Gravity

1. Gravity ISCI 2002 Chapter 5

2. What is Gravity? • (1). Gravity is a force of attraction that exists between any two masses, any two bodies, any two particles • (2). Attraction that exists between all objects • Throughout the universe • (3). Gravitationalforce is proportional to the masses of the two objects that are attracting each other. • so that an object with twice the mass will attract with twice the force.

3. Gravity and Distance: Inverse Square Law Any point source which spreads its influence equally in all directions without a limit to its range will obey the inverse square law. This comes from strictly geometrical considerations. The intensity of the influence at any given radius r is the source strength divided by the area of the sphere. Being strictly geometric in its origin, the inverse square law applies to diverse phenomena. Point sources of gravitational force, electric field, light, sound or radiation obey the inverse square law. It is a subject of continuing debate with a source such as a skunk on top of a flag pole; will it's smell drop off according to the inverse square law?

4. Inverse – Square Law and Gravity The greater the distance from the Earth’s center, the less gravitational force. See figure 5.7. The girl at the top of the ladder weighs ¼ less than she weighs on the Earth. As you move twice the distance from the Earth’s center your weight (gravitational effect) decreases by ¼.

5. Newton’s Law of Universal Gravitation The Force of Gravity is dependent on: (1). Distance between objects (2). Mass of those objects G = gravitational constant (similar to pie) The constant of proportionality G is known as the universal gravitational constant. It is termed a "universal constant" because it is thought to be the same at all places and all times, and thus universally characterizes the intrinsic strength of the gravitational force.

6. Newton’s Law of Universal Gravitation

7. Weightlessness • (1). Weight is determined by • Mass x acceleration due to gravity • (2). If you notaccelerating, you will not experience weight. • (3). Your weight is a force that is applied against a floor, scale, etc. • (4). Elevator in freefall – supporting force is decreased (bottom of the elevator)

8. Weightless in Space • Although the Earth's gravity has a lesser effect on an astronaut orbiting the Earth in a spaceship than on a person on the surface of the Earth, this is not the reason why an astronaut experiences weightlessness. The space shuttle, International Space Station and most other manned vehicles don't get that far from the Earth. The Earth's gravitational attraction at those altitudes is only about 11% less than it is at the Earth's surface. If you had a ladder that could reach as high as the shuttle's orbit, your weight would be 11% less at the top. Put another way, a person who weighs 100 pounds on the Earth's surface would weigh about 89 pounds at the top of the ladder. • The reason why the person wouldn't feel weightless is because they are being pushed by the ladder - it is keeping them from falling. If they were to jump off the ladder, then they would feel weightless, at least up until the time they splatted on the ground. This is why astronauts feel weightless. The astronaut, the spaceship and everything inside it are falling towards the Earth. The reason why the astronaut doesn't go splat is because the Earth is curved and the astronaut, the spaceship and everything inside it are moving 'sideways' fast enough that, as they fall towards the Earth, the surface of the Earth curves away from them. They are always falling towards the Earth, but they never get there.

9. The reason why you don't see gravitational effects between objects in a spacecraft is because gravity is a very, very weak force. Of the four basic forces that scientists are sure about, gravity is, by far, the weakest one. Have you ever tripped and fallen down? Well, it took the whole planet to do that to you. Have you ever seen a sock stick to a shirt after it has come out of a dryer? That static cling, created by a slight imbalance of charge between the sock and the shirt, is stronger than the gravitational attraction of the Earth. The gravitational attraction between two small objects in a spacecraft would be overwhelmed by other forces, such as the force of the air being circulated throughout the spacecraft. Although the force of attraction is there, it is so weak that special care would have to be taken to notice it.

10. Projectile Motion • (1). Calculating the distance of an object falling vertically. (d = 1/2gt2) • (2). For a projectile there are two forces: • X direction (horizontal) • Y direction (vertical) force of gravity.

11. Projectile Motion • The force of gravity acts downward and is unable to alter the horizontal motion. There must be a horizontal force to cause a horizontal acceleration. (And we know that there is only a vertical force acting upon projectiles.) The vertical force acts perpendicular to the horizontal motion and will not affect it since perpendicular components of motion are independent of each other. Thus, the projectile travels with a constant horizontal velocity and a downward vertical acceleration.

12. Forces and Projectiles

13. Non-Horizontally Launched Projectiles • Now suppose that our cannon is aimed upward and shot at an angle to the horizontal from the same cliff. In the absence of gravity (i.e., supposing that the gravity switch could be turned off) the projectile would again travel along a straight-line, inertial path. An object in motion would continue in motion at a constant speed in the same direction if there is no unbalanced force. This is the case for an object moving through space in the absence of gravity. However, if the gravity switch could be turned on such that the cannonball is truly a projectile, then the object would once more free-fall below this straight-line, inertial path. In fact, the projectile would travel with a parabolictrajectory. The downward force of gravity would act upon the cannonball to cause the same vertical motion as before - a downward acceleration. The cannonball falls the same amount of distance in every second as it did when it was merely dropped from rest (refer to diagram below). Once more, the presence of gravity does not affect the horizontal motion of the projectile. The projectile still moves the same horizontal distance in each second of travel as it did when the gravity switch was turned off. The force of gravity is a vertical force and does not affect horizontal motion; perpendicular components of motion are independent of each other.

15. Projectiles and Range • (1). Range refers to the distance travelled by a projectile (horizontally) • (2). The same range can be obtained from two different projection angles • Add up to 90 degrees • Object thrown into the air at 60 degrees will have the same range as an object thrown in the air at 30 degrees (same speed)

16. In the absence of air drag or resistance, speed lost while going up equals speed gained while going down. Air drag is a reality. It will affect the range of projectiles. They fall short of a predicted parabolic path with no air resistance or drag.

17. How can you calculate the range of a launched projectile? • (1). If you know the initial velocity, you can use the formula to determine the range or (d) • V = d/t • Rearranged would be: • d = (v)(t)

18. How do Satellites Stay in Orbit? • Satellites stay in orbit due to the balance of two factors: velocity, or the speed at which it would travel in a straight line • the gravitationalpull between the Earth and the satellite. • Satellites never fall into the Earth this because Earth is round and curves. The Earthcurvesapproximately5metersdownwardforevery8000metersalongitshorizon. In order for a satellite to successfully orbit the Earth, it must travel a horizontal distance of 8000 meters before falling a vertical distance of 5 meters. Since a horizontally-launchedprojectilefalls a verticaldistance of 5meters in its firstsecondofmotion, a orbiting projectile must be launchedwith a horizontalspeed of 8000m/s. When launched at this speed, the projectile will fall towards the Earth with a trajectory which matches the curvature of the Earth. As such, the projectile will fall around the Earth, always accelerating towards it under the influence of gravity, yet never colliding into it since the Earth is constantly curving at the same rate. Such a projectile is an orbiting satellite. • Man-made satellites circle the Earth in many ways including polar and geostationary orbits.

19. How do Satellites Stay in Orbit? • Polar orbit: The satellite in a polar orbit travels over the North and South Poles. A polar orbit may be from several hundred miles to several thousand miles above Earth. This type of satellite circles the Earth approximately 14 times each day. Because the Earth is turning more slowly than the satellite, the satellite gets a slightly different view on every revolution. Over the course of a few days, a satellite in a polar orbit will cover almost all the planet. • Geostationary orbit: The satellite in a high-altitude, geostationary orbit circles the earth once every 24 hours, the same amount of time it takes for the Earth to spin on its axis. The satellite turns eastward (like our Earth) along the Equator. It stays above the same point on Earth all the time. To maintain the same rotational period as the Earth, a satellite in geostationary orbit must be 22,237 miles above the Earth. At this distance, the satellite can view a huge portion of the Earth's surface. Because the high-altitude satellite appears to remain fixed in one position (it's really orbiting at the same rate as the Earth turns), it requires no tracking to receive its downlink signal. That is why when we turn our home satellite dish on to receive the TV signal from a particular geostationary satellite, we don't have to keep jumping up to adjust its position. • One of the advantages of geostationary satellites is that imagery is obtained and displayed every 30 minutes, compared to imagery transmitted by polar orbiting platforms taken every 6-12 hours.

20. Satellites and Orbits