What is the necessary orbital speed for a satellite to remain in a circular orbit 300 km above the Earth?

To determine the necessary orbital speed for a satellite in a circular orbit 300 km above the Earth's surface, we can use the formula for orbital speed, which is derived from the balance of gravitational force and centripetal force:

[ v = \sqrt{\frac{GM}{r}} ]

Where:

• ( G ) is the gravitational constant, approximately ( 6.674 \times 10^{-11} , \text{m}^3/\text{kg} \cdot \text{s}^2 )

• ( M ) is the mass of the Earth, roughly ( 5.972 \times 10^{24} , \text{kg} )

• ( r ) is the distance from the center of the Earth to the satellite, which is the sum of the Earth's radius and the height of the orbit.

The average radius of the Earth is about 6371 km. So, when the satellite is 300 km above the Earth's surface, the total radius ( r ) is calculated as:

[ r = 6371 , \text{km} + 300 , \text{km} = 6671 , \text{km} =