One of Kepler's laws relates the square of the orbital period to what other quantity? The radius The square root of the radius The radius squared The radius cubed
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The semi-major axis is essentially the average distance of the planet from the sun. In simpler terms, if we consider a circular orbit, the semi-major axis is the radius. Show more…
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Kepler's Third Law 1. THE LAW OF PERIODS: The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit. 2. Consider a circular orbit with radius r (the radius of a circle is equivalent to the semimajor axis of an ellipse). Applying Newton's second law to the orbiting planet yields 3. Using the relation of the angular velocity, ω, and the period, T; 4. r must (for ellipses) be replaced by a, but the formula still holds.
Sri K.
The squares of the periods of planetary orbits are proportional to the cube of the orbital radii. For orbits about the Sun, period and distance are correlated, not independent. If you know the distance of a planet from the Sun, there is only one speed and one period it can have if in a natural orbit. There cannot be another body in the same orbit as Earth moving faster or slower than Earth does. We derived this result by considering circular orbits. Kepler and Newton showed it holds more generally for all non-circular – elliptical – orbits. In that case, the radius R is replaced by the average distance from the Sun (also known as the semi-major axis length) denoted a. The formula can be simplified by expressing a in units of A.U.s (1 AU = average Earth-Sun distance = 149,600,000 km) and the period (which we now denote by P) in Earth-years. With those unit conversions, one gets: a^3 = P^2 This result is known as Kepler’s third law. Both of the following questions can be quickly answered using this result. Q5) If a planet orbits the Sun at an average distance of 10 AU (ten times further from the Sun than the Earth is, near Saturn’s orbit), what is its orbital period? Q6) To have an orbital period of 10 years, what average distance must the body have from the Sun?
Jeff V.
Kepler's Third Law can be stated as "The orbital period, T, squared divided by the semi-major axis, s, cubed is a constant for all planets in orbit around the Sun." Use Newton's Universal Law of Gravity to determine the constant, T^2s^3, in terms of the mass of the Sun, M, and any other constants.
Madhur L.
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