The Kepler constant, denoted as k, is a mathematical constant used in Kepler's laws of planetary motion. It is equal to the square root of the gravitational constant G times the mass of the central body, divided by the semi-major axis of the orbit cubed. The Kepler constant helps to describe the relationship between the orbital period and the size of the orbit for a celestial body orbiting around another body under the influence of gravity. **

The Kepler Conjecture is a mathematical problem proposed by German astronomer and mathematician Johannes Kepler in 1611. It deals with the most efficient way to pack spheres in a container, such as a box or a crate. The conjecture states that the most efficient way to pack spheres is in a pyramid-like arrangement, with each sphere touching a certain number of neighboring spheres. The conjecture was finally proven by American mathematician Thomas Hales in 1998, using complex computer-assisted methods. The Kepler Conjecture has important implications in fields such as materials science and engineering, where efficient packing of spheres is crucial. **

Johannes Kepler was a German astronomer and mathematician who is best known for his laws of planetary motion. He worked closely with Tycho Brahe and used Brahe's precise astronomical data to develop his laws, which revolutionized our understanding of the movement of planets. Kepler also made significant contributions to the field of optics and is considered one of the key figures in the scientific revolution of the 17th century. His work laid the foundation for Isaac Newton's theory of universal gravitation. **

Yes, Johannes Kepler is featured on the German 10 Deutsche Mark coin, which was minted from 1969 to 2001. The coin commemorates the 400th anniversary of Kepler's birth and features his portrait on the obverse side. Additionally, there are commemorative coins and medals that have been issued in various countries to honor Kepler's contributions to astronomy and mathematics. These coins are sought after by collectors and can be found in numismatic circles. **

The Johannes Kepler School in Karlsruhe is a secondary school that offers a focus on mathematics, natural sciences, and technology. It provides a specialized education for students interested in these fields, with a curriculum designed to prepare them for further studies or careers in STEM-related fields. The school is named after the famous astronomer Johannes Kepler, known for his work in the field of astronomy and mathematics. **

The 2nd law of Kepler, also known as the law of equal areas, states that a line segment joining a planet and the sun sweeps out equal areas during equal intervals of time. This means that a planet moves faster when it is closer to the sun and slower when it is farther away, in order to maintain the equal area sweep. This law helps to describe the speed at which a planet orbits the sun and the changing velocity as it moves along its elliptical path. **

Stock dividends are additional shares of a company's stock that are distributed to existing shareholders as a form of dividend payment. Instead of receiving cash, shareholders receive more shares of the company's stock. This can be a way for a company to reward its shareholders without using cash, and it can also help to increase the number of shares outstanding. Stock dividends are typically expressed as a percentage, such as a 5% stock dividend, which means that for every 100 shares owned, the shareholder would receive an additional 5 shares. **

Yes, it can be worth investing in a stock portfolio with small amounts of money. Even small investments can grow over time through the power of compounding. Additionally, investing in a diversified portfolio of stocks can help spread risk and potentially provide better returns compared to keeping money in a savings account. With the accessibility of low-cost investment platforms and fractional shares, it is easier than ever to start investing with small amounts of money. However, it's important to do thorough research and consider the potential risks before investing. **