The acceleration due to gravity calculated this way works well for objects near the Earth’s surface. How would you have to change the above equation if the object was 100,000 meters above the ground?
(Note: this question refers to Newton’s equation for the force of gravity between two objects. How would that change if the radius of the earth or distance were increased by 100,000 meters. To help you answer this question, please review your textbook, chapter 3, Newton’s law of Gravitation section.)
F=(6.67 x10-11N.m2/kg2)(m1)(m2)
100,0002
g is inversely proportional to the square of the distance from the center of the earth.
100 km above the earth's surface, g is reduced by a factor [6370/(6370+100)]^2 = 0.969
That would make it 9.51 m/s^2
6370 km is the radius of the earth.
To calculate the acceleration due to gravity for an object 100,000 meters above the ground, we need to consider the change in distance between the object and the center of the Earth.
The equation you provided is Newton's law of gravitation, which calculates the force of gravity between two objects with masses m1 and m2. However, in this case, we are only concerned with the effect of the Earth on the object.
The force of gravity, F, between an object and the Earth can be expressed as:
F = (G * m1 * m2) / r^2
Where:
- G is the gravitational constant (6.67 x 10^(-11) N.m^2/kg^2)
- m1 and m2 are the masses of the objects
- r is the distance between the objects' centers of mass
For an object 100,000 meters above the ground, the distance between the object and the center of the Earth would be the sum of the Earth's radius (r0 ≈ 6,371,000 m) and the new distance (h = 100,000 m).
Therefore, the new distance, r, would be:
r = r0 + h
Substituting this value into the gravitational force equation:
F = (G * m1 * m2) / (r0 + h)^2
Hence, to calculate the acceleration due to gravity at a distance of 100,000 meters above the ground, you would modify the above equation with the new distance as shown.
The equation for the force of gravity between two objects, as given by Newton's law of gravitation, is:
F = (G * m1 * m2) / r²
where F is the force of gravity, G is the gravitational constant (6.67 x 10^-11 N.m²/kg²), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
To calculate the acceleration due to gravity near the Earth's surface, we use the relationship:
g = (G * M) / r²
where g is the acceleration due to gravity, G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth to the object.
If the object is 100,000 meters above the ground, the distance between the center of the Earth and the object would be the radius of the Earth plus 100,000 meters. Let's say the radius of the Earth is R.
So, the new distance (r') would be:
r' = R + 100,000 meters
Therefore, the equation for the acceleration due to gravity at a height of 100,000 meters above the ground would be:
g' = (G * M) / (R + 100,000)²
Note that we are considering the Earth's radius (R) to be constant and only increasing the distance (r) from the surface by 100,000 meters.