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## Gravitational Field & Gravitational Force

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**“Action at a distance”**• The gravitational force is an attractive force between two masses. • Gravity is a field force. The masses don’t need to be in contact with each other to cause attraction.**Backpack, apples, ect.**• Jumping with a large backpack on is a lot harder than jumping with a small backpack on. • Why? • Gravity must have something to do with the mass of the object (ie. Backpack)**Backpack, apples, ect.**Earth, moon,… • Dropping an object on Earth is different than dropping that same object on the moon. • The object will fall to the ground in both scenarios, but the rates are different. Why? • The moon is less massive than the Earth, so falling (caused by gravity) must be directly related to the mass of one object (the Earth or the moon) causing a second object (an apple, a ball) to fall.**What about distance between the two masses?**• It turns out, the gravitational force decreases with distance, but not linearly. • If you double the distance between two objects the force of gravity between them decreases by a factor of 4. • If you quadruple the distance between two objects, the force of gravity decreases by a factor of 16! • This is the inverse square law:**So what is gravity?**• Gravity is the force of attraction between two masses. Where: G = Universal Gravitational Constant = 6.67x10-11 N.m2/kg2 M1 = Mass of one object (in kg) m2 = Mass of other object (in kg) r = distance between objects (measured center to center in meters)**Example: Determine the force of gravitational attraction**between the earth (m = 5.98x1024 kg) and a 70. kg physics student flying in an airplane 40000 ft (12,000 m) above the surface of the Earth (radius of Earth = 6.3781x106m). M1 = 5.98x1024 kg m2 = 70. kg r = 12,000m + 6.3781x106m = 6.3901x106m Fgravity = 683.77 ~ 680 N**Field Force**• Gravity is a field force, meaning the two masses will attract each other even when they aren’t in contact with each other. • This force of attraction will cause the masses to accelerate towards each other. • Masses create gravitational fields around themselves. Any other mass in that gravitational field will experience a force of attraction. • It is this gravitational field that causes gravity to be able to act at a distance on other masses.**Any object near the surface of the Earth will accelerate**towards the Earth at 9.8 m/s2 Any object that is 3.8x108 m from the surface of the Earth will accelerate towards the Earth at 0.00272 m/s2 Earth’s Gravitational Field**Calculating Gravitational Fields:**Where: g = gravitational field G = Universal Gravitational Constant = 6.67x10-11 N.m2/kg2 M1 = Mass of the object CREATING the field (in kg) r = distance from the center of the object creating the field to the point you are looking at. Units:**Calculate Earth’s Gravitational Field. MEarth = 5.98x1024**kg & radius of Earth = 6.3781x106m g = 9.80 m/s2**A satellite is halfway between the Earth and the moon. What**is the net gravitational field at that location. MEarth = 5.98x1024 kg Mmoon = 7.36x1022 kg 1.9x108m 1.9x108m = 0.0109 N/kg **What does a gravitational field of 0.0109 N/kg mean?**This mass CREATES the Gravitational field This mass EXPERIENCES the Gravitational field The Gravitational field • Any object placed at that location will accelerate towards the Earth at 0.0109 m/s2 regardless of it’s mass. • It will also let us calculate the force of gravity on any object placed at that location using F = mg Gravitational field “g”**Back to the satellite: If a 150 kg satellite is placed in**orbit halfway between the Earth and the moon, what will the force of gravity be on the satellite? g = 0.0109 N/kg Fgravity = mg Fgravity = (150kg)(0.0109N/kg) Fgravity = 1.6 N**The satellite is in orbit around the Earth (instead of**floating off in a straight line towards Jupiter). What is the magnitude/strength of the centripetal force? This is what we will be talking about tomorrow… Fgravity = 1.6 N**What we already know: The water under the**moon is closer to the moon than the center of the Earth is. So the moon’s gravity pulls harder on the water and the water “heaps up” under the moon.**But what about the bulge on**the other side?**The New Part: The center of the Earth**is closer to the moon than the water on the OPPOSITE side of the Earth. The moon pulls the Earth away from the water, and it appears to “heap up” too.**Spring Tides**Neap Tides