Question

Two Jupiter-size planets are released from rest 1.30×10¹¹ m apart.

what are their speeds as they crash together?

Answer 1

given

two Jupiter-size planets are released from rest 1.30 x 10¹¹ m apart = r

here two Jupiter sized planets are released from rest

and

mass of planet = 1.89 x 10²⁷ kg

R = 70000 kg

U_initial = - G M² / r

= - 6.67 x 10^-11 x ( 1.89 x 10²⁷ )² / 1.3 x 10¹¹

= - 1.83276 x 10³³ J

PE_fnal , r = 70000 + 70000

= 140000 km

= 14 x 10⁷ m

U_final = - G M² / r

= - 6.67 x 10^-11 x ( 1.89 x 10²⁷ )² / 1.4 x 10⁷

U_final = - 1.7 x 10³⁷ J

U_final - U_initial = 2 KE

- 1.7 x 10³⁷ - 1.83276 x 10³³ = 2 KE

- 1.7 x 10³⁷ - 1.83276 x 10³³ = 2 KE

KE of each planet is = - 0.5 x 1.7 x 10³⁷

= - 8.5 x 10³⁶ J

v = ( 2 KE / m )^1/2

= ( 2 x 8.5 x 10³⁶ / 1.89 x 10²⁷ )^1/2

v = 94840.439 m/sec