Two heavenly bodies both with radii of 4×103 miles and masses of 8×1024 kg are separated...

Part a)

let the speed of one body be 'x'

and

the speed of other body be 'y'.

Applying law of conservation of momentum,

M₁*x = M₂*y

since,

M₁ = M₂, & x = y

Also,

applying law of conservation of energy,

loss in potential energy = gain in kinetic energy

or

-G*M₁*M₂/D + G*M₁*M₂/(R₁+R₂) = 0.5*M₁*x² + 0.5*M₂*y²

[(-6.67*10^-11)/(1.609*4*10⁷) + (6.67*10^-11)/(1.609*4*10³*2)]*8*10²⁴ = 0.5*x² + 0.5*y²

using the two equations,

we get x = y = 2.037*10⁵ m/s

Part b)

Apply law of conservation of momentum,

M₁*x = M₂*y

let M₁ = 2*M₂, so we get,

2x = y

conserving energy,

-G*M₁*M₂/D + G*M₁*M₂/(R₁+R₂) = 0.5*M₁*x² + 0.5*M₂*y²

or (-6.67*10^-11/(1.609*4*10^7) + 6.67*10^-11/(1.609*4*10^3*2))*2*8*10^24 = 0.5*2*x^2 + 0.5*(2x)^2

Solving the two equations,. we get

x = 1.66*10^5 m/s

y = 3.33*10^5 m/s

Hence speed of more massive planet = 1.66*10⁵ m/s