Let G be the universal gravitational constant and mp be the mass of the planet a satellite is orbiting. Which equation could be used to find the velocity of the satellite if it is placed in a low Earth orbit?(1 point)

To find the velocity of a satellite in a low Earth orbit, we can use the formula for orbital velocity derived from the law of gravitation:

\[ v = \sqrt{\frac{G m_p}{r}} \]

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 altitude of the satellite is typically around 200 km above the surface of the Earth. The radius \( r \) would then be the radius of the Earth (approximately 6,371 km) plus the altitude of the satellite (200 km):

\[ r = 6,371 \text{ km} + 200 \text{ km} = 6,571 \text{ km} \]

Thus, the correct representation for velocity, substituting into the formula would be:

\[ v = \sqrt{\frac{G m_p}{6,571 \text{ km}}} \]

None of the equations provided exactly match with this form using 6,571 km, but given the context, the closest would utilize \( 7,000 \text{ km} \) as a rough estimate for the altitude plus Earth's radius:

So the most appropriate answer from the options would be:

\[ v = \sqrt{\frac{G m_p}{7,000 \text{ km}}} \]

Thus, the correct choice from the responses given is:

**v=1(7,000 km)Gmp−−−−−√**