Let G be the universal gravitational constant and m 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)

Question

Responses

v=1200 kmGmp−−−−√
v=1200 kmGmp−−−−√

v=17000 kmGmp−−−−√
v=17000 kmGmp−−−−√

v=√Gmp(200km)
v=√Gmp(200km)

v=Gmp(7000km)−−−−−−√
v is equal to square root of the fraction with numerator cap g m p and denominator 7000 kilometers end root
Question 2
Let G be the universal gravitational constant and m 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 geostationary orbit?(1 point)
Responses

v=Gmp15,522 km−−−−−−−√
v=Gmp15,522 km−−−−−−−√

v=Gmp7,324 km−−−−−−√
v=Gmp7,324 km−−−−−−√

v=Gmp42,164 km−−−−−−−√
v=Gmp42,164 km−−−−−−−√

v=Gmp48,115 km−−−−−−−√
v=Gmp48,115 km−−−−−−−√
Question 3
Which factor is not needed when calculating the velocity of a satellite orbiting a planet?(1 point)
Responses

the mass of the planet
the mass of the planet

the mass of the satellite
the mass of the satellite

the orbital radius of the satellite
the orbital radius of the satellite

the universal gravitational constant
the universal gravitational constant

Answer 1

Question 1

To find the velocity \(v\) of a satellite in a low Earth orbit, we can use the equation derived from the gravitational force and the centripetal force required to keep the satellite in orbit. The correct formula to find the orbital velocity is:

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

For low Earth orbit, where the average altitude is about 200 km above the Earth's surface, the radius \(r\) is approximately \(6371 \text{ km} + 200 \text{ km} = 6571 \text{ km}\). However, since none of the options precisely corresponds to this, amongst the given responses, the most relevant choice would be:

\[ v = \sqrt{G m_p (200 \text{ km})} \]

This indicates that you are considering the altitude directly, though more typically you would use the total radius from the center of the Earth.

Question 2

To find the velocity of a satellite in a geostationary orbit, you would also use a similar equation:

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

For a geostationary orbit, the radius is approximately \(42,164 \text{ km}\) from the center of the Earth. So the correct response would be:

\[ v = \sqrt{G m_p (42,164 \text{ km})} \]

Question 3

When calculating the velocity of a satellite orbiting a planet, you only need the mass of the planet, the orbital radius of the satellite, and the universal gravitational constant. The mass of the satellite does not factor into the calculation of orbital velocity. Thus, the correct response is:

the mass of the satellite