To find the velocity of a satellite in a low Earth orbit, we use the formula for orbital velocity, which is derived from the balance of gravitational force and centripetal force. The formula is given by:
\[ v = \sqrt{\frac{G m_p}{r}} \]
where:
- \( v \) is the orbital velocity,
- \( G \) is the universal gravitational constant,
- \( m_p \) is the mass of the planet (Earth in this case),
- \( r \) is the distance from the center of the planet to the satellite.
In low Earth orbit, the radius \( r \) can be approximated as the radius of the Earth plus the altitude of the satellite. For example, if the satellite is at an altitude of 200 km, and the radius of the Earth is approximately 6,371 km, then \( r \) would be approximately 6,571 km or 7,000 km.
The correct expression from the responses given corresponds to the formula:
\[ v = \sqrt{\frac{G m_p}{r}} \]
So, assuming the distance is measured from the center of the planet (approximately 7,000 km), the correct equation from the options given would be:
\[ v = \sqrt{\frac{G m_p}{(7,000 \text{ km})}} \]
Thus the response that fits is:
v = Gmp(7,000 km)−−−−−−−√