Explanation:
Abstract
Most planetary systems are formed within stellar clusters, and these environments can shape their properties. This paper considers scattering encounters between solar systems and passing cluster members, and calculates the corresponding interaction cross-sections. The target solar systems are generally assumed to have four giant planets, with a variety of starting states, including circular orbits with the semimajor axes of our planets, a more compact configuration, an ultracompact state with multiple mean motion resonances, and systems with massive planets. We then consider the effects of varying the cluster velocity dispersion, the relative importance of binaries versus single stars, different stellar host masses, and finite starting eccentricities of the planetary orbits. For each state of the initial system, we perform an ensemble of numerical scattering experiments and determine the cross-sections for eccentricity increase, inclination angle increase, planet ejection, and capture. This paper reports results from over 2 million individual scattering simulations. Using supporting analytic considerations, and fitting functions to the numerical results, we find a universal formula that gives the cross-sections as a function of stellar host mass, cluster velocity dispersion, starting planetary orbital radius, and final eccentricity. The resulting cross-sections can be used in a wide variety of applications. As one example, we revisit constraints on the birth aggregate of our Solar system due to dynamical scattering and find N ≲ 104 (consistent with previous estimates).
60% change from 500 to 800
Answer:
The perimeter of the triangle is 2+√2
Explanation:
Since one of the angles of the triangle is 90°, the triangle in question is a right angled triangle.
Since two angles of the triangle are also equal, then two of the its sides will be equal.
Let the opposite and the adjacent sides of the triangle be 1. To get the hypotenuse side, we will apply the Pythagoras theorem which States;
Hypotenuse² = Adjacent²+opposite²
Hyp² = 1²+1²
Hyp = √1²+1²
Hyp = √2
The third side of the triangle is √2.
The perimeter of the triangle will be the sum of all its sides i.e 1+1+√2
= 2+√2
The perimeter of the triangle will be 2+√2
Gross domestic product tracks the health of a country's economy. It represents the value of all goods and services produced over a specific time period within a country's borders. Economists can use GDP to determine whether an economy is growing or experiencing a recession.
Mountains have an extremely important role in influencing global and regional climates and weather conditions. They cover around one-quarter of the earth's land surface and are home to 720 million people around the world. Indirectly, billions more living downstream also benefit from mountains.
Mountains provide us with freshwater, energy, food, biodiversity, and medicinal products – resources that may become very rare in the coming decades.
