# physics

On July 15, 2004, NASA launched the Aura spacecraft to study the earth's climate and atmosphere. This satellite was injected into an orbit 705 {\rm km} above the earth's surface, and we shall assume a circular orbit.

How many hours does it take this satellite to make one orbit? (T=?hours)

How fast (in {\rm km/s} )is the Aura spacecraft moving? (v=?km/s)

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1. A boat propelled so as to travel with a speed of 0.50m/s in still water, moves directly ( in a straight line) across the river that is 60m wide. The rivers flows with a speed of 0.30m/s. How long in a seconds does it take the boat to across the river?

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2. On the earth surface g = GM/R^2
And at the height h
g" = GM/ [R+h]^2
g" = R^2/ [ R+h]^2•g
g" = {R/ [ R+h] }^2•g
g" = {6378/ 7083}^2•9.81 = 7.95 m/s^2

T^2 = 4π^2•(R+h) /g"
T^2 = 4π^2•7083 /7.95
T = 187.54s = 0.052 hour.

v = 2•π •[R+h] / T
v = 2•π •[7.083] / 187.54s
v = 0.24 km /s

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3. I've mistaken in the previous post.
New version:

m•a(norm) = GM/ [R+h] ^2,
m•v^2/(R+h) = GM/ [R+h] ^2,,
v = sqrt[GM/(R+h)] =sqrt [6.67•10^-11•5.97•10^24/7.1•10^6] =
= 7490 m/s =7.49 km/s
T = 2 •π(•R+h)/v =2 •π•7.1•10^6/7490= =5960 s =1.65 h

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