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Orbital speed is the velocity a satellite needs to maintain in order to stay in orbit around a celestial body like Earth. When a satellite is positioned, for example, 890 km above Earth's surface, its speed ensures that gravity's pull and the satellite's momentum are balanced. This balance lets it move along a curved path, effectively "falling" around Earth rather than towards it.
To find the orbital speed, we use the formula: \( v = \sqrt{\frac{GM}{r}} \). Here, \( G \) represents the gravitational constant, \( M \) is Earth's mass, and \( r \) is the total radius from Earth's center to the satellite.
Applying these values to our formula provides insights into the kind of speed, approximately 7461 m/s, the satellite requires, ensuring it doesn't drift away or crash down.

The orbital period is the time it takes for a satellite to complete a full journey around Earth. Essentially, it's the satellite's "day". To ascertain this period, we employ the formula \( T = \frac{2\pi r}{v} \), where \( r \) is the circular orbit's radius and \( v \) is the orbital speed.
By calculating using the provided satellite altitude, we estimate the period to be about 6168 seconds. For clarity, we convert it to hours, resulting in around 1.71 hours.
Understanding the orbital period helps in knowing not just how fast the satellite orbits, but also in planning tasks like communication or imaging, where timing is key.

The gravitational constant, symbolized as \( G \), is a fundamental natural force measuring the attraction between two masses. It plays a vital role in calculating gravitational forces, especially in scenarios involving planetary bodies and their satellites.
In calculations like those for satellite orbits, \( G \) is used along with Earth's mass to determine essential properties like speed and orbital period. The defined value is \( 6.674 \times 10^{-11} \, \text{m}^3\,\text{kg}^{-1}\,\text{s}^{-2} \), which is crucial in formulating the balances of gravitational force that keep satellites in orbit.

Earth's mass is a fundamental element when computing satellite orbits. It provides a measure of the gravitational force exerted by Earth on nearby objects. Known to be approximately \( 5.972 \times 10^{24} \) kg, this mass is integral to understanding how Earth wields its gravitational strength to keep satellites from soaring into deep space or plummeting back to its surface.
When plugged into orbital equations, Earth's mass combines with the gravitational constant to determine how fast and how long satellites orbit, enabling us to predict satellite behavior and manage orbital mechanics effectively.