Neptune's largest moon, Triton, has an orbital period of 5.88 days and is 3.55 x 105 km from the planet. At what distance (in m) would the moon need to be to escape the planet at its current cin velocity? Part 1 of 4 Newton's interpretation of Kepler's Third Law describes how the distance between any two bodies and the orbital period are related: p² -- (472),² GM where G = 6.67 x 10-11 m³/s2/kg. Part 2 of 4 We can use this expression to determine the mass of the planet-moon system. Convert kilometers to meters using 1 km = 1,000 m. (Enter your answer to at least three significant figures.) m = m Convert the period into seconds. (Enter your answer to at least three significant figures.) Psec = Pdays (24hr) (3,600 s) 1 day. 1 hr Psec = seconds Now solve the expression for M and plug in the period in seconds and the distance in meters. (47²)(rm) ³ G (Psec)² M = M = kg

Neptune's largest moon, Triton, has an orbital period of 5.88 days and is 3.55 x 105 km from the planet. At what distance (in m) would the moon need to be to escape the planet at its current cin velocity? Part 1 of 4 Newton's interpretation of Kepler's Third Law describes how the distance between any two bodies and the orbital period are related: p² -- (472),² GM where G = 6.67 x 10-11 m³/s2/kg. Part 2 of 4 We can use this expression to determine the mass of the planet-moon system. Convert kilometers to meters using 1 km = 1,000 m. (Enter your answer to at least three significant figures.) m = m Convert the period into seconds. (Enter your answer to at least three significant figures.) Psec = Pdays (24hr) (3,600 s) 1 day. 1 hr Psec = seconds Now solve the expression for M and plug in the period in seconds and the distance in meters. (47²)(rm) ³ G (Psec)² M = M = kg

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter7: Gravity

Section: Chapter Questions

Problem 15PQ: When Sedna was discovered in 2003, it was the most distant object known to orbit the Sun. Currently,...

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Question

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Neptune's largest moon, Triton, has an orbital period of 5.88 days and is 3.55 x 105 km from the planet. At what distance (in m) would the moon need to be to escape the planet at its current circular
velocity?
Part 1 of 4
Newton's interpretation of Kepler's Third Law describes how the distance between any two bodies and the orbital period are related:
477²
GM
where G = 6.67 x 10-11 m³/s2/kg.
Part 2 of 4
We can use this expression to determine the mass of the planet-moon system.
Convert kilometers to meters using 1 km = 1,000 m. (Enter your answer to at least three significant figures.)
rm =
m
Convert the period into seconds. (Enter your answer to at least three significant figures.)
24 hr
P sec
Psec =
p2
p² =
=
M =
M =
thr) (³,61
Pdays 1 day
Now solve the expression for M and plug in the period in seconds and the distance in meters.
(4π²) (rm) ³
2
G
(Psec)²
3,600 s
1 hr
seconds
kg

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Once we have the mass, we can determine the magnitude of the circular velocity of the moon using the expression:
GM
Vc =
Vc
m/s

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