In the best case scenario for a gravity boost, a spacecraft approaches a planet very closely and does a U-turn around it, heading back exactly in the direction it came (see the image below). Before Collision V After Collision If the spacecraft was initially going to the right with a speed of 3 km/s, and the planet was going to the left at a speed of 14 km/s, what would be the fastest the spacecraft could be going after the U-turn, in km/s?

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Chapter1: Units, Trigonometry. And Vectors
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Please check if my work below is correct for the question. And that the answer is correct. And also what is the limit on how many gravity assists a single spacecraft can get. Is it one, two, three, none, or there is limits. I keep getting either two or their is no limits
In the best case scenario for a gravity boost, a spacecraft approaches a planet very
closely and does a U-turn around it, heading back exactly in the direction it came
(see the image below).
Before Collision
After Collision
If the spacecraft was initially going to the right with a speed of 3 km/s, and the
planet was going to the left at a speed of 14 km/s, what would be the fastest the
spacecraft could be going after the U-turn, in km/s?
Transcribed Image Text:In the best case scenario for a gravity boost, a spacecraft approaches a planet very closely and does a U-turn around it, heading back exactly in the direction it came (see the image below). Before Collision After Collision If the spacecraft was initially going to the right with a speed of 3 km/s, and the planet was going to the left at a speed of 14 km/s, what would be the fastest the spacecraft could be going after the U-turn, in km/s?
V₁ = (1 + v)
V₁ = (3 km/s + 14 km/s) = 17 km/s
= (17 km/s + 14 km/s)
= 31 km/s
Transcribed Image Text:V₁ = (1 + v) V₁ = (3 km/s + 14 km/s) = 17 km/s = (17 km/s + 14 km/s) = 31 km/s
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