1. What Does It Mean for the Moon to "Fall" Toward Earth?
The Moon looks still in the night sky, but it orbits Earth once every 27.3 days. Its average orbital speed is about 1.022 kilometers per second, and its average distance from Earth is about 384,400 kilometers. [1]
In this context, "falling" means something specific. If Earth's gravity did not exist, the Moon would fly off in a straight line. Instead, gravity constantly pulls the Moon toward Earth, bending its path from a straight line into a nearly circular orbit. This bending is what we call falling. [4]
It is important to note that the Moon is not getting closer to Earth. The 1.4 millimeters per second is the amount it deviates from a straight line, not the amount its distance shrinks. Because the Moon keeps moving sideways while it falls, the amount it would drift away along a straight line is balanced by the amount gravity bends its path, so it keeps circling Earth at a steady distance. [4]
2. How Do You Calculate That the Moon Falls 1.4 Millimeters Per Second?
You can calculate this value with a calculator. An object moving in a circle has acceleration toward the center. The size of this acceleration is the speed squared divided by the radius. For the Moon, (1.022 km/s)² ÷ 384,400 km equals about 0.00272 meters per second squared. [1]
The distance an object falls is half the acceleration multiplied by time squared. For 1 second, half of 0.00272 is about 0.00136 meters, or 1.4 millimeters. This value is an approximation assuming the Moon's path is a circle, calculated from NASA data, and it matches the value found in university lecture materials. [4]
You can see the same number using a different method. If the Moon moved straight for 1 second, the Pythagorean theorem shows its distance from Earth would increase by about 1.4 millimeters. Gravity causes the Moon to deviate from the straight line by about 1.4 millimeters. The Moon stays at a steady distance because these two effects balance. [4]
1.4 millimeters is about the width of three mechanical pencil leads (0.5 mm each) lined up. This small deviation continues every second, keeping the Moon in a nearly circular path. [4]
3. Why Does an Apple Fall 3,600 Times Farther Than the Moon in One Second?
The average gravity at Earth's surface is about 9.82 meters per second squared. If you drop an apple, it falls about 4.9 meters in 1 second (half of 9.82). Dividing 4.9 meters by the Moon's 1.4 millimeters gives about 3600. In one second, the Moon falls about 1/3600th as far as an object at Earth's surface. [2]
Where does 3600 come from? Earth's average radius is about 6,371 kilometers. Dividing the Moon's average distance (384,400 km) by Earth's radius gives about 60.3, or roughly 60 times. If gravity decreases with the square of the distance, then at 60 times the distance, gravity should be 1/60², or 1/3600, of surface gravity. [2] [3]
The ratio of how they fall (about 3600) matches the ratio predicted by distance (60²). This supports the idea that the Moon and the apple are pulled by the same gravity. The 60 times figure is an average; the Moon's orbit is elliptical, so the distance changes during the month. [3]
According to a story recorded later by Conduitt, Newton thought of this in 1666 while sitting in his mother's garden in Lincolnshire. He wondered if the gravity pulling the apple also reached the Moon. The part about the apple hitting his head is considered a myth; the record only says he was thinking in the garden. [3]
4. Why Does the Moon's Sideways Motion Keep It From Crashing Into Earth?
Newton imagined throwing a stone horizontally from a high mountain. If thrown slowly, it hits the ground. Thrown faster, it lands farther away. At just the right speed, the stone falls continuously but moves forward enough to circle Earth and return to the top. If thrown faster than the speed needed for a circular orbit, but slower than escape speed, it follows an elliptical path. [7]
This story appears in "A System of the World," published in 1728 after Newton's death. However, Newton himself did not compare the Moon to a cannonball; applying this analogy to the Moon is a modern explanation. [7]
Objects closer to Earth need to move faster to stay in orbit. The International Space Station (ISS) travels at about 5 miles per second (about 8 kilometers per second) and orbits 16 times a day. [8] This is much faster than the Moon's 1 kilometer per second. The ISS is close to Earth where gravity is strong, so it needs high speed to fall around Earth. The Moon is far away where gravity is weak, so it can orbit slowly. [8]
5. How Accurate Was Newton's Check of Gravity and the Moon's Orbit?
Newton tested this idea around 1666 by calculating the Moon's orbit. His result was within 16% of the known value. Around 1680, using a new value for Earth's size, his calculation improved to within 1.6%. [5] This shows that the idea of universal gravity was supported gradually as numbers were corrected, rather than being perfect from the start. [5]
Newton organized these ideas in his 1687 book, "Principia." He stated that since the Moon is about 60 Earth radii away, its fall should be 1/60² of surface gravity. [6]
Today, the Moon is moving away from Earth by about 3.8 centimeters per year. [1] It is still falling, but the reason for its retreat involves tides, which is a separate topic. [1]
6. How Can You Try the Moon-Fall Calculation Yourself?
You can verify this with a calculator. Divide 384,400 by 6,371 to get about 60. Multiply 60 by 60 to get 3,600. Divide 4.9 by 3,600 to get about 0.00136 meters. These three steps connect the apple and the Moon. [3]
You can also observe this with balls. In a wide, clear space with an adult nearby, gently drop one ball and throw another firmly sideways from the same height, making sure no one is in the path of the balls. If two people listen, they should hear the balls hit the ground at almost the same time. This shows that the time it takes to fall is almost the same, even if the ball is moving sideways. [3]
Next time you see the Moon, remember that it is falling 1.4 millimeters every second. Newton's "Moon test" is also explained on NASA's education site. [3]