Satellites feel the gravitational pull of the earth. Theyremain in orbit because

Question

Satellites feel the gravitational pull of the earth. Theyremain in orbit because of their velocity, which acts to counteractgravity. (the satellite wants to fly out in a straight line, butgravity forces it to curve towards earth.) If acommunications satellite needs to be 36,000 km above the equator,how fast must it travel to remain at that height (to totallycounteract gravity)? I'll guide you throught it...

a.) Assuming the satellite travels in a perfect circle, whatis the radius of the satellite's travel (The radius of the earth is6375 km.)

b.) At the satellite's altitude, the acceleration of gravity is.222m/s^2, what is the tangenital velocity that the satellite musthave to remain in orbit?

c.) How long will the satellite take to orbit the earth?

Explanation / Answer

The radius of the satellite's travel is the radius of the earthplus the height the satellite needs to be above the earth. a) 6375km + 36000km = 42375 km In this problem the acceleration of gravity is the same as thecentripetal acceleration so it can be solve by the equation centripetal acceleration= v^2/ r 0.222 m/s^2 = (v^2)/(42375000 m) v^2 = 0.222(42375000) v^2 = 9407250 v = 3067.124 m/s b) the tangential velocity is 3067.124 m/s The time to orbit the earth once is the period, T. T = (2r)/v    = (266249977.4)/(3067.124)    = 86807.699 seconds    = 1446.795 minutes    = 24.113 hours C) the satellite will take 24.113 hours or 1446.795 minutes.Or youcould say 86807.699 seconds

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

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