What is the change in velocity, Av, required for a spacecraft to escape the influence of Earth's gravity? How many times the initial velocity of the spacecraft is this? Assume the spacecraft begins in a circular orbit of altitude h above Earth's surface.
What is the change in velocity, Av, required for a spacecraft to escape the influence of Earth's gravity? How many times the initial velocity of the spacecraft is this? Assume the spacecraft begins in a circular orbit of altitude h above Earth's surface.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![**Title: Understanding Escape Velocity for Spacecraft**
**Introduction:**
In this educational explanation, we will discuss the concept of change in velocity (\(\Delta v\)) required for a spacecraft to escape Earth's gravitational influence. We will also determine how many times this change is compared to the initial velocity of the spacecraft. For this scenario, assume the spacecraft starts in a circular orbit at an altitude \(h\) above Earth's surface.
**Key Concepts:**
1. **Change in Velocity (\(\Delta v\)):** This is the amount by which the spacecraft's velocity needs to be increased to overcome Earth's gravitational pull.
2. **Escape Velocity:** The minimum velocity required for an object to break free from the gravitational attraction of a celestial body without any further propulsion.
3. **Circular Orbit:** A path where the force of gravity provides the exact centripetal force needed to keep an object moving in a circle at a constant altitude \(h\).
**Explanation:**
To calculate the change in velocity, one must consider the spacecraft's current orbital velocity and the additional velocity needed to reach escape velocity. The formula for escape velocity from a planet's surface is:
\[ v_{\text{escape}} = \sqrt{\frac{2GM}{R}} \]
Where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the distance from the planet's center.
While in orbit at altitude \(h\), the gravitational pull is reduced, thus slightly lowering the escape velocity.
**Conclusion:**
By understanding these calculations and concepts, we can determine the necessary \(\Delta v\) to break free from Earth's gravitational hold and explore the broader universe. Students can apply this knowledge to potential real-world scenarios and spacecraft design challenges.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7237bf46-4025-4c4f-b170-df7369a74fb6%2F66ef756d-b347-4768-b852-7af69cd0f231%2Fvdyhh0q_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Escape Velocity for Spacecraft**
**Introduction:**
In this educational explanation, we will discuss the concept of change in velocity (\(\Delta v\)) required for a spacecraft to escape Earth's gravitational influence. We will also determine how many times this change is compared to the initial velocity of the spacecraft. For this scenario, assume the spacecraft starts in a circular orbit at an altitude \(h\) above Earth's surface.
**Key Concepts:**
1. **Change in Velocity (\(\Delta v\)):** This is the amount by which the spacecraft's velocity needs to be increased to overcome Earth's gravitational pull.
2. **Escape Velocity:** The minimum velocity required for an object to break free from the gravitational attraction of a celestial body without any further propulsion.
3. **Circular Orbit:** A path where the force of gravity provides the exact centripetal force needed to keep an object moving in a circle at a constant altitude \(h\).
**Explanation:**
To calculate the change in velocity, one must consider the spacecraft's current orbital velocity and the additional velocity needed to reach escape velocity. The formula for escape velocity from a planet's surface is:
\[ v_{\text{escape}} = \sqrt{\frac{2GM}{R}} \]
Where:
- \( G \) is the gravitational constant,
- \( M \) is the mass of the planet,
- \( R \) is the distance from the planet's center.
While in orbit at altitude \(h\), the gravitational pull is reduced, thus slightly lowering the escape velocity.
**Conclusion:**
By understanding these calculations and concepts, we can determine the necessary \(\Delta v\) to break free from Earth's gravitational hold and explore the broader universe. Students can apply this knowledge to potential real-world scenarios and spacecraft design challenges.
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