space probe approaches a planet and goes into a low orbit. If the orbiting probe's velocity is Vx = -v sin(wt), Vy = v cos(wt), v = 7.55 x 103 m/s, w = 1.16 x 103 radians/s, at is the average magnitude of acceleration of the probe, in m/s?, if it remains in orbit for 30 minutes? m/s2
space probe approaches a planet and goes into a low orbit. If the orbiting probe's velocity is Vx = -v sin(wt), Vy = v cos(wt), v = 7.55 x 103 m/s, w = 1.16 x 103 radians/s, at is the average magnitude of acceleration of the probe, in m/s?, if it remains in orbit for 30 minutes? m/s2
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![### Orbital Mechanics Problem
A space probe approaches a planet and goes into a low orbit. If the orbiting probe's velocity is given by:
\[ v_x = -v \sin(\omega t), \]
\[ v_y = v \cos(\omega t), \]
where:
\[ v = 7.55 \times 10^3 \ \text{m/s}, \]
\[ \omega = 1.16 \times 10^{-3} \ \text{radians/s}, \]
and the probe remains in orbit for \( 30 \) minutes, determine the average magnitude of acceleration of the probe in \( \text{m/s}^2 \).
### Calculation
The box below is for entering the calculated average acceleration:
\[ \boxed{\ \ \ \ \ } \ \text{m/s}^2 \]
---
In this problem, we are given the velocity components \( v_x \) and \( v_y \), and we need to find the average acceleration of the probe. Given that the time the probe remains in orbit is 30 minutes, you need to convert this to seconds for calculations.
Ensure you apply the correct orbital mechanics formulas and principles to arrive at the solution. The average magnitude of acceleration should be calculated using the information provided.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F862d67f6-41ff-41a6-a751-26ec3266bc03%2F044d18e0-ef56-494a-93f7-6caab5b54445%2Firnj00c.png&w=3840&q=75)
Transcribed Image Text:### Orbital Mechanics Problem
A space probe approaches a planet and goes into a low orbit. If the orbiting probe's velocity is given by:
\[ v_x = -v \sin(\omega t), \]
\[ v_y = v \cos(\omega t), \]
where:
\[ v = 7.55 \times 10^3 \ \text{m/s}, \]
\[ \omega = 1.16 \times 10^{-3} \ \text{radians/s}, \]
and the probe remains in orbit for \( 30 \) minutes, determine the average magnitude of acceleration of the probe in \( \text{m/s}^2 \).
### Calculation
The box below is for entering the calculated average acceleration:
\[ \boxed{\ \ \ \ \ } \ \text{m/s}^2 \]
---
In this problem, we are given the velocity components \( v_x \) and \( v_y \), and we need to find the average acceleration of the probe. Given that the time the probe remains in orbit is 30 minutes, you need to convert this to seconds for calculations.
Ensure you apply the correct orbital mechanics formulas and principles to arrive at the solution. The average magnitude of acceleration should be calculated using the information provided.
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