CONCEPT PART!! Two satellites are in circular orbits around the earth. The orbit

Question

CONCEPT PART!! Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 360 km above theearth's surface, while that for satellite B is at a height of 720km. A) Which satellite has the greater orbital speed? Explain youranswer. B) The speed of a satellite in a circular orbit is given by (v= ([GMe)/r] ). In this expression, do you substitutethe heights of 360x103 m and720x103 for the term r? Explain your answer. PROBLEM PART!! Find the orbital speed for each satellite. Check to seethat your answers are consistent with your answers to the CONCEPTPART. CONCEPT PART!! Two satellites are in circular orbits around the earth. The orbit for satellite A is at a height of 360 km above theearth's surface, while that for satellite B is at a height of 720km. A) Which satellite has the greater orbital speed? Explain youranswer. B) The speed of a satellite in a circular orbit is given by (v= ([GMe)/r] ). In this expression, do you substitutethe heights of 360x103 m and720x103 for the term r? Explain your answer. PROBLEM PART!! Find the orbital speed for each satellite. Check to seethat your answers are consistent with your answers to the CONCEPTPART.

Explanation / Answer

the gravitational force between satellite and the earthis F = (GMm/r^2) -------------(1) the gravitational force between them is balanced by thecentripetal force acting between them therefore we get F = (m * v^2/r) ------------(2) from (1) and (2) we get (GMm/r^2) = (m * v^2/r) or v = (GM/r)^(1/2) here,r = R + h or v = (GM/R + h)^(1/2) ------------(3) G = 6.67 * 10^-11 Nm^2/kg^2,M = 5.9742 * 10^24 kg,R = 6378.1km = 6378.1 * 10^3 m and h is the height of the satellite above theearth's surface. A)the satellite which is moving at a smaller height above thesurface of the earth will have a greater orbital speed.This isbecause the orbital speed of the satellite is inverselyproportional to the square root of the distance of thesatellite. B)The speed of a satellite in a circular orbit is givenby v = [GMe)/r] in the above expression we do not substitute the heights forthe term r.This is because the term r is equal to (R + h) where Ris the radius of earth and h is the height of satellite above thesurface of earth. The orbital speed for each satellite can be obtained bysubstituting h1 = 360 * 10^3 m in equation (3) and h2 = 720 * 10^3m in equation (3).

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