Fast Moving Projectiles: Satellites

The Earth satellite is simply a projectile that falls around the Earth rather than into it.

A common misconception is that satellites orbiting at high altitudes are free from gravity.

The high altitude only allows the satellites to go above atmosphere, but they are in the field of the Earth gravity.

Question

A newspaper report reads in part, “ The space shuttle orbits Earth at an altitude of nearly 200 miles and is traveling at a speed of 18,000 mph. The shuttle remains in orbit because the gravitational force pulling it toward Earth is balanced by the centrifugal force (the force of inertia) that is pulling it away from Earth”. Explain why this newspaper should hire a new reporter.

Questions

A vine is just strong to support Tarzan when he is hanging straight down. However, when he tries to swing from tree to tree, the same vine breaks at the bottom of the swing. How could it happen?

A common misconception is that satellites orbiting at high altitudes are free from gravity.

The high altitude only allows the satellites to go above atmosphere, but they are in the field of the Earth gravity.

Rotational Motion

Aristotle: There are two sets of natural laws: one for earthly events, and another, altogether different, for motion in the heavens.

The Concept of Gravity

Newton’s Law of Universal Gravitation

Whenever a body has a force exerted on it, that force is exerted by some other body.

Every object on the surface of the Earth feels the force and this force is directed toward the center of the Earth.

What about accepting this idea: force, “acting at a distance” ?

What is the Centripetal Acceleration of the Moon?

aM ~ g/3600

The Universal Law of Gravity

Force ~ mass1 x mass2/distance2

Question

1. The Moon falls around the Earth than straight into it. If tangential velocity were zero, how would the Moon move?

2. According to the equation for gravitational force, what happens to the force between two bodies if the mass of one of bodies is doubled? If both masses are doubled?

Newton’s Law of Universal Gravitation

Every particle in universe attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. This force acts along the line joining the two particles.

F = G m1m2/r2

The Universal Gravitational Constant G

F = Gm1m2/d2

G = 6.67 10-11 Nm2/kg

Gravity and DistanceThe Inverse Square Law

The inverse square law holds for gravity and for all phenomena wherein the effect from a localized source spreads uniformly throughout the surrounding space: the electric field of an electron, light from a match….

Questions

1. If there is an attractive force between all objects, why do we not feel gravitating toward massive buildings in out vicinity?

2. Consider an apple at the top of the tree that is pulled by Earth’s gravity with a force of 1 N. If the tree were twice as tall, would the force of gravity be only ¼ as strong? Defend your answer.

Weight and Weightlessness

To be more general we now refine the definition of weight: weight of something is the force it exerts against a support.

Question

In what sense is drifting in space far away from all celestial bodies like stepping off the table?

Ocean Tides

Question

We know that both the Moon and the Sun produce our ocean tides, and we know that the Moon plays the greater role because it is closer. Does it closeness mean it pulls with more gravitational force than the Sun on the Earth oceans?