This problem is posted in the Expert Q and A but my numbers don\'t match up at a

Question

This problem is posted in the Expert Q and A but my numbers don't match up at all and I"ve punched them in about a dozen times now.

1) Two identical stars, each having a mass and radius equal to that of our sun (M = 2 x 1029 kg and R = 7 x 108 m), are initially at rest in outer space. Their initial separation is the same as the distance between our sun and the earth, D = 1.5 x 1011 m. Their gravitational interaction causes the stars to be pulled toward one another. Find the speed of the stars just before they collide.

1. Find UG

UG=-GMM/D=-(6.87*1011)(2*1029)(2*1029)/(1.5*1011)=-1.832*1059

2. Find KE.

KE=2*1/2mv2=(2*1029)v2 *sorry about the tiny font for this section, this interface is being weird*

3. Find U=-GMM/D=-(6.87*1011)(2*1029)(2*1029)/2*(7*108)=-1.96*1061

4. UG=K+U, solve for v. Are my numbers really, really off?

Explanation / Answer

here,

mass,m = 2 * 10^29 kg
radius. r = 7 * 10^8 m
seperation distance, D = 1.5*10^11 m
Gravitational Constant, G = 6.67*10^-11 m^3/kg.s^2

From Conservation of Energy we have :
initial Energy = Final Energy
-Gm^2/D = 0.5*mv^2 - Gm^2/r

solving for velocity, v

v = (2Gm^2(1/r - 1/d))/m)
v = (2Gm(1/r - 1/d)))
v = (2* 6.67*10^-11* 2*10^29 *( 1/(7 * 10^8) - 1/(1.5 * 10^11) ) )
v = 3.793 * 10^10 m/s

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