1) How could we use Newton\'s Law of Universal Gravity and the Second Law to cal
ID: 1288679 • Letter: 1
Question
1) How could we use Newton's Law of Universal Gravity and the Second Law to calculate the acceleration due to gravity "g"?
2) Why do you think it is easier to launch a satellite into orbit near the equator? And in what direction are they typically directed? Hint: The required orbital speed is about 8 km/sec.
3) Why do astronauts float in the space station as it orbits Earth? Is this because they experience no gravitational force from Earth? If you dare, try to use Newton's Law of Gravity to estimate how much less a person weighs in the space station than on the ground.
Please answer in full-detail sentences. Thanks!
Explanation / Answer
1]
From, Newton's Law of Universal Gravitational field, F= GMm/r2
From, Newton's second Law, F= ma= mg [under action of gravity]
GMm/r2 = mg
g= GM/r2
Thus we get thhe acceleration due to gravity g= GM/r2
2]
When a spacecraft is launched into orbit, it should end up spinning around the Earth quickly enough not to be pulled back in by the Earth's gravity.
Vorbital speed=8 km/sec.
Vorbital speed = [GM/r]1/2
Plugging the values for G=6.67*10-11Nm2/kg2 [Gravitational constant] and M=6*1024 kg [mass of earth]
we get, r=GM/V2orbital speed
Plugging the values we get r= 6.3*106m [equal to the radius of earth]
3]
The Earth's gravitational attraction at these altitudes is only about 11% less than it is at the Earth's surface. The gravitational attraction between two small objects in a spacecraft would be overwhelmed by other forces, such as the force of the air being circulated throughout the spacecraft.Hence astronauts float in the space station as it orbits Earth.
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