Asked by sand
Two identical planets, each of mass M, have their centers a distance D apart. Halfway between them, at gravitational equilibrium, lies a satellite of mass m. The satellite is then displaced a small distance and released, after which it undergoes SHM.
a) In what direction must the satellite be displaced: along the line joining the two planets, or perpendicular to that line?
b) What is the period of the satellite’s SHM?
a) In what direction must the satellite be displaced: along the line joining the two planets, or perpendicular to that line?
b) What is the period of the satellite’s SHM?
Answers
Answered by
drwls
a) perpendicular. The equilibrium is unstable in the other direction.
b) P = 2 pi sqrt(k/m) for SHM
k is the restoring force per unit perpendicular displacement. m is the satellite's mass
For a small displacement y (<<D), the restoring force is
F = 2*GMm/D^2*[y/(D/2)], so
k = F/y = 4GMm/D^3
P = 4 pi sqrt(GM/D^3)
M is the planet's mass and G is the universal constant of gravity.
b) P = 2 pi sqrt(k/m) for SHM
k is the restoring force per unit perpendicular displacement. m is the satellite's mass
For a small displacement y (<<D), the restoring force is
F = 2*GMm/D^2*[y/(D/2)], so
k = F/y = 4GMm/D^3
P = 4 pi sqrt(GM/D^3)
M is the planet's mass and G is the universal constant of gravity.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.