Difficult# Speeding into Orbit

APPH12-TJFALG

What velocity is required to have a $1250\text{ kg}$ satellite orbit the Earth in a circular orbit that is at an altitude of $4{,}500\text{ km}$ above the surface?

Assume:

- The mass of the Earth (${m}_{E}$) is $5.97 \times {10}^{24}\text{ kg}$.
- The radius of the Earth (${r}_{E}$) is $6.38 \times {10}^{6}\text{ m}$.
- The universal gravitational constant is $G= 6.67\times { 10 }^{ -11 }\frac { \text{m}^{ 3 } }{\mathrm{kg\cdot s^{ 2 } } }$