g = 9.81 m/s at the Earh\'s surface, and gravity obeys an inverse square law: To

Question

g = 9.81 m/s at the Earh's surface, and gravity obeys an inverse square law: To maintain a body of mass. m moving at constant speed along a circular path of radius r an acceleration of a = v2/r is required. How can the body's speed remain constant when a non-zero acceleration is involved? Explain. Is any force involved required? Explain. Is any work involved/required? Explain A new LEO(low earth orbit) satellite communication system is to use satellites in circular earth orbits at height of 780 km. Assuming the Earth to be a perfect sphere of radius 6330 km, calculate: The orbital speed of the satellites The orbital period To, in the form hours : mins : secs

Explanation / Answer

a.
(1) If acceleration is perpendicular to v then v changes direction but not magnitude.
(2) any acceleration has to come from a force since F=ma
(3) remember W=Fd cos, where is the angle between F and d. if the force is perpindicular to the direction you are moving =90. and cos 90=0 so W=0

b.

(1)

so we know F=G m1 m2/r2

we also know that a=v2/r

so we use F=ma and get Gm1 m2/r2=m2v2/r

so v2=Gm1/r=Gm1/(R+h) where R is the radius of the earth and m1 is mass of earth, so

v2=6.67E-11*5.97E24/(6370E3+780E3) so v=7463 m/s

(2) since we are at consant speed v=d/t if we choose the distance to be the circumference t is the period

7464=2(6370E3+780E3)/t so t=6019 seconds

remember 1 hour - 3600 seconds

so there is 1 hour in there with 2419 seconds after the hour.

2419 seconds/60=40.32 minutes and there are 19 seconds left

so 1 hour: 40 minutes: 19 seconds

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