You are explaining why astronauts feel weightless whileorbiting in the space shu

Question

You are explaining why astronauts feel weightless whileorbiting in the space shuttle. Your friends respond that theythought gravity was just a lot weaker up there. Convince them andyourself that it isn't so by calculating the acceleration ofgravity 234 km above the Earth's surfacein terms of g. (One g is, of course, 9.8m/s2.)
I've tried many ways to find the answer, but I just cannotfigure it out. Please help! You are explaining why astronauts feel weightless whileorbiting in the space shuttle. Your friends respond that theythought gravity was just a lot weaker up there. Convince them andyourself that it isn't so by calculating the acceleration ofgravity 234 km above the Earth's surfacein terms of g. (One g is, of course, 9.8m/s2.)
I've tried many ways to find the answer, but I just cannotfigure it out. Please help!

Explanation / Answer

Use the formula g=Gm/r^2, where G= 6.67300 ×10-11 m3 kg-1s-2, m=mass ofearth, and r is the radius between the astronauts and the centre ofthe earth (radius of earth)+234 000m. -Divide the answer from the formula by 9.8m/s^2 and you willhave your answer in terms of g. Also, I believe why they feel weightless even though there is stillgravity is because the are orbiting around the earth, therefore,the acceleration normal to their path (due to circular motion) isin the same direction as gravity. Just like if you were freefalling, then you would feel weightless.

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