(c) The velocity of objects in circular orbits are constant (unlike in ellipotical orbits). This allows us to find rhe velocity of each star. What is the velocity (, and 12) of each star in this binary system? Report your answer in units of kilometers per second (km/s). Hint: you will need to convert period to seconds and orbital radii to meters, and then finally convert your answer from m/s to km/s. Use the following formula for each star, noting that they have they must share the same perood (p): 1 = 2πα, and pv₂ = 2α (d) In reality, it would be unlikely for astronomers to know the masses of bianryb stars and find radii, period and velocities. Instead, they often observe velocities and period of the stars motion using the doppler-shift method and then calculate their masses. If two stars form a binary system with a circular obit that has a period of p = 544 days, with each star's velocity given by v₁ = 98.5 km/s and v₂ = 177 km/s, then what are the masses (m, and m₂) of each star? Report your answer in units of solar masses (Mo). Hint: work mostly backwards through the steps laid out in parts (a) through (c) above, but be prepared to rearrnage some equations (especially those in part (a)). Convert everything to base units of seconds, kilograms and meters until you get your final answer, and then convert that to solar mass.
(c) The velocity of objects in circular orbits are constant (unlike in ellipotical orbits). This allows us to find rhe velocity of each star. What is the velocity (, and 12) of each star in this binary system? Report your answer in units of kilometers per second (km/s). Hint: you will need to convert period to seconds and orbital radii to meters, and then finally convert your answer from m/s to km/s. Use the following formula for each star, noting that they have they must share the same perood (p): 1 = 2πα, and pv₂ = 2α (d) In reality, it would be unlikely for astronomers to know the masses of bianryb stars and find radii, period and velocities. Instead, they often observe velocities and period of the stars motion using the doppler-shift method and then calculate their masses. If two stars form a binary system with a circular obit that has a period of p = 544 days, with each star's velocity given by v₁ = 98.5 km/s and v₂ = 177 km/s, then what are the masses (m, and m₂) of each star? Report your answer in units of solar masses (Mo). Hint: work mostly backwards through the steps laid out in parts (a) through (c) above, but be prepared to rearrnage some equations (especially those in part (a)). Convert everything to base units of seconds, kilograms and meters until you get your final answer, and then convert that to solar mass.
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Chapter1: The Study Of Minerals
Section: Chapter Questions
Problem 1LR
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Transcribed Image Text:(c) The velocity of objects in circular orbits are constant (unlike in ellipotical orbits). This allows us to find rhe
velocity of each star. What is the velocity (, and 12) of each star in this binary system? Report your answer in
units of kilometers per second (km/s). Hint: you will need to convert period to seconds and orbital radii to
meters, and then finally convert your answer from m/s to km/s. Use the following formula for each star, noting
that they have they must share the same perood (p):
1 = 2πα,
and
pv₂ = 2α
(d) In reality, it would be unlikely for astronomers to know the masses of bianryb stars and find radii, period and
velocities. Instead, they often observe velocities and period of the stars motion using the doppler-shift method
and then calculate their masses. If two stars form a binary system with a circular obit that has a period of p =
544 days, with each star's velocity given by v₁ = 98.5 km/s and v₂ = 177 km/s, then what are the masses
(m, and m₂) of each star? Report your answer in units of solar masses (Mo). Hint: work mostly backwards
through the steps laid out in parts (a) through (c) above, but be prepared to rearrnage some equations
(especially those in part (a)). Convert everything to base units of seconds, kilograms and meters until you get
your final answer, and then convert that to solar mass.
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