The discussion revolves around determining the height at which a geostationary satellite must be placed above the Earth's surface. The context involves concepts from orbital mechanics and gravitational forces.
Participants are actively engaging with the problem, discussing relevant equations and attempting to connect concepts. Some guidance has been provided regarding substituting variables in equations, indicating a productive direction in the exploration of the problem.
There is a mention of the assumption of a circular orbit and the requirement for the satellite's orbital period to match one day, which is crucial for maintaining a geostationary position. Participants express uncertainty about the velocity and its relationship to altitude.
Hmm... I guess they want me to use [tex]F_c=m_ca_c=m_c\frac{v^2}{r}[/tex]. Also [tex]F_c=\frac{Gm_cM_E}{r^2}[/tex] which led me to conclude that [tex]r=\frac{GM_E}{v^2}[/tex]. But the velocity is unknown so I'm stuck. At last I could calculate it but only in function of the altitude (using the formula [tex]v=\omega r[/tex]) which is precisely what I'm looking for...They mean that the orbital period is 1 day, so that the satellite is always directly over the same place on Earth.
Also, assume a circular orbit. What equations do you know that apply to:
1. gravity
2. circular motion
fluidistic said:Hmm... I guess they want me to use [tex]F_c=m_ca_c=m_c\frac{v^2}{r}[/tex]. Also [tex]F_c=\frac{Gm_cM_E}{r^2}[/tex] which led me to conclude that [tex]r=\frac{GM_E}{v^2}[/tex]. But the velocity is unknown so I'm stuck. At last I could calculate it but only in function of the altitude (using the formula [tex]v=\omega r[/tex]) which is precisely what I'm looking for...
fluidistic said:[tex]r=\frac{GM_E}{v^2}[/tex]. But the velocity is unknown so I'm stuck. At last I could calculate it but only in function
of the altitude (using the formula [itex]v=\omega r[/itex]) which is precisely what I'm looking for...