Question

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) v=1(200 km)Gmp−−−−√ v=Gmp(200 km)−−−−−−√ v=Gmp(7,000 km)−−−−−−−√ v=1(7,000 km)Gmp−−−−√

Answer 1

The equation that can be used to find the velocity of the satellite if it is placed in a low Earth orbit is $\sqrt{\frac{2Gm_p}{R} }$.

The given parameters;

• mass of the planet, = $m_p$

The potential energy of the satellite is calculated as;

$V = \frac{Gm_pM}{R}$

where;

• M is mass of Earth
• R is the distance of the satellite from the center of the Earth

At the low Earth orbit, the potential energy at the maximum height will be equal to kinetic energy at the low Earth orbit.

$\frac{1}{2} Mv^2 = \frac{Gm_pM}{R} \\\\v^2 = \frac{2Gm_p}{R} \\\\v= \sqrt{\frac{2Gm_p}{R} }$

Thus, the equation that can be used to find the velocity of the satellite if it is placed in a low Earth orbit is $\sqrt{\frac{2Gm_p}{R} }$.

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