Answer:
(a)


(b) Kinetic Energy of planet with mass m₁, is KE₁ = 1.068×10³² J
Kinetic Energy of planet with mass m₂, KE₂ = 2.6696×10³¹ J
Step-by-step explanation:
Here we have when their distance is d apart

Energy is given by

Conservation of linear momentum gives
m₁·v₁ = m₂·v₂
From which
v₂ = m₁·v₁/m₂
At equilibrium, we have;
which gives
multiplying both sides by m₂/m₁, we have

Such that v₁ =


Similarly, with v₁ = m₂·v₂/m₁, we have

From which we have;
and

The relative velocity = v₁ + v₂ =

v₁ + v₂ =

(b) The kinetic energy KE =


Just before they collide, d = r₁ + r₂ = 3×10⁶+5×10⁶ = 8×10⁶ m
= 10333.696 m/s
=2583.424 m/s
KE₁ = 0.5×2.0×10²⁴× 10333.696² = 1.068×10³² J
KE₂ = 0.5×8.0×10²⁴× 2583.424² = 2.6696×10³¹ J.