Modeled after the two satellites problem (slide 12 in lecture13, universal gravity), imagine now if the period of the satellite is exact 88.59 hours, the earth mass is 5.98 x 1024 kg, and the radius of the earth is 3958.8 miles, what is the distance of the satellite from the surface of the earth in miles? use g=6.67x 10 -11 nm2/kg2. your answer could be a large number on the order of tens of thousands, just put in the raw number you get, for example, 12345.67.

  R = 6.3456 10⁴  mile

Explanation:

For this exercise we will use Newton's second law where force is gravitational force

      F = m a

The satellite is in a circular orbit therefore the acceleration is centripetal

      a = v² / r

Where the distance is taken from the center of the Earth

     G m M / r² = m v² / r

     G M / r = v²

The speed module is constant, let's use the uniform motion relationships, with the length of the circle is

     d = 2π  r

     v = d / t

The time for a full turn is called period (T)

Let's replace

     G M / r = (2π r / T)²

     r³ = G M T²²2 / 4π²

     r = ∛ (G M T² / 4π²)

We have the magnitudes in several types of units

      T = 88.59 h (3600 s / 1h) = 3.189 10⁵ s

      Re = 6.37 10⁶ m

Let's calculate

     r = ∛ (6.67 10⁻¹¹ 5.98 10²⁴ (3,189 10⁵)²/4π²)

     r = ∛ (1.027487 10²⁴)

     r = 1.0847 10⁸ m

This is the distance from the center of the Earth, the distance you want the surface is

     R = r - Re

     R = 108.47 10⁶ - 6.37 10⁶

     R = 102.1 10⁶ m

Let's reduce to miles

      R = 102.1 10⁶ m (1 mile / 1609 m)

      R = 6.3456 10⁴  mile

carbon is found in all living things. carbon atoms move constantly through

living organisms, the oceans, the atmosphere, and the earth’s crust in what is

known as the carbon cycle. the directions taken by carbon atoms through this

cycle are very complicated and can take millions of years to make a full circle.

all animals, from humans to the dinosaurs are part of the carbon cycle. when

animals eat food, they get carbon in the form of carbohydrates and proteins.

in animals, oxygen combines with food in the cells to produce energy for daily

activity and then gives off carbon. the carbon combines with oxygen to form

carbon dioxide (co2) and is released back into the atmosphere as a waste

product when animals breathe and exhale.

from 145-65 million years ago, earth was much

hotter than today and covered with dense,

tropical swamp forests. the trees and other

plants were immense and

provided an endless supply of

food for the giant animals that

roamed the land. somewhere in

the air above one of these

forests, a lone carbon atom has joined

up with two oxygen atoms to form a molecule of co2.

the co2 molecule was sucked into the tiny holes (stomata) on the leaf of a

fern plant and joined with sunlight, chlorophyll and water to make food and

energy in the plant’s cells through photosynthesis. the oxygen (o2) from the

co2 molecule was sent back into the atmosphere; the carbon atom (c) was

detached and used to make a molecule of sugar.

if that carbon atom had been eaten instead, a totally

different situation would have developed. let’s say

that a giant plant-eating dinosaur (herbivore) ate the

fern for breakfast, and swallowed the carbon in the

fern in the form of carbohydrates and proteins. in

the process of respiration, oxygen combined with

the carbohydrates and proteins in the dinosaur’s cells

to provide energy for its daily activity.  

the inner core.

good luck: )

klicker