Many people mistakenly believe that the astronauts that orbit the Earth are “above gravity.” Calculate g for space-shuttle territory, 200 kilometers above the Earth’s surface. Earths’ mass is 6 X 10 to the 24th and its radius is 6.38 X 10 to the 6th (6380 km). Your answer is what percentage of 9.8 m/s squared?
My answer was: 6.27 X 10 to the -1
accel= GMe/d^2=6.67E-11*6E24/(6.58E6)^2
=9.24
which is about 94 percent.
There is no guarantee that Jiskha teachers will be online at all hours in all subjects.
You did not calculate g, which you asked for, and you did not express the ratio to sea level g as a percent.
You can use the ratio (6380/6580)^2 to get the ratio of g at 200 km to the earth-surface value. It is NOT 0.627
drwls.. what do you mean about Jiskha teachers? No I mean at the college I go to I'm taking this class online, and the teacher is not helpful at all, even when we ask questions. Thank you.
Well, if you take the Earth's mass of 6 X 10 to the 24th and its radius of 6.38 X 10 to the 6th, you can use the formula for the acceleration due to gravity (g = GM/r^2), where G is the universal gravitational constant.
Plugging in the values, you get:
g = (6.67 X 10^-11 N m^2/kg^2) * (6 X 10^24 kg) / (200 km + 6.38 X 10^6 m)^2
After calculating that, you'll find that g in space-shuttle territory 200 kilometers above the Earth's surface is approximately 1.14 m/s^2.
So, the answer to your question is that the acceleration due to gravity in space-shuttle territory is about 11.6% of 9.8 m/s^2. But remember, just because it's a smaller value doesn't mean the astronauts are "above gravity" per se. Gravity is still present, just at a reduced strength. They are weightless in space due to their free-falling state in orbit, but gravity is still there, clowning around!
To calculate the value of g at a specific distance above Earth's surface, we can use the formula for the gravitational acceleration:
g = (G * M) / r^2
Where:
- g is the gravitational acceleration
- G is the universal gravitational constant (approximately 6.67 x 10^-11 N(m/kg)^2)
- M is the mass of Earth
- r is the distance from Earth's center
In this case, we want to calculate g at a distance of 200 kilometers above Earth's surface, meaning the distance from the center of the Earth would be the radius of Earth (6.38 x 10^6 m) plus 200 kilometers (200,000 meters).
Substituting the given values into the formula:
g = (6.67 x 10^-11 N(m/kg)^2 * 6 x 10^24 kg) / (6.58 x 10^6 m)^2
g ≈ 0.9537 m/s^2
To find the percentage of this value compared to 9.8 m/s^2 (acceleration due to gravity at Earth's surface), we can calculate:
percentage = (g / 9.8 m/s^2) * 100
percentage ≈ (0.9537 m/s^2 / 9.8 m/s^2) * 100 ≈ 9.74%
Therefore, the value of g at 200 kilometers above the Earth's surface is approximately 9.74% of 9.8 m/s^2.