Angular Acceleration of the Earth
Garvitational Constant:
Radius of the Earth:
Angle that the tidal bulge leads the moon by (given):
Height of the tidal bulge (given):
Mass of the Earth:
Density of water:
Tidal acceleration
Density of the bulges:
Volume in the bulges:
Mass in the bulges:
Torque of the bulges:
Rotational inertia of the earth:
Angular acceleration of the Earth:
Radial Velocity of the Moon
Mass of the Moon:
Mean distance between the Earth and Moon now:
Rotational period of the Earth:
Radius of the moon:
Orbital period of the moon:
Orbital velocity of the moon:
Angular velocity of the moon:
Angular velocity of the Earth:
Rotational velocity of the Earth:
Rotational inertia of the moon:
Ratio of the moon's roatational inertia to the Earth's rotational inertia:
Period of the moon's orbit:
Derivative of the total angular
momentum w/ respect to time:
Solving for the radial velocity:
Extrapolating Forward (and backward) in Time
Orbital kinetic energy of the moon:
Gravitational potential energy of the moon:
Rotational kinetic energy of the moon:
Rotational kinetic energy of the Earth:
Total energy of the system today:
Total angular momentum today:
Difference in total angular energy from today as a function of mean distance
(I switch from w to W in this section to avoid confusion since I am now talking about angular velocities that are changing with distance)
Solving for Wearth:
Solving for Ediff
Figure 2
Visual guess of the equilibrium distance:
Solving for the angular velocity of the moon at equilibrium:
guess value for solve block:
Solve Block:
Length of a day at equilibrium:
Mean distance of moon at equilibrium:
Roche Limit:
The Roche limit for the moon in Earth radii:
The Roche limit for the moon in current Earth-moon distances:
Rate of energy loss:
Rate of energy loss today (given):
Combined angular velocity of the system:
Experimentally determining a function for the rate of energy loss:
Guess function for rate of energy loss:
Figure 3
o - Today
Time between two distances:
Figure 4