what physical law/s were used during the "burns" of Apollo 13 to adjust its path/trajectory and get it home?
I know the thrusters used Newton's third law. What else?
action and reaction (force on exhaust equal and opposite to force on rocket.)
conservation of momentum
velocity of exhaust* mass of exhaust + velocity of vehicle * mass of vehicle after exhaust fired = original velocity of vehicle * original mass of vehicle
note velocity of exhaust negative as a rule
gravity G M Mearth/r^2 = Force on vehicle toward earth center
Note do not forget centripetal acceleration m v^2/r
During the "burns" of Apollo 13 to adjust its path and trajectory, several physical laws were utilized. Apart from Newton's third law, the following laws were also relevant:
1. Newton's first law or the law of inertia: This law states that an object at rest will stay at rest, and an object in motion will continue moving in a straight line at a constant speed unless acted upon by an external force. This law was crucial in keeping the spacecraft on its original trajectory until intentional maneuvers were made.
2. Conservation of angular momentum: Angular momentum is the property of an object that is rotating or in circular motion. The conservation of angular momentum states that the total angular momentum of a system remains constant unless an external torque is applied. By adjusting the spacecraft's rotation using thrusters, engineers were able to control and change its angular momentum, hence altering its trajectory.
3. Conservation of linear momentum: Linear momentum is the product of an object's mass and velocity. The conservation of linear momentum states that the total linear momentum of a system remains constant unless acted upon by an external force. By firing the spacecraft's engines or thrusters, the resulting change in velocity and mass distribution allowed for adjustments to the spacecraft's trajectory while conserving linear momentum.
4. Kepler's laws of planetary motion: These laws describe the motion of planets and other celestial bodies in orbits around a central mass. While Apollo 13 was not in orbit around a planet, these laws still played a role in understanding the overall dynamics of the spacecraft's trajectory and determining the necessary adjustments to bring it back safely to Earth.
In summary, during the burns of Apollo 13, engineers and astronauts relied on Newton's third law, Newton's first law, conservation of angular momentum, conservation of linear momentum, and Kepler's laws of planetary motion to adjust the spacecraft's path and trajectory, ultimately ensuring its safe return home.