Let G be the universal gravitational constant and m_{D} 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) v = sqrt((G*m_{p})/(15.522km)); v = sqrt((G*m_{p})/(7, 324km)); v = sqrt((G*m_{p})/(48, 115km)); v = sqrt((G*m_{p})/(42.164km))
The equation that could be used to find the velocity of the satellite if it is placed in a geostationary orbit is:
v = sqrt((G*m_{p})/(42.164km))
To find the velocity of a satellite in a geostationary orbit, we can use the equation:
v = sqrt((G * m_{D}) / r)
where v is the velocity of the satellite, G is the universal gravitational constant, m_{D} is the mass of the planet, and r is the distance between the satellite and the center of the planet.
Out of the given options, the correct equation is:
v = sqrt((G * m_{D}) / (42.164km))
To find the velocity of a satellite in a geostationary orbit around a planet with mass m_d, we can use the formula:
v = √((G * m_d) / r)
where:
- v represents the velocity of the satellite
- G is the universal gravitational constant
- m_d is the mass of the planet
- r is the distance from the center of the planet to the satellite
In the given options, we need to choose the equation that has the correct value for r to match a geostationary orbit.
A geostationary orbit is one in which the satellite remains fixed relative to a point on the planet's surface. This means that the satellite's orbital period is equal to the planet's rotational period. For Earth, the rotational period is about 24 hours.
To achieve this, the satellite needs to orbit at a specific height above the planet's surface. This height is such that the time it takes for the satellite to complete one orbit matches the rotational period of the planet.
For Earth, a geostationary orbit is achieved at an altitude of approximately 35,786 kilometers (22,236 miles). This value represents r in the formula.
Now let's evaluate the given options to identify the one that matches a geostationary orbit:
v = √((G * m_p) / 15,522 km)
v = √((G * m_p) / 7,324 km)
v = √((G * m_p) / 48,115 km)
v = √((G * m_p) / 42,164 km)
None of the given options have 35,786 km as the value for r, which is the correct altitude for a geostationary orbit around Earth. Therefore, none of the provided equations can be used to find the velocity of a satellite in a geostationary orbit.