Calculate the speed of a satellite moving in a stable circular orbit about the Earth at a height of 4800 km (the mass of Earth 5.98 × 1024kg and the radius of Earth 6380 km)

The speed of a satellite in a stable circular orbit is determined by the mass and radius of the body it is orbiting, as well as the altitude of its orbit. To calculate the speed of a satellite in this situation, we can use the following formula:

$v = \sqrt{\frac{GM}{R} + h}$

where $v$ is the speed of the satellite, $G$ is the gravitational constant, $M$ is the mass of the Earth, $R$ is the radius of the Earth, and $h$ is the altitude of the satellite's orbit. Plugging in the values from the question, we get:

$v = \sqrt{\frac{(6.67 \times 10^{-11})(5.98 \times 10^{24})}{(6380 \text{ km} \times 1000 \text{ m/km})} + (4800 \times 1000)}$

This simplifies to:

$v = \sqrt{\frac{3.98 \times 10^{14}}{6380000} + 4.8 \times 10^6}$

And finally, to:

$v = \sqrt{6.26 \times 10^7 + 4.8 \times 10^6}$

Which gives us a final result of:

$v = 7.65 \times 10^3 \text{ m/s}$

This is equivalent to about 27,300 km/h, or 16,900 mph.