Consider a spacecraft in an elliptical orbit aroundthe earth. At the low point,

Question

Consider a spacecraft in an elliptical orbit aroundthe earth. At the low point, or perigee of its orbit, it is 420 kmabove the earth’s surface; at the high point, or apogee, itis 3,717 km above the earth’s surface. What is the period ofthe spacecraft’s orbit? Give your answer in seconds inscientific notation to three significant digits. (Note: Useappendix F for the necessary data.) This isnt the exactnumbers from the problem but other than that its the same. Consider a spacecraft in an elliptical orbit aroundthe earth. At the low point, or perigee of its orbit, it is 420 kmabove the earth’s surface; at the high point, or apogee, itis 3,717 km above the earth’s surface. What is the period ofthe spacecraft’s orbit? Give your answer in seconds inscientific notation to three significant digits. (Note: Useappendix F for the necessary data.) This isnt the exactnumbers from the problem but other than that its the same.

Explanation / Answer

the force between spacecraft and Earth is F = G * (m * M/r^2) ---------------(1) the centrippetal force on the spacecraft is F = (m * v^2/r) v = (2r/T) or F = m * (4^2r/T) ------------(2) from (1) and (2) G * (m * M/r^2) = m * (4^2r/T) or T = (4^2 * r^3/GM) r = 420 km = 420 * 10^3 m,G = 6.67 * 10^-11 Nm^2/kg^2 and M =5.9742 * 10^24 kg

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