Starting from newton’s law of universal gravitation, show how to find the speed of the moon in its orbit from the earth-moon distance of 3.9 × 108 m and the earth’s mass. assume the orbit is a circle.

1010.92 m/s

Explanation:

According to Newton's law of universal gravitation:

(1)

Where:

is the gravitational force between Earth and Moon

is the Gravitational Constant  

is the mass of the Earth

is the mass of the Moon

is the distance between the Earth and Moon

Asuming the orbit of the Moon around the Earth is a circular orbit, the Earth exerts a centripetal force on the moon, which is equal to :

(2)

Where is the centripetal acceleration given by:

(3)  

Being the orbital velocity of the moon

Making (1)=(2):

(4)

Simplifying:

(5)

Making (5)=(3):

(6)  

Finding :

(7)

(8)

Finally:

-first use of geothermal energy occurred more than 10,000 years ago in north america by american paleo-indians

-the first industrial use of geothermal energy began near pisa, italy in late 18th century

-in 1904, italian scientist piero ginori conti invented the first geothermal electric power plant in which steam was used to generate the power

-with the above experiment, the first geothermal plant in usa started in 1922 with a capacity of 250 kilowatts

-however, in 1946 first ground-source geothermal heat pump installed at commonwealth building in portland, oregon

-during the 1960’s, pacific gas and electric began operation of first large scale geothermal power plant in san francisco, producing 11 megawatts

-in 1973, when oil crisis began many countries began looking for renewable energy sources and by 1980’s geothermal heat pumps (ghp) started gaining popularity in order to reduce heating and cooling costs

-as effect of climate change started showing results, governments of various countries joined hands to fight against it, for which kyoto protocol was signed in japan in 1997, laid out emission targets for rich countries and required that they transfer funds and technology to developing countries, 184 countries have ratified it

hope this

a.   mass number from atomic number