What factors led Atlantic community states to seek ways to access Asian markets by avoiding the Mediterranean late in the 15th and early in the 16th-centuries, and what factors enabled the Europeans to quickly assert their hegemony over indigenous peoples in the Americas and to compel Eastern potentates to yield to European commercial demands or to accept Western political control?

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To understand the factors that led Atlantic community states to seek ways to access Asian markets and Europeans to assert their hegemony over indigenous peoples in the Americas, we need to look at the historical context and key elements that contributed to these developments.

1. Motivation for alternative trade routes to Asia:
In the late 15th and early 16th centuries, European powers, particularly Portugal and Spain, were motivated to find alternate trade routes to Asia due to several factors:
- The Ottoman Empire controlled the land-based trade routes through the Mediterranean, imposing high taxes and limiting access.
- The desire to bypass Muslim intermediaries in the spice trade and establish direct trade connections with Asia.
- Growing demand for luxury goods in Europe, including spices, silks, and other valuable commodities.

2. Technological advancements:
Advancements in navigation and shipbuilding technology played a crucial role in enabling European explorers to undertake long, overseas voyages. Notable developments include:
- The development of the caravel, a fast and maneuverable ship that could sail closer to the wind, allowing for longer voyages.
- The invention of the astrolabe and improvements in navigational instruments, aiding sailors in determining their latitude and longitude more accurately.
- The adoption of the compass, which provided reliable directional guidance.

3. Christopher Columbus and the discovery of the Americas:
Christopher Columbus's transatlantic voyages in the late 15th century resulted in the "discovery" of the Americas. This discovery brought several advantages to the European powers:
- Access to vast new territories with abundant resources and potential for colonization.
- The discovery of precious metals, particularly gold and silver, which fueled European economic growth.
- The establishment of colonies, providing bases for further exploration and expansion.

4. Superior military technology:
European powers possessed more advanced military technology compared to indigenous peoples they encountered, giving them an upper hand. Some significant advantages included:
- Firearms, such as muskets and cannons, which gave Europeans a significant edge in battles.
- Improved armor and fighting techniques, providing better protection for European soldiers.
- The presence of organized and disciplined armies, enabling efficient conquest of indigenous populations.

5. Disease and demographic impact:
The unintentional introduction of European diseases, to which indigenous populations had no immunity, resulted in devastating epidemics. This factor significantly impacted indigenous societies, weakening them and facilitating European domination.

6. Political and economic rivalries:
European powers were engaged in fierce competition and rivalries among themselves. This competition drove them to assert their dominance over territories and establish control over valuable resources and trade routes. This drive for economic and political supremacy motivated them to demand concessions from Eastern potentates and indigenous peoples.

It is essential to note that the factors listed above contributed to the overall narrative but may not represent the complete picture across every situation or region. Historical processes are complex and multifaceted, and the specific circumstances varied depending on the time, location, and parties involved.