Orbital Air
Orbital Air
Physics problem... orbital periods, help please?
A satellite of mass 215 kg is launched from a site on Earth's equator into an orbit at 190 km above the surface of Earth.
(a) Assuming a circular orbit, what is the orbital period (s) of this satellite?
(b) What is the satellite's speed (m/s) in its orbit?
(c) What is the minimum energy (J) necessary to place the satellite in orbit, assuming no air friction?
10 points for best answer!
By equating the gravitational force to the centripetal force needed to keep the satellite in orbit, one can derive the relationship:
T² = 4π²r³/GM
Here T = period
r = distance from Earth's center (190 km + radius of earth)
G = universal gravitational constant
M = mass of earth
(a) Solve for T to get period
(b) The angular velocity is 2π/T, and the linear velocity is
the angular velocity times r (the distance defined above)
or distance/time = 2πr/T
(c) The satellite's energy = mv²/2 where m is its mass and v is the velocity you just calculated
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