Three Chapter 6

• Newton's first application of his laws was Halley's comet.
• Other applications were made to objects in space.
• Newton suggested that artificial satellites could be put in orbit.
  • If a cannon fires shells horizontally, as the speed of the shells increases, distance travelled increases.
  • Eventually, a critical velocity is reached where the shell would circle the earth (Move sideways enough so that it always misses the Earth).
• Newton used the universal law of gravity with his third law to explain tides.

· At A, water is pulled towards the moon.

· At B, gravity is lower than at other places and so the water is higher. The Earth shields the moon's gravitational pull, and because the Earth rotates, the water is thrown out into space.

· These high tides stay relatively stationary with respect to the moon, but not with respect to the Earth's surface.

· The sun also plays a role. If the moon, Earth, and the sun line up, tides are higher than usual (spring tides).

· If the sun-Earth line is perpendicular to the Earth-moon line, tides are not as high (neap tides).

· Tides occur at different times of the day in a changing pattern because of the

o Earth's rotation.

o Lunar orbital period.

o Earth's orbital period.

· One new planet and one planetoid were discovered because of Newton's Universal Law of gravity.

o Small deviations (perturbations) were observed in the elliptical orbits of known planets.

o These perturbations could be explained by Newton's Universal Law of Gravity, if there was a planet beyond Uranus.

o Calculations predicted the location of the planet, and it was found (Neptune).

o Perturbations in Neptune's orbit led to the discovery of the planetoid Pluto (1930).

· If a satellite goes into a circular orbit, then there is a centripetal force causing the motion.

· The centripetal force is caused by gravitational force.

· Note that the above relationship tells us that the greater the orbit, the slower the speed.

· The above equation does not tell us that the greater the orbit, the smaller the kinetic energy of the satellite near launch. (In fact, the greater the orbit, the greater the kinetic energy needed at launch to get to orbit.

o E.G. Calculate the speed required by a satellite to maintain an orbit 100 km above the earth's surface. The radius of the Earth is 6.38 X 10⁶ m.

• Geosynchronous Orbit - Orbits that have a 24 h period.
  • The satellite stays in one place with respect to the Earth's surface.
  • Geosynchronous orbits are used for
    • communication satellites
    • navigational systems
• Synchronous Orbit - A more general term used to replace geosynchronous orbit when referring to other planets besides the Earth that satellites are orbiting.

• There are two other equations for Fc.

· These other two forms can be equated to Fg to get equations for satellites in orbit.

· By equating the portion of the above equation which has period in it, to Newton's Universal Law of Gravity, and then rearranging, we find

· In the above equation, M is the mass of the planet the satellite orbits, and T is the period of the satellite's orbit.

· For a geosynchronous orbit, the radius of the orbit must be

• For Pluto to have the gravitational effect on Uranus and Neptune that it does have, it would have to be 1000 times more massive.
• Therefore, speculation is that there may be a 9th planet called "Humphrey."
• Humphrey may have been responsible for pulling pluto (once a moon) away from Neptune.
• Calculations do not reveal a close enough location for Humphrey.
• It may be possible to locate it by looking for relative motion with respect to the background stars.
• Humphrey probably has a very elongated orbit and a period of about 800 years.
• There are of course, other theories which try to explain the irregularities in these planets' orbits.

• The solar system began with a large glob of hot gas in slow rotation.
• As cooling occurs, contraction occurs and the rate of rotation increases.
• Increased rotation caused a bulge at the equator of this hot gas cloud. This bulge occurs because centripetal force was insufficient to hold the cloud in a somewhat spherical shape.
• Irregularities in the density of the resulting disk of gas, resulted in gas being gravitationally attracted to denser regions. These denser regions eventually formed into the planets.
• The large bulge at the center of the disk of gas gravitationally contracted to form the sun.

Home

November 5, 2013