Question

Use Kepler's third law to determine how many days it takes a spacecraft to travel i an elliptical orbit from a point 7 397 km from the Earth's center to the Moon, 385 000 km from the Earth's center 10 Your response differs from the correct answer by more than 10%. Double check your calculations, d

Answer 1

Hi,

Hope you are doing well.

According to kepler's law, Time period is given by

2 2

The average of the nearest and farthest distances from Earth's center on the elliptical orbit to moon is,

7397 km385000 km Tr

r - 196198.5 km

We have,

9.8 m/S

R-6378 × 10° m

$\therefore$ Time taken by the aircraft is given by,

47T2 9.8 m/s2 × (6378 × 103 m)2 × (196 198.5 × 1000 m

T"-7.479140287 × 10n S

T-V7.479 140287 × 1011 s2

T864820.2291 s

$\mathbf{\therefore T=10\;days}$

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