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Sol-Earth · Interactive Learning

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Gravity & Fields

01 Guided Lesson

Every particle attracts every other particle in the universe with a force proportional to the product of their masses.

Mm
Key Insight

More massive objects create a stronger gravitational pull.

The gravitational force is inversely proportional to the square of the distance between the centers of the masses. If you double the distance, the force becomes one-fourth as strong.

rF_g
Key Insight

Gravity weakens very quickly as you move away from a planet.

In orbit, a satellite moves sideways so fast that as it falls toward the planet, the surface curves away beneath it. It is constantly in free-fall.

F_g
Key Insight

Orbits are just falling while moving sideways fast enough to miss the ground.

02 Interactive Formula

Hover symbols
FgF_g==GG⋅·MM⋅·mmrr2^2

Hover over a variable in the formula above, or see glossary below:

FgF_g
Gravitational Force
Newtons (N)
GG
Gravitational Constant
N⋅m²/kg²
MM
Mass 1 (Attractor)
Kilograms (kg)
mm
Mass 2 (Satellite)
Kilograms (kg)
rr
Distance
Meters (m)

03 Worked Practice

"Engineers use this exact law to calculate the precise trajectories of spacecraft, ensuring they can slingshot around planets or establish stable orbits without burning excess fuel."

Q: Calculate the gravitational force between Earth (M = 5.97 \times 10^{24} kg) and a 1000 kg satellite in Low Earth Orbit (r = 6.7 \times 10^6 m).
  • 1.Identify given values and the gravitational constant G \approx 6.674 \times 10^{-11}.
  • 2.Plug values into the formula: F_g = G \frac{M \cdot m}{r^2}.
  • 3.Substitute the numbers: F_g = (6.674 \times 10^{-11}) \frac{5.97 \times 10^{24} \cdot 1000}{(6.7 \times 10^6)^2}.
  • 4.Calculate the result.
Result:
F_g \approx 8870 \text{ N}