Gravitation: Forces and Escape Velocity

Gravity is… the force that attracts a body toward the center of the earth, or toward any other object that has mass.

Acceleration due to gravity does not depend on an object’s mass Galileo hypothesized that heavier objects would fall to the ground faster than lighter objects, but he was wrong! When he dropped a light ball and a heavy ball from the leaning Tower of Pisa, they hit the ground at the same instant. Astronauts verified this on the moon by dropping a hammer and a feather. Question: Why doesn’t this happen on Earth?

Newton’s Law of Universal Gravitation Every mass exerts a force of attraction on every other mass. Larger masses have a greater pull Objects close together pull more on each other than objects farther apart The Sun and the planets exert a gravitational force on each other You exert a gravitational force on other people in the room!

Gravitational Force When 2 masses are separated by a distance (r), they exert an equal and opposite force on each other, regardless of the difference in mass! r m1 Fg -Fg m2 The proportionality constant, G is called the universal gravitational constant. Its value in the SI system of units is, G = 6.67  10-11Nm2/kg2.

The Law of Universal Gravitation states that every object in the universe is attracted to every other object in the Universe! Greater the masses = greater the force of attraction Greater the distance = smaller the force of attraction

Law of Universal Gravitation

Law of Universal Gravitation Jimmy is attracted to Betty. Jimmy’s mass is 90.0 kg and Betty’s mass is 57.0 kg. If Jim is standing 10.0 meters away from Betty, what is the gravitational force between them? G: m1=90.0; m2=57.0; r=10.0; G=6.67x10-11 Nm2/kg2 U: FG E: FG = Gm1m2 / r2 S: FG = (6.67x10-11 Nm2/kg2)(90.0 kg)(57.0 kg) / (10.0 m)2 S: FG = (3.42x10-7 Nm2) / (100. m2) FG = 3.42x10-9 N

Law of Universal Gravitation The Moon is attracted to the Earth. The mass of the Earth is 6.0x1024 kg and the mass of the Moon is 7.4x1022 kg. If the Earth and Moon are 345,000 km apart, what is the gravitational force between them? G: G = 6.67x10-11 Nm2/kg2; m1= 6.0x1024 kg; m2= 7.4x1022 kg; r=345,000km = 34,500,000m = 3.45×108m U: FG E: FG = Gm1m2 / r2 S: FG = (6.67x10-11 Nm2/kg2) × S: FG = 2.49x1020 N (6.0x1024 kg)(7.4x1022 kg) (3.45x108 m)2

What happens to the gravitational force when mass changes?

What happens to Gravity when Distance Changes?

Surface Gravity Mass is the amount of matter in an object. (triple beam balance) Weight is the force of pull on a mass due to gravity (scale) Objects on the Moon weigh less than objects on Earth but have the same mass.

Surface Gravity cont. This is because surface gravity is less The Moon has less mass than the Earth, so the gravitational force is less Gravitational force is equal to mass multiplied by gravity Fg = mg On Earth, g = 9.8 m/s2 g on the Moon is only 1/6 of Earth’s gravity, so a 120 pound object on Earth would only weigh 20 pounds on the moon!

Orbits and Centripetal Force If we tie a mass to a string and swing the mass around in a circle, some force is required to keep the mass from flying off in a straight line This is a centripetal force The tension in the string provides this force. In space, centripetal force and gravitational force are the same.

Orbits – Gravity and Inertia Newton’s First Law (law of inertia) – An object will maintain its velocity until acted upon by a net force. A moving object in space will keep its horizontal velocity forever. BUT… There is a gravitational pull between objects with mass (vertical free-fall).

SO… An object that is in orbit is a projectile that is in constant free-fall AROUND the object it’s orbiting.

Orbits We can find the mass of a large object by measuring the velocity of a smaller object orbiting it, and the distance between the two. We can also use this information to calculate the smaller object’s orbital velocity.

Calculating Escape Velocity Escape velocity is the velocity necessary for an object to escape the gravity of a large object.

What Escape Velocity Means to NASA If an rocket is launched with a velocity less than the escape velocity, it will eventually return to Earth If the rocket achieves a speed higher than the escape velocity, it will leave the Earth, and will not return!

Escape Velocity is for more than just Rockets! Escape velocity helps us determine which planets have an atmosphere and which don’t. Low-mass planets like Mercury have a low escape velocity. Gas particles near the planet can escape easily, so they don’t have much of an atmosphere. Massive planets like Jupiter, have very high escape velocities, so gas particles have a difficult time escaping. Massive planets tend to have thick atmospheres.