Gravitational acceleration is the acceleration experienced by objects due to Earth’s gravity. Its standard value is 9.80665 m/s², though it varies with location.
Discover FizziQ
How to measure it in class
Steps:
- Direct method: open FizziQ, select absolute acceleration and place the smartphone flat on a table. The displayed value corresponds directly to g.
- Free fall method: film the fall of a ball with FizziQ and use video analysis to measure the successive positions of the ball at each frame.
- From the measured positions, calculate the velocity at each instant and verify that the acceleration is constant. Determine the value of g from the slope of the velocity-time graph.
- Compare the obtained value with the theoretical value of 9.81 m/s². Discuss sources of discrepancy: air resistance, video measurement precision, local conditions.
- As an extension, calculate g from pendulum period measurements.
Scientific activities on this topic
Seven experiments are described in detail in an article about gravity that we published on our blog.
Here are some activities that can be done in class or at home:
- Calculate the value of gravitational acceleration g by measuring the free fall duration of a smartphone: https://www.fizziq.org/en/activities/galileo/
- Verify Newton’s law of gravitation by measuring variations in g with altitude: https://www.fizziq.org/en/activities/lighter/
- Study the effect of latitude on gravitational acceleration g
- Conduct a thought experiment with Einstein
- Compare the period of a pendulum on Earth and on the Moon
- Calculate linear acceleration or how to neutralize gravity
- Trajectory of a fall by kinematic analysis and calculation of g
Learn more
Gravitational acceleration varies with:
- Altitude (decreases with height)
- Latitude (slightly higher at poles)
- Local geology (density variations)
Formula
The value of g at Earth’s surface is derived from the law of universal gravitation:
g = G x M / R²
Meaning: g: gravitational acceleration (m/s²) G: universal gravitational constant (6.674 x 10⁻¹¹ N·m²/kg²) M: mass of the Earth (5.972 x 10²⁴ kg) R: radius of the Earth at the point considered (approximately 6,371 km)
Examples
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A ball dropped from the top of a building accelerates by 9.81 m/s every second
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An object weighs about 17% less on the Moon, where g equals 1.62 m/s²
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A skydiver in free fall accelerates at 9.81 m/s² before air resistance compensates
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The difference in g between the poles and the equator changes an object’s weight by 0.5%
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Precision scales must be recalibrated when moved between distant cities
FAQ
Q: Why does g vary according to location? A: The Earth is not a perfect sphere: it is flattened at the poles. The radius is smaller there, so g is larger. Additionally, Earth’s rotation creates a centrifugal acceleration that reduces g at the equator.
Q: What is the difference between mass and weight? A: Mass is an intrinsic property of matter, invariable. Weight is the force exerted by gravity on that mass. We have P = m x g. Weight varies with g, mass does not.
Q: Are G and g the same thing? A: No. G (capital) is the universal gravitational constant, identical everywhere in the universe. g (lowercase) is the local gravitational acceleration, which depends on location.
Q: Can g be measured precisely with a smartphone? A: Yes, with a precision of about 1 to 2%. The accelerometer directly gives a value of g, and free fall analysis with video can achieve similar precision.
Q: Why do we say astronauts are in weightlessness? A: In the ISS, astronauts are in permanent free fall around the Earth. The value of g there is still 8.7 m/s², but since everything falls together, they feel no apparent weight.
Related concepts
Universal gravitation - Free fall - Weight - Mass - Acceleration - Gravitational force - Parabolic trajectory