What mathematical formula relates to the distances of the first six planets from the sun?

What mathematical formula relates to the distances of the first six planets from the sun?

• A. Kepler's laws
• B. Bode's law
• C. Newton's law of gravitation
• D. Universal law of gravitation

Answer: (B)

Bode's law, also known as the Titius-Bode law, provides a mathematical formula that estimates the distances of the planets from the Sun in our solar system, particularly for the first six planets. This law suggests a simple progression of the distances of planets from the Sun based on an arithmetic sequence. It states that if you take the sequence 0, 3, 6, 12, 24, and 48 (which are created by doubling the previous term), and then add 4 to each term, you get values that approximate the semi-major axes of the planets, measured in astronomical units (AU).

For instance, using this law, the distances for Mercury, Venus, Earth, Mars, Jupiter, and Saturn can be derived quite closely to their actual distances from the Sun. The simplicity and regularity of this formula made it historically significant, even though modern astronomy recognizes that there are more nuanced factors influencing planetary distance.

This concept stands apart from Kepler's laws, which describe the motion of planets and their elliptical orbits, rather than providing a numerical method to estimate their distances. Newton's laws of gravitation pertain to the forces acting on the planets and their motion but do not specifically relate to the distances