Parent Satellite Average orbital radius r(km) Period T y) IT2 (km3 , Earth Moon

Question

Parent Satellite Average orbital radius r(km) Period T y) IT2 (km3 , Earth Moon 3.84x105 1.01×1018 3.34x1024 3.35x1024 3.35x1024 3.35x1024 3.35x1024 3.35x1024 3.35x1024 3.33x1024 0.00485 (1.77 d) | 3. 19× 1021 0.00972 (3.55 d) 3.20x1021 0.0196 (7.16 d) 3.19x1021 0.07481 Sun Mercury5.79x 10 0.2409 1.082x108 1.496x108 2.279x108 7.783x 108 1.427x109 Venus 0.6150 Earth 1.000 1.881 11.86 29.46 164.8 Mars Jupiter Saturn Neptune 4.497x 10 5.90x109 4.22x105 6.71x10 Pluto 248.3 Jupiter lo Europa Ganymede 1.07x106 Callisto 1.88x10 0.0457 (16.19 d)|3.20x10

Explanation / Answer

Here ,

accroding to Kepler's third law

T^2/R^3 = constant

Now , time period of satellite , T = 12 h

T = 12/(24 * 365)

T = 0.0013698 year

Now , for the satellite ,

r^3/T^2 = 1.01 *10^18

r^3/(0.0013698)^2 = 1.01 *10^18

r = 12375 km

the orbital radius of satellite is 12375 km

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