater will be its escape velocity and lower will be the escape of molecules into the space. Moon’s mass is only 1.12% of the earth’s mass and thus her escape velocity is only 2.4 km/s whereas it is 11.4 km/s for earth, this lets moon lose all the gases on her surface, whereas earth retains it. Moreover, earth’s magnetic field traps (owing to Lorentz’s Force)  the escaping ions (ions are created because of ionizing radiations from the sun) and does not let them escape while moon do not have any magnetic field, thus it is another factor for her not having atmosphere.

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Regards