Assume the orbital of a lunched satellite around the earth is circular. Show tha

Question

Assume the orbital of a lunched satellite around the earth is circular. Show that there is only one speed that a satellite can have if the satellite is to remain in an orbit with a fixed radius and it does not depend on the mass of the satellite. What is the speed and height H above the earth's surface at which all synchronous satellite (regardless of mass) must be placed in orbit, assuming the earth is spherical? If a synchronous satellite has a mass m. How much additional kinetic energy is needed for it to escape from the earth? Please help me figure out this problem?

Explanation / Answer

a) Since force of gravity must balance the centripetal force wehav e Fg= Fc Fg= GmM/R2 Fc =mV2/R so GmM/R2   = mV2/R G M/R    = V2 finally V= ( GM/R) M- mas of the planet R - distance from the sat to teh center of the planet orradius of the orbit G - universal gravitational constant b) the speed V'=V and since H= R -Ro ; where Ro is teh radius of the Earthwe have V= ( GM/(H + Ro) ) c) Total kintic energy energy equal to to potential energyplus final kinetic energy Ke max= Pe + Kefinal Pe= Peg = GmM/R Kefinal = 0.5m V2   Ke max= GmM/R + 0.5m V2   = m( GM/R + 0.5 V2 ) Pe= Peg = GmM/R Kefinal = 0.5m V2   Ke max= GmM/R + 0.5m V2   = m( GM/R + 0.5 V2 )

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.