(Solved): Your spacecraft is in a circular Earth orbit at altitude 1000km. (altitude is above the ground no ...

Your spacecraft is in a circular Earth orbit at altitude $1000\mathrm{km}$. (altitude is above the ground not from the center of the Earth - watch out for this!). You want to reach point pt2, as shown, at an altitude of 10,000 km. To accomplish this, you fire thrusters at point pt 1 . What is the circular orbit velocity? What speed change is required at $pt1$ ? What will be your velocity $v_2$ when you pass through point $pt2$ ? What is your velocity $v_3$ at the intermediate position shown $pt3(6000\mathrm{km}$ altitude)? The radius of the Earth is $R_E=6378\mathrm{km}$