Asked by k.
State in your own words what is meant by Newton's law of universal gravitation.
How does friction with the atmosphere affect the speed of an artificial satellite ?
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Newton’s law of universal gravitation (in simple terms)
- Any two masses pull on each other with a force that is directly proportional to the product of their masses and gets weaker the farther apart they are.
- The force acts along the line joining their centers and follows an inverse-square rule: F = G m1 m2 / r^2, where G is the gravitational constant and r is the distance between the masses.
- This universal attraction is what keeps planets, moons and artificial satellites in orbit.
How atmospheric friction (drag) affects a satellite
- The thin atmosphere at low Earth altitudes exerts a drag force opposite the satellite’s direction of motion. That drag is roughly Fd ≈ ½ Cd ρ A v^2 (depends on atmospheric density ρ, satellite cross‑section A, drag coefficient Cd and speed v).
- Drag does negative work on the satellite, removing kinetic + potential (orbital) energy. As a result the orbit decays: the satellite loses altitude, its orbital period shortens, and eventually it will re‑enter and burn up if not corrected.
- Instantaneously drag reduces the satellite’s tangential speed. However, because the orbital speed required for a lower circular orbit is larger (v = √(GM/r)), a satellite spiraling downward can end up moving faster at a lower altitude even though its total mechanical energy has decreased.
- Net practical effect: gradual slow-down from drag leads to altitude loss, increased atmospheric heating, and eventual re‑entry unless propulsion is used to boost the orbit.
- Any two masses pull on each other with a force that is directly proportional to the product of their masses and gets weaker the farther apart they are.
- The force acts along the line joining their centers and follows an inverse-square rule: F = G m1 m2 / r^2, where G is the gravitational constant and r is the distance between the masses.
- This universal attraction is what keeps planets, moons and artificial satellites in orbit.
How atmospheric friction (drag) affects a satellite
- The thin atmosphere at low Earth altitudes exerts a drag force opposite the satellite’s direction of motion. That drag is roughly Fd ≈ ½ Cd ρ A v^2 (depends on atmospheric density ρ, satellite cross‑section A, drag coefficient Cd and speed v).
- Drag does negative work on the satellite, removing kinetic + potential (orbital) energy. As a result the orbit decays: the satellite loses altitude, its orbital period shortens, and eventually it will re‑enter and burn up if not corrected.
- Instantaneously drag reduces the satellite’s tangential speed. However, because the orbital speed required for a lower circular orbit is larger (v = √(GM/r)), a satellite spiraling downward can end up moving faster at a lower altitude even though its total mechanical energy has decreased.
- Net practical effect: gradual slow-down from drag leads to altitude loss, increased atmospheric heating, and eventual re‑entry unless propulsion is used to boost the orbit.
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