The most basic experiment is to pick up a stone and let it go. The stone will fall back to the ground. But this experiment is not very informative. A person on the ground can't tell the difference between a falling stone and the Earth moving towards it. This can be seen in the images below.
A stone falling due to gravity.
The Earth approaching a stationary object (no gravity).
In any case, a person on the ground sees only how the distance between the stone and the ground is shortened.
In fact, the movement of the Earth cannot be the cause of falling objects. This is because objects fall differently at various points on the Earth’s surface.
The following equations allow us to calculate how an object falls (assuming its initial velocity is zero):
d = (g * t * t) / 2
t = ((2 * d) / g) ** (1/2)
Where:
d is the distance traveled by the object (meters),
g is the acceleration of gravity (m/s2),
t is the time (seconds).
The acceleration of free fall in New York City is approximately 9.802 m/s2 (32.16 ft/s2), while in Rio de Janeiro it is approximately 9.788 m/s2 (32.11 ft/s2). Therefore, we can calculate the time it takes for a small lead ball to fall from a height of 1000 meters (0.62 miles) in each city.
In New York:
((2 * 1000) / 9.802) ** (1/2) = 14.278 seconds
In Rio de Janeiro:
((2 * 1000) / 9.788) ** (1/2) = 14.292 seconds
The difference in time between the two cities is about 0.014 seconds. Is this a very small difference?
If we assume that the reduction in the distance between the Earth and the ball is caused by the Earth's movement toward the ball, it follows that the Earth must distort, as different regions of it move at varying speeds. These distortions are substantial - within just ten hours, New York City would rise 9,072,000 meters (5,637 miles) above Rio de Janeiro. Such drastic changes would be impossible to overlook, particularly given the coastal locations of both cities on the Atlantic Ocean.
To verify this information, we could compare the acceleration of free fall between New York and Rio by directly measuring it at the same time in both locations.
Alternatively, we could take a different approach to this problem. Although it may be simpler, it is also less obvious. We need a spring scale that can measure weight with an accuracy of 0.01 grams. Digital scales are similar to spring scales in some ways. The readings from digital scales depend on how much the sensor is compressed, so they should work as well.
If gravity did not exist, the only thing that could make a spring or digital scale measure weight would be the Earth's accelerated motion. In that case, identical scales with identical weights should give the same reading in different locations. However, that's not how it works in reality.
For instance, if a scale in New York registers a weight of 100 grams (3.527 ounces), the same scale with the same mass in Rio de Janeiro would display 99.86 grams (3.522 ounces) - a difference of 0.14 grams (0.005 ounces).
You can calculate the scale readings using the following formula:
w2 = (w1 / g1) * g2
Where:
w1 is the weight of the object at location A (grams),
w2 is the weight of the object at location B (grams),
g1 is the acceleration due to gravity at location A (m/s2),
g2 is the acceleration due to gravity at location B (m/s2).
The best way to test this is to conduct an experiment as described below.
The experiment requires two experimenters, two identical digital scales and two identical weights. In New York, the experimenters perform four weighings: on the first scale with the first weight; on the first scale with the second weight; on the second scale with the first weight; on the second scale with the second weight. The measurement results must be the same for all four weighings. Next, one of the experimenters must travel to Rio de Janeiro. He should take one scale and one weight with him. In Rio, the experimenter needs to weigh a weight on a scale. Then he should contact a colleague who remained in New York to compare the results. If desired, long-term observations can be carried out.
It is even better if measurements are carried out simultaneously in many locations of the planet.
For those interested in more information, the table below shows data on gravitational acceleration in various cities:
| City | g (m/s2) | g (ft/s2) |
| Mexico City, Mexico | 9.779 | 32.08 |
| Quito, Ecuador | 9.780 | 32.09 |
| Bangkok, Thailand | 9.780 | 32.09 |
| Manila, Philippines | 9.780 | 32.09 |
| Mumbai, India | 9.785 | 32.10 |
| Rio de Janeiro, Brazil | 9.788 | 32.11 |
| Cairo, Egypt | 9.793 | 32.13 |
| Cape Town, South Africa | 9.796 | 32.14 |
| Los Angeles, USA | 9.796 | 32.14 |
| Sydney, Australia | 9.797 | 32.14 |
| Tokyo, Japan | 9.798 | 32.15 |
| New York City, USA | 9.802 | 32.16 |
| Chicago, USA | 9.804 | 32.17 |
| Toronto, Canada | 9.806 | 32.17 |
| Seattle, USA | 9.811 | 32.19 |
| London, UK | 9.811 | 32.19 |
| Stockholm, Sweden | 9.818 | 32.21 |
| Oslo, Norway | 9.819 | 32.21 |
| Reykjavik, Iceland | 9.822 | 32.22 |
| Anchorage, USA | 9.825 | 32.23 |
The acceleration of free fall also depends on height. The higher the altitude, the lower the acceleration of gravity. At the base of mountains, it has one value, while at the summit it is slightly lower. For high mountains, this difference can be quite significant. To verify this statement, one needs to climb mountains. However, climbing some mountain peaks can be fraught with health risks and even danger to life. Hiking in mountains requires knowledge, experience, and a good physical condition. Here are some examples of mountains with significant altitude differences from base to summit: Chimborazo, Cotopaxi, Huascaran, Kilimanjaro, Everest, Nanga Parbat, Denali, Mauna Kea.
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