Satellites Dynamics lesson 4

Law of universal gravitation Any mass is able to attract another mass The attraction force is directly proportional to the product of the two masses The attraction force is indirectly proportional to the distance between their centres squared A proportionality constant appears: The constant of universal gravitation G Any mass is able to attract another mass The attraction force is directly proportional to the product of the two masses The attraction force is indirectly proportional to the distance between their centres squared A proportionality constant appears: The constant of universal gravitation G M · m Fg = · G r2

Fg and Fg are a pair of action-reaction forces!! A 3rd law evidence M Fg Fg m M · m Fg = G · M is attracting m with a force of: r2 m · M m is attracting M with a force of: Fg = G · r2 Fg and Fg are a pair of action-reaction forces!! same magnitude same direction opposite sense

Why does the Moon not fall? Earth & Moon I Houston, we have a problem!! - The Earth is attracting the Moon Fg - There is no other force on the Moon - Fg is an unbalanced force - It should induce a change in the Moon’s motion Why does the Moon not fall? Fg is actually changing Moon’s motion, but not its speed, it‘s changing the direction of its velocity. Fg is actually changing Moon’s motion, but not its speed, it‘s changing the direction of its velocity.

Earth & Moon II v Fg direction v Fg Fg v Fg v The force of attraction of the Earth, changes one property of the Moon’s velocity: Fg direction v Why? Fg Fg v A force perpendicular to a velocity, produces a change in the direction, not in the magnitude of the velocity A force perpendicular to a velocity, produces a change in the direction, not in the magnitude of the velocity A force perpendicular to a velocity, produces a change in the direction, not in the magnitude of the velocity A force perpendicular to a velocity, produces a change in the direction, not in the magnitude of the velocity Fg v

Tides Low tide High tide High tide Low tide A high tide here? The Moon attracts large masses of water Where does the attraction come from? · · · · High tide High tide 18:00 h 24:00 h 12:00 h 6:00 h Low tide rotational sense

Artificial satellites - They are specially designed to follow an orbit. - They are specially designed to follow an orbit. Trajectory described around the Earth video - Their period and frequency are accurately known. - Their period and frequency are accurately known. Period (T): time needed to complete a whole lap. I.S. units: s Frequency (n): number of laps per second. I.S. units: s-1 - Their applications are huge. - Their applications are huge. telecommunications meteorology military research Hispasat Astra Meteosat NOAA NAVSTAR GPS Hubble MIR

Satellite’s orbits Geostationary orbit Polar orbit video video list of satellites video video