Universal Gravitation Using the Law of Universal Gravitation

Objectives Relate weightlessness to objects in free fall. Describe gravitational fields. Distinguish between inertial mass and gravitational mass. Contrast Newton's and Einstein's views about gravitation.

Motion of Planets and Satellites An object is said to be in orbit if it is traveling fast enough that when it falls 4.9 m per second, that it does so at the point where the Earth has curved 4.9 m away from the horizontal.

Motion of Planets and Satellites So, since the Earth curves away from a line tangent to its surface at a rate of 4.9 m for every 8 km, the altitude of the object would not have changed. The object at Earth's surface will fall toward Earth at the same rate that Earth's surface curves away. To ignore air, the object must be above 150 km above the Earth's surface.

Motion of Planets and Satellites To solve for the speed of an object in circular orbit, set Newton's Law of Universal Gravitation equal to Newton's 2nd Law (F=ma or F=mv2/r.) GMEM / r2 = mv2 / r so……… v = √GME / r

Motion of Planets and Satellites To find time for a satellite to circle the Earth, use: T = 2 π √ r3/ GME V & T are independent of the mass of the object. More force is required to put a more massive object into orbit. The mass of the object/satellite is limited by the capacity of the rocket used to launch it.

Motion of Planets and Satellites These two equations can be used for any body in orbit about another. The mass of the central body would replace ME & r would be the distance from the sun to the orbiting body.

Weight and Weightlessness As you move farther from the Earth's center, or as d becomes larger, the acceleration due to gravity is reduced.

Weight and Weightlessness Astronauts have weight because the gravitational force is exerted on them, but no apparent weight. You sense weight when something exerts a force back on you, (a chair, floor, etc.) But, if you are both accelerating toward Earth together, then there are no contact forces exerted on you. Ex: dropping the cup full of water out a window! Your apparent weight is zero and you experience weightlessness.

The Gravitational Field Michael Faraday developed the concept of the magnetism field to explain how magnets attract objects. This field concept was applied to gravity, that anything with a mass is surrounded by a gravitational field. It's the field that interacts with objects, resulting in a force of attraction, which is how gravity acts over a distance.

The Gravitational Field The strength of the field varies inversely with the square of the distance from the center of the earth.

Two Kinds of Mass Inertial mass of an object is measured by applying a force to the object and measuring its acceleration. Gravitational mass is the mass used in the Universal Law of Gravitation, which determines the size of the gravitational attraction between two objects.

Two Kinds of Mass Mg = r2 Fg / GM If you measure the attractive force exerted on an object by another object of mass m at a distance r, then you can define the gravitational mass by: Mg = r2 Fg / GM

Two Kinds of Mass Ex: A truck has a block of ice in its bed. The truck accelerates and the ice slides backward. This is as a result of inertial mass. If the truck climbs a hill at a constant speed, the ice slides backward as a result of gravitational mass. It is attracted downward toward Earth.

Einstein's Theory of Gravity To explain the origin of gravity, Einstein proposed that g is not a force, but an effect of space. Mass changes the space around it, causing space to be curved, and other bodies are accelerated because of the way they follow the curve.

Einstein's Theory of Gravity Light is affected the same way. If an object is massive and dense enough, light leaving it will be bent back to it. This is called a black hole.