Universal Gravitation
the result of putting them together
(mobj)g = G × [(me)(mobj)]/r²
mass
-the amount of matter present in an object -a scalar quantity and -in SI units measured in kg
conversion factor for universal gravitation
6.673 × 10⁻¹¹ newton meters²/kilograms²
Newton's first law of motion, also referred to as the law of inertia
A heavier object has more inertia than a lighter one That's because more force is needed to change its state, whether from motion to rest or from rest to motion. An object's mass determines how heavy or light it is.
The greater the mass of the object, the greater the pull of gravity.
Gravity is directly proportional to the mass of the object.
Newton proposed that the force of gravity (Fg)
follows an inverse square law with respect to the distance between two bodies
As the gravity of the moon is about one-sixth of that of Earth, we can assume that the acceleration due to gravity on the moon is
g = 9.8 m/s² ÷ 6 = 1.63 m/s²
Because the distance between Earth's center and any object on its surface is more or less equal to Earth's radius (r), we can also write this equation as
g = G × (me)/(r²e) where rE is the radius of Earth, which is taken as 6.38 × 10⁶ meters. Take care not to mix up G and g. G is the universal gravitational constant and g is the acceleration due to gravity
On Earth, Fg is inversely proportional to
the square of the distance to Earth's center from the object If that distance is doubled, the value of Fg decreases by a factor of 4; if the distance is tripled, it decreases by a factor of 9.
force formula
∑F = ma
Objects located on the surface experience a greater pull than objects farther away.
-As we go farther from the center of Earth, its gravitational pull weakens. -We can conclude that the value of g is inversely proportional to the distance from Earth's center.
The acceleration due to gravity decreases with distance. We know that the value of g at sea level is 9.8 meters/second². Let's use this formula to find Earth's mass.
-g = 9.8 m/s² -G = 6.673 × 10⁻¹¹ Nm²/kg² -distance of object = radius of Earth = 6.38 × 10⁶ m g = G × (me)/r² 9.8 = 6.673 × 10⁻¹¹ × [(me)/6.38 × 10⁶)²] me = 5.98 × 10²⁴ kg
The force of gravity is directly proportional to
both masses, that is, Earth's mass as well as the object's
As the mass of the object (mobj) appears on both sides of the equation, it can be canceled out The following equation represents the fact that acceleration due to gravity is a product of the universal gravitational constant Earth's mass divided by the square of the object's distance from the center of Earth.
g = G × (me)/r²
gravitational force on the moon
one-sixth what it is on Earth
Because the moon is 60 times farther from Earth than an object on Earth's surface
the Earth's gravitational pull on it is only 1/3600 of the pull the moon would experience if it were sitting in a field on Earth's surface
On Earth, the acceleration due to gravity (g) is 9.80 meters/second². Using this value, we can calculate the weight of an object. If an object has a mass of 1.0 kilogram, its weight, which is the force of gravity, will be
Fg = mg = (1.0 kg)(9.8 m/s²) = 9.8 N
inverse square law
Fg = α 1/r² -Fg is the force of gravity between Earth and the object -r represents the distance between the center of Earth and that of the object
The expression of gravitational force can be rewritten like this, where mE is the mass of Earth, mob j is the mass of the object and r is the distance between them.
Fg α [(me)(mobj)]/r²
Here's how the law is expressed, where m1 and m2 are masses of the two objects and r is the distance between them.
Fg α m1m2/r²
law of gravitation
Objects attract other objects with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts regardless of the medium that separates the two objects.
weight formula
Fg = mg Fg = weight g = acceleration due to gravity
gravitational force
-insignificant for most day-to-day objects you encounter -very significant for celestial objects with huge masses, like Earth, its sun, its moon, and the galaxy
weight
-the force acting on an object that has mass -not a property of the object -it is the pull exerted by the surface on which the object exists -vector quantity -varies according to the gravitational force
An astronaut is on a spacewalk 300 kilometers above Earth's surface. If the astronaut's mass is 70 kilograms, what is the force of interaction between Earth and the astronaut? (Earth's radius is 6.38 × 106 meters.)
Earth's mass = 5.94 × 10²⁴ kg and G = 6.673 × 1⁻¹¹ Nm²/ kg² total radius r = 300 + (6.38 × 10⁶) m = 6.38 × 10⁶ m Fg = G × m1m2/r² = (6.673 × 10⁻¹¹) × [(5.94 × 10²⁴)(70)]/(6.38 × 10⁶) = 6.8 × 10² N Note that 300 kilometers is a small value compared to Earth's radius. When calculated to three significant figures, the total radius is still 6.38 × 10⁶ meters. So, the astronaut's weight in space is almost the same as it is on Earth. She's not really weightless; she's just orbiting!
Newton's third law
Every action has an equal and opposite reaction. If Earth exerts a pull on an object, the object exerts an equal and opposite pull on Earth.
Fg = mobjg, where g is the acceleration due to gravity and its value is 9.8 meters/second² at sea level.
Fg = G × [(me)(mobj)]/r²
This expression can also be represented in the form of an equation using G as the universal gravitational constant.
Fg = G × [(me)(mobj)]/r²
Again, this expression can be represented as an equation using G as the universal gravitational constant.
Fg = G × m1m2/r²
What is the acceleration of the moon toward Earth, due to their mutual attraction? The mass of Earth is 5.98 × 10²⁴ kilograms, the distance between them is 3.8 × 10⁸ meters, and G = 6.673 × 10⁻¹¹ newton meters²/kilogram².
Fg = G × m1m2/r² g = G × (m1/r²) = 6.673 × 10⁻¹¹ × [5.98 × 10²⁴/(3.8 × 10⁸)²] = 2.8 × 10⁻³ m/s²
An asteroid floating in space attracts a skyscraper on Earth with a gravitational force of 12 newtons from a given distance. If the distance between the two objects is reduced to half, what is the changed force of attraction between them?
If the distance decreases by a factor of 2, then the force will increase by a factor of 4 (that is, 2²). So the new force is 4 times the original force.
The value of acceleration due to gravity on the planet Saturn (gSaturn) is about 11.2 meters/second². How much will an object weighing 490 newtons on Earth weigh on Saturn? Remember, gravitational acceleration on Earth (gEarth) is 9.8 meters/second².
The mass of object on Earth is 490 ÷ 9.8, which is 50 kilograms. On Saturn, it will be 50 × 11.2, or 560, newtons.