The Big Idea
Over 2500 years ago Aristotle proposed two laws of physics governing motion. One for ‘Earthly bodies’ (objects on Earth) that states objects naturally go in straight lines and one for ‘Heavenly bodies’ (objects in space) that states objects naturally go in circles. This idea held steady for 2,000 years, until Isaac Newton in a triumph of brilliance declared that there is one law of physics that governs motion and he unified “earthly” bodies and “heavenly” bodies with the The Universal Law of Gravitation. Newton used the universal law of gravity to prove that the moon is accelerating towards Earth just as a body on Earth is falling towards Earth. The acceleration of both the moon and the object on Earth is calculated using the same formula. This theory is so well regarded that it has been used to hypothesize the existence of black holes and dark matter, later verified by observation. The search to unify the laws of physics into one theory continues today and is often referred to as the yet undiscovered Grand Unified Theory (GUT).
Key Equation: The Universal Law of Gravity
FG = Gm1m2 / r 2
; the force of gravity between an object with mass m1 and
another object of mass m2 and a distance between them of r.
G = 6.67 x 10-11 Nm2/kg2 ; the universal constant of gravity
g = Gm / r 2
People’s Physics Book
; gravitational field strength or gravitational acceleration of a planet with mass m and radius r. Note that this is not really a separate equation but comes from Newton’s second law and the law of universal gravitation.
Ch 12- 1
When using the Universal Law of Gravity formula and the constant G above, make sure to use units of meters and kilograms.
Newton invented calculus in order to prove that for a spherical object (like Earth) one can assume all of its mass is at the center of the sphere (thus in his formula, one can use the radius of Earth for the distance between a falling rock and Earth). An orbital period, T, is the time it takes to make one complete rotation. If a particle travels a distance 2πr in an amount of time T, then its speed is distance over time or 2πr/T.
Objects in orbit around each other, orbit about the center of mass for the system. For the Earth and moon the center of mass is somewhere inside of Earth. So while the moon orbits Earth, the Earth also orbits the moon (manifested as a slight wobble).
To find the speed of a planet or satellite in an orbit, realize that the force of gravity is the centripetal force. So set the force of gravity equal to mv2/r, where v is the speed of the planet, m is the mass of the planet or satellite and r is the distance of the planet to the sun or the satellite to the Earth.
The Geo-synchronous orbit is that orbit for which the satellite takes the same amount of time to orbit the planet as the planet takes to make one revolution. For satellites to be over the same place of the planet at all times, it must be in a Geo-synchronous orbit. Some data needed for the problems:
The radius of Earth is 6.4 x 106 m
The mass of Earth is about 6.0 x 1024 kg
The mass of Sun is about 2.0 x 1030 kg
The Earth-Sun distance is about 1.5 x 1011 m
The Earth-Moon distance is about 3.8 x 108 m
People’s Physics Book
Ch 12- 2
Gravity Problem Set
1. Which is greater – the gravitational force that the Earth exerts on the moon, or the force the moon exerts on the Earth? Why doesn’t the moon fall into the earth?
2. Which is greater – the gravitational force that the Sun exerts on the moon, or the force the Earth exerts on the moon? Does the moon orbit the Earth or the Sun? Explain.
3. Suppose you’re standing in an elevator on a bathroom scale. Draw a FBD for you and label the two forces acting on you. Describe how the scale reading compares to your weight when a.
The elevator is at rest
The elevator is moving up at a constant speed
The elevator is...
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