Universal Gravitation and Satellite Motion

What is the escape speed for objects leaving Earth's gravitational pull?

11.2 seconds

If we drop a ball from rest, how far will it fall vertically in the first second? If we instead move our hand horizontally and drop it (throw it), how far will it fall vertically in the first second?

5m

what is the orbital speed for a satellite?

8km/s

How much time does it take for a satellite to close orbit the Earth?

90 minutes

What do the distances 8000 m and 5m have to do with a line tangent to Earth's surface?

A geometric fact about the curvature of Earth is that its surface drops a vertical distance of nearly 5 meters for every 8000 meters tangent to its surface.

How far above the earth should a sattelite be

A satellite must stay about 150 km or more above Earth's surface to keep from burning due to friction of the atmosphere.

Ellipse

An ellipse is the closed path taken by a point that moves in such a way that the sum of its distances from two foci is constant.

Where in an elliptical orbit is the speed of a satellite minimum?

Apogee

How does the moon and earth fall without crashing into the sun or each other?

Because of their Tangential Velocity- same goes for other planets

Kepler's Second Law

Each planet moves so that an imaginary line drawn from the sun to any planet sweeps out equal areas of space in equal time intervals.

Newton's Law of universal gravitation

Every object attracts every other object with a force that for any two objects is directly proportional to the mass of each object

Newton's Law of universal gravitation formula

F= G(m1m2/d^2)

How does the force of gravity depend on the distance between two objects?

Force of gravity is inversely proportional to the square of the distances between 2 objects centers.

G (scientific notation)

G = 6.67 x 10^-11 N x m^2 / kg^2

Inverse Square Law

Gravity decreases according to the inverse square law. The force of gravity weakens as the square of distance. When a quantity varies as the inverse square of its distance from its source, it follows an inverse-square law.

Why is the sum of PE and KE for a satellite in a circular orbit is constant?

In a circular orbit, the distance between a planet's center and the satellite's center is constant. This means that the PE of the satellite is the same everywhere in orbit. So by the law of conservation of energy, the KE is also constant - thus, the speed is constant in any circular orbit.

What scientist explained the ellipses?

Isaac Newton

What scientist discovered that these paths are ellipses?

Johannes Kepler

Earth's magnetic field

Magnetic lines of force from Earth's polar north and south, acting like a giant magnet; which also protects the earth from solar winds

Do you escape from Earth's gravity if you're above the atmosphere? By being on the moon? Defend your answers

No; in the gravitational equation, d would have to approach infinity for F to approach zero.

Where in an elliptical orbit is the speed of a satellite maximum?

Perigee

How do we measure weight?

Pressure against the Earth is the sensation we interpret as weight.

How does the force of gravity between two bodies change when the distance between them is doubled?

The force is 1/4 as much, in accord with the inverse-square law.

How does the force of gravity between two objects depend on their masses?

The greater the mass, the larger the gravitational force an object exerts on another if they are equally distant. The closer two objects are to each other, the stronger the gravitational pull is between them.

How does the intensity of light, radiation, and sound change when a point source is twice as far away?

The intensity is 1/4 as much, in accord with the inverse square law.

Kepler's First Law

The path of each planet around the sun is an ellipse with the sun at one focus.

Kepler's Third Law

The square of the orbital period of a planet is directly proportional to the cube of the average distance of the planet from the sun.

What scientist gathered accurate data on planetary paths around the sun?

Tycho Brahe

Tangential velocity

Velocity that is parallel (tangent) to a curved path.

weightlessness

Weightlessness is not the absence of gravity; rather it is the absence of a support force.

Why does the gravitational force change the speed of a satellite in elliptical orbit?

When the initial speed is more than 8 km/s, the satellite overshoots the circular path and moves away from Earth, against the force of gravity. therefore loses speed and at such a point, the satellite will slow to a point where it no longer recedes away from Earth and is now pulled back towards it. The speed lost in receding is regained as it falls back toward Earth. The satellite rejoins its path with the same speed it had initially, repeating this procedure over and over again it falls into an elliptical orbit

gravitational field

a force field that exists in the space around every mass or group of masses

spring tide

a high or low tide that occurs when the sun, Earth, and moon are all lined up. Spring tides occur during a new or full moon.

black holes

a mass that has collapsed to so great a density that its enormous local gravitational field prevents light from escaping

satellite

a projectile moving fast enough to fall continually around Earth rather than into it.

neap tide

a tide just after the first or third quarters of the moon when there is the least difference between high and low tides.

ocean tides

caused by differencees in the gravitational pull of the moon on opposite sides of the earth

Newton and Gravity

created law of universal gravitation: every object in the universe attracts every other object

In a circular orbit, is the speed of a circling satellite changed by gravity?

no

escape speed

the minimum speed necessary for an object to escape permanently from a gravitational field that holds it.

What is G and how was it reported?

the universal gravitation constant, G, in the equation describes the strength of gravity.

what is the gravitational field at earth's center?

zero

Earth's gravitational field

•Earth can be thought of as being surrounded by a gravitational field that interacts with objects and causes them to experience gravitational forces. •The strength of the Earth's gravitational field, like the strength of its force on objects, follows the inverse-square law. •Earth's gravitational field is strongest near the Earth's surface and weaker at greater distances from Earth.

Newton- Falling Moon & Falling Apple

•Newton understood the concept of inertia, that without an outside force, moving objects continue to move at constant speed in a straight line. •He knew that if an object undergoes a change in speed or direction, then a force is responsible. •Newton reasoned that the moon, is falling toward Earth for the same reason an apple falls from a tree - both are pulled by Earth's gravity.

is the sum of PE and KE also constant for a satellite in elliptical orbit?

•The PE is greatest when the satellite is at apogee and least when the satellite is at perigee. •The KE will be least when the PE is most, and the KE will be most when the PE is least .•At every point in the orbit, the sum of the KE and the PE is constant.