- Circular motion of satellite about the planet means the satellite is moving at same speed but constantly changing direction. This means that it has centripetal acceleration.
- Newton's Law of Acceleration gives a ∝ F, meaning, acceleration a happens when there is a resultant force F and these 2 quantities must be in the same direction.
- In the case of the satellite, the resultant force F [called centripetal force in this case] is provided by the gravitational force of the planet on the satellite.
Answer:
- As mentioned in the explanation/answer above,
centripetal force = gravitational force
mω2nR = GMm/(nR)2
(2π/T)2n3R3=GM
(4π2/T2)n3R3=GM
- Since density ρ of planet equals mass M of planet divided by volume V of the planet and that V = (4/3)πR3, then we can divide both sides by that volume.
(4π2/T2)n3R3/ (4/3)πR3 = GM / (4/3)πR3
where M / (4/3)πR3 = ρ
(4π2/T2)n3R3/ (4/3)πR3 = GM / (4/3)πR3
3πn3/T2 = Gρ
- Rearranging the above equation so that only density ρ is at one side of equal sign,
3πn3/GT2 = ρ
Answer:
- The data given are the values of R, the nR, and the T.
- The value of T must first be converted to seconds.
- The n can be determined by dividing the distance between 2 centres nR by the radius of Earth R.
- Substitute the given data into the expression in (b).
- ρ = 3πn3/GT2
- ρ = 5.54 x 103 kg m-3
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