The figures show a hypothetical planetary system at two different times. The system has a star S and three planets, labeled A, B, and C. The table provides the mass of each body in the system, as well as their spatial coordinates (x, y) in their initial and final positions. The spatial coordinates of the bodies are given in Astronomical Units (AU). Initital Position Body S A B C Mass (kg) mg = 2.3863 × 10³⁰ mA = 2.1957 × 1028 m³ = 6.2841 × 1026 mc = 7.8063 x× 1027 (0,0) (0.4815, 0) (0.4373, 1.3397) (0, 1.6711) Final Position (xs, ys) (0, -0.4913) (-1.6007, 0) (-0.8443,-0.7481) The initial velocity of the center of mass of the system is zero. Find the magnitude ds of the star's displacement from the origin in its final position.

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Chapter1: Units, Trigonometry. And Vectors
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The initial velocity of the center of mass of the system is zero.
Find the magnitude de of the star's displacement from the origin in its final position.
ds =
C
S (0,0)
Initial Position
A
B
AU
B
С.
S
A
Final Position
Transcribed Image Text:The initial velocity of the center of mass of the system is zero. Find the magnitude de of the star's displacement from the origin in its final position. ds = C S (0,0) Initial Position A B AU B С. S A Final Position
The figures show a hypothetical planetary system at two different times. The system has a star S and three planets, labeled A, B,
and C. The table provides the mass of each body in the system, as well as their spatial coordinates (x, y) in their initial and final
positions. The spatial coordinates of the bodies are given in Astronomical Units (AU).
Initital Position
Body
S
A
B
с
Mass (kg)
mg = 2.3863 × 10³⁰
mA = 2.1957 × 1028
mB = 6.2841 × 1026
mc = 7.8063 × 1027
The initial velocity of the center of mass of the system is zero.
Find the magnitude ds of the star's displacement from the origin in its final position.
C
S (0,0)
(0,0)
(0.4815, 0)
(0.4373, 1.3397)
(0, 1.6711)
A
Final Position
(xs, ys)
(0, -0.4913)
B
(-1.6007, 0)
(-0.8443,-0.7481)
B
●
С.
S
A
Transcribed Image Text:The figures show a hypothetical planetary system at two different times. The system has a star S and three planets, labeled A, B, and C. The table provides the mass of each body in the system, as well as their spatial coordinates (x, y) in their initial and final positions. The spatial coordinates of the bodies are given in Astronomical Units (AU). Initital Position Body S A B с Mass (kg) mg = 2.3863 × 10³⁰ mA = 2.1957 × 1028 mB = 6.2841 × 1026 mc = 7.8063 × 1027 The initial velocity of the center of mass of the system is zero. Find the magnitude ds of the star's displacement from the origin in its final position. C S (0,0) (0,0) (0.4815, 0) (0.4373, 1.3397) (0, 1.6711) A Final Position (xs, ys) (0, -0.4913) B (-1.6007, 0) (-0.8443,-0.7481) B ● С. S A
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