Gravitational acceleration above the Earth's surface

In summary, to find the altitude above Earth's surface where the gravitational acceleration is 4.9 m/s^2, you can use the equation g=GM/r^2 and solve for h by plugging in the values for g, G, and M. However, there seems to be an error in the computation as the correct answer should be approximately 2.00e6m instead of 2.00e7m.
  • #1
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At what altitude above the Earth's surface would the gravitational acceleration be 4.9 m/s^2?

I thought this what very simple but apparently it is not since I got the wrong answer and can't figure out what I did wrong.
I used g= GM/r^2= GM/(R+h)^2 R being radius of Earth and h being the altitude.

g= 4.9m/s^2

4.9= (6.73e-11)(5.98e24)/(6.37e6+ h)^2
4.9= 3.99e14-(6.37e6+h)^2
solved for h and got 2.00e7m

Can someone tell me where I went wrong? Thanks
 
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  • #2
The approach is OK, but the computation has an error. You really only need the radius of the Earth and g at the surface to do this, but your approach is OK too.

9.8m/s^2 = GM/R^2
4.9m/s^2 = GM/(R+h)^2
2 = (R+h)^2/R^2 <== dividing 1st eq by 2nd eq
etc
 
  • #3


I would first check the units used in the calculation. The gravitational constant G is typically expressed in units of m^3/kg*s^2, while the mass of the Earth M is in units of kg, and the radius of the Earth R and altitude h are in units of meters. It is important to make sure all units are consistent in order to get the correct answer.

Next, I would check the equation used for gravitational acceleration above the Earth's surface. The correct equation is g=GM/(R+h)^2, where M is the mass of the Earth, R is the radius of the Earth, and h is the altitude above the Earth's surface. It appears that a negative sign was mistakenly used in the equation provided, which could have resulted in the wrong answer.

Using the correct equation, I would plug in the values and solve for h as follows:

g= 4.9 m/s^2
M= 5.98e24 kg
R= 6.37e6 m
h= unknown

4.9= (6.73e-11*5.98e24)/(6.37e6+h)^2
4.9= 4.024e14/(6.37e6+h)^2
(6.37e6+h)^2= 4.024e14/4.9
h= (sqrt(4.024e14/4.9)-6.37e6) m
h= 1.99e7 m

Therefore, the altitude above the Earth's surface where the gravitational acceleration is 4.9 m/s^2 is approximately 19,900,000 meters. It is important to double check the calculations and make sure the units are correct in order to get an accurate answer.
 

1. What is gravitational acceleration above the Earth's surface?

Gravitational acceleration above the Earth's surface refers to the force of gravity acting on objects as they move away from the Earth's surface. It is essentially the rate at which an object's speed and direction change as it moves farther from the Earth.

2. How does gravitational acceleration above the Earth's surface differ from that on the surface?

Gravitational acceleration above the Earth's surface is weaker compared to that on the surface. This is because the further an object is from the Earth's surface, the weaker the pull of gravity is on it. This decrease in gravitational force is proportional to the square of the distance from the Earth's center.

3. What is the value of gravitational acceleration above the Earth's surface?

The value of gravitational acceleration above the Earth's surface varies depending on the altitude and distance from the Earth's center. On average, it is approximately 9.8 meters per second squared (m/s²) at the Earth's surface, but decreases as altitude increases.

4. How does the mass of an object affect its gravitational acceleration above the Earth's surface?

The mass of an object has no effect on its gravitational acceleration above the Earth's surface. This is because the force of gravity is determined by the mass of the Earth, not the mass of the object. However, the mass of an object will affect the force needed to move it against the Earth's gravity.

5. How can gravitational acceleration above the Earth's surface be calculated?

Gravitational acceleration above the Earth's surface can be calculated using the formula a = GM/r², where a is the gravitational acceleration, G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth. This formula can be used to calculate acceleration at any altitude above the Earth's surface.

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