- #1
AntiElephant
- 25
- 0
I'm trying to understand mathematically, if possible, why it is that the Earth bulges at the equator as a result of its rotation and how exactly gravity manages to keep it all together. Would the better approach be to keep myself in a rotating frame of reference? I lack some knowledge of Netwon's Laws in non-inertial frames of reference but maybe just enough to understand what is going on here.
I want to focus on a point (a "piece" of Earth's matter) on the Earth's surface, along the equator, to understand why it bulges outwards. If the Earth was initially stationary and spherical, then the only force acting on this piece would be gravity [itex] F_{grav} [/itex]. As the Earth gradually begins to rotate a centrifugal force [itex] F_{centrif} [/itex] appears pointing in a direction outwards, opposite to the axis of rotation, a fictitious force as a result of being in a non-inertial frame of reference.
The total force on this piece would be [itex] F_{grav} - F_{centrif} [/itex]. If [itex] F_{centrif} <= F_{grav} [/itex] then surely the piece would still have a resulting force pointing towards the centre of the Earth and the Earth would remain spherical? If/once [itex] F_{centrif} > F_{grav} [/itex] then the piece would "fly" off from the Earth (in a stationary frame, this would be a result of inertia). Have I looked at this too simplistically? How, then is it that the Earth bulges and instead isn't at either of the extremes - either spherical or stuff "flying" off as a result of inertia?
I want to focus on a point (a "piece" of Earth's matter) on the Earth's surface, along the equator, to understand why it bulges outwards. If the Earth was initially stationary and spherical, then the only force acting on this piece would be gravity [itex] F_{grav} [/itex]. As the Earth gradually begins to rotate a centrifugal force [itex] F_{centrif} [/itex] appears pointing in a direction outwards, opposite to the axis of rotation, a fictitious force as a result of being in a non-inertial frame of reference.
The total force on this piece would be [itex] F_{grav} - F_{centrif} [/itex]. If [itex] F_{centrif} <= F_{grav} [/itex] then surely the piece would still have a resulting force pointing towards the centre of the Earth and the Earth would remain spherical? If/once [itex] F_{centrif} > F_{grav} [/itex] then the piece would "fly" off from the Earth (in a stationary frame, this would be a result of inertia). Have I looked at this too simplistically? How, then is it that the Earth bulges and instead isn't at either of the extremes - either spherical or stuff "flying" off as a result of inertia?