To find the velocity of a satellite in a low Earth orbit, we use the formula for circular orbital velocity, which is given by:
\[ v = \sqrt{\frac{G \cdot m}{r}} \]
Here, \( v \) is the orbital velocity of the satellite, \( G \) is the universal gravitational constant, \( m \) is the mass of the Earth (in this case, since we're talking about a low Earth orbit), and \( r \) is the distance from the center of the planet (Earth) to the satellite.
When we're talking about a low Earth orbit, this typically means the satellite is orbiting relatively close to the Earth's surface compared to the planet's radius. However, the satellite is not at the Earth's surface itself; it is some distance above it. Therefore, \( r \) is not just the radius of the Earth, but the radius of the Earth plus the height of the orbit above the Earth's surface.
The Earth's average radius is approximately 6371 km. If a satellite is in a low Earth orbit 700 km above the Earth's surface, the total distance \( r \) from the center of the Earth to the satellite is:
\[ r = 6371 \text{ km} + 700 \text{ km} \]
\[ r = 7071 \text{ km} \]
To find the velocity, we plug this value of \( r \) into the orbital velocity formula:
\[ v = \sqrt{\frac{G \cdot m}{7071 \text{ km}}} \]
Since none of the options provided (700 km)Gm, (0km)Gm, or something related to (7000) exactly matches the form of the correct equation, they all are incorrect based on the information about calculating the velocity of a satellite in orbit. The correct formula must include \( G \), \( m \), and the total distance \( r \) from the center of the Earth to the satellite. Since no correct equation was provided among the options, none of the above answers would be correct. If forced to choose, I would have to indicate that none of the provided options is correct, as they all fail to incorporate the full equation necessary for determining the satellite's velocity in low Earth orbit.
