Kepler's Laws and Newtonian Gravity
Kepler found three laws that describe how the planets move; Newton explained why with gravity. Learn the three laws, the inverse-square law, and how T squared is proportional to r cubed - with the calculations to match.
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How the planets move
Two people cracked planetary motion. Johannes Kepler found three laws that *describe* how the planets move. Isaac Newton then *explained* why - with gravity. This module covers Kepler's three laws, Newton's inverse-square law of gravitation, and the key relationship T squared is proportional to r cubed - with the calculations to go with them.
Orbit words
Four terms describe an orbit:
Match each law to what it says
- Kepler's first law
- Kepler's second law
- Kepler's third law
- Newton's law of gravitation
- Orbits are ellipses with the Sun at one focus
- A line to the Sun sweeps equal areas in equal times
- Period squared is proportional to radius cubed
- Every mass attracts every other mass
The shape of an orbit
According to Kepler's first law, what shape is a planet's orbit?
- An ellipse
- A perfect circle
- A square
- A spiral
The inverse-square law
Newton's law of gravitation is F = G m1 m2 / r squared. The force depends on the two masses and, crucially, on 1 divided by the distance squared. That "squared" matters: if you double the distance, the force falls to a quarter (because 2 squared = 4). Gravity weakens quickly as things move apart.
True of gravity
Select the TWO statements that are true of gravity and orbits.
- Gravity provides the centripetal force that keeps a planet in orbit
- If the distance doubles, the gravitational force falls to a quarter
- Gravity only acts on very large objects
- Gravity pushes planets away from the Sun
Describe versus explain
Kepler and Newton did different jobs. Keep them apart.
Kepler's third law: find the period
A planet orbits the Sun at a mean distance of r = 4 AU. Using Kepler's third law in solar-system units, T squared = r cubed (T in years, r in AU), what is its orbital period T in years? (Hint: 4 cubed = 64, and the square root of 64 is...)
Fast and slow
Kepler's second law (equal areas in equal times) means a planet moves FASTEST when it is...
- Closest to the Sun (at perihelion)
- Farthest from the Sun (at aphelion)
- It always moves at a constant speed
- Over the Sun's poles
The inverse-square law in numbers
Two masses attract with a gravitational force F. If the distance between them is DOUBLED, the new force becomes F divided by n. What is the number n? (Hint: the force depends on 1 / r squared.)
Put it together
A planet's orbit is an _____ with the Sun at one _____. It moves fastest at _____, when closest to the Sun. Kepler's third law states that T squared is proportional to r _____. Newton explained all this with _____, whose force obeys an inverse-square law.
Order by orbital period
Because T squared is proportional to r cubed, planets farther from the Sun take longer to orbit. Put these planets in order of orbital period, SHORTEST first.
- Mercury (0.24 years)
- Venus (0.62 years)
- Earth (1.0 years)
- Mars (1.88 years)
- Jupiter (11.9 years)
Plot Kepler's third law
This graph plots T squared (year squared) up the y-axis against r cubed (AU cubed) along the x-axis. Earth is already marked at (1, 1). Because T squared = r cubed, the data lie on a straight line. Plot the point for a planet at r = 2 AU: its r cubed = 8, so its T squared = 8. Plot (8, 8).
The grade-9 link
The top answers connect Newton to Kepler: gravity is the *cause*, Kepler's laws are the *consequence*. The Sun's gravity provides the centripetal force, and that same inverse-square force is why orbits are ellipses and why T squared is proportional to r cubed. Be ready to calculate: use T squared = r cubed to find a period, and remember that doubling a distance quarters the gravitational force. Describe with Kepler, explain with Newton, and back it with numbers - top band.