Use this equation to calculate the approximate speed of the space station given the distance between the centre of the Earth and the space station that you found in part (b). Note that the mass of the Earth (mearth) is 5.972 x 1024 kg. Report the speed in units of km/hour. How does this compare to the known average speed of the International Space Station, 27600 km/hour? If your result is not reasonably close to the actual speed, try repeating your calculation/check your work.

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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f) Assume that the space station orbits the Earth with uniform circular motion. This means that the
magnitude of the acceleration of the space station is given by a = v²/r. In addition, the net force
on the space station is equal to m,tation*a (Newton's Second Law, as always), and the force on
the space station is F = - G*m,tation*Mearth/r?. Using these equations, we can derive a formula for
the speed of the space station as it orbits Earth:
Fnet = m*a (towards centre of earth for uniform circular motion)
Inserting Newton's Law of Universal Gravitation and the formula for centripetal acceleration,
G*mstation *mearth/r² = mstation*Vstation/r,
and dividing both sides by mstation and multiplying both sides by r, we get:
G*marth/r = v, and finally we arrive at our formula for the speed of the station,
Vstation = V(G*mearth/r), ...note that this is meant to be a square root symbol.
Use this equation to calculate the approximate speed of the space station given the distance
between the centre of the Earth and the space station that you found in part (b). Note that the
mass of the Earth (mearth) is 5.972 x 1024 kg. Report the speed in units of km/hour. How does this
compare to the known average speed of the International Space Station, 27600 km/hour? If
your result is not reasonably close to the actual speed, try repeating your calculation/check your
work.
Transcribed Image Text:f) Assume that the space station orbits the Earth with uniform circular motion. This means that the magnitude of the acceleration of the space station is given by a = v²/r. In addition, the net force on the space station is equal to m,tation*a (Newton's Second Law, as always), and the force on the space station is F = - G*m,tation*Mearth/r?. Using these equations, we can derive a formula for the speed of the space station as it orbits Earth: Fnet = m*a (towards centre of earth for uniform circular motion) Inserting Newton's Law of Universal Gravitation and the formula for centripetal acceleration, G*mstation *mearth/r² = mstation*Vstation/r, and dividing both sides by mstation and multiplying both sides by r, we get: G*marth/r = v, and finally we arrive at our formula for the speed of the station, Vstation = V(G*mearth/r), ...note that this is meant to be a square root symbol. Use this equation to calculate the approximate speed of the space station given the distance between the centre of the Earth and the space station that you found in part (b). Note that the mass of the Earth (mearth) is 5.972 x 1024 kg. Report the speed in units of km/hour. How does this compare to the known average speed of the International Space Station, 27600 km/hour? If your result is not reasonably close to the actual speed, try repeating your calculation/check your work.
Distance from earth to the space station is 6378 km
Distance from earth center to the earth surface is 6798 km
Transcribed Image Text:Distance from earth to the space station is 6378 km Distance from earth center to the earth surface is 6798 km
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