2. In a binary star system, the two stars orbit the center of mass of the system. If both stars have the same mass M, the center of mass will be midway between the stars. Assume the orbital radius is R. Answer in terms of G, M and R. 0. Determine the orbital speed of the stars. (Your answer should not be the same as the answer for 1b.) Note that the Earth and moon also actually both orbit around the center of mass of the Earth-moon system. However, the Earth is so much more massive than the moon that the center of mass is very close to the center of the Earth and as an approximation we say the moon orbits around the Earth. * b. A space probe is exactly halfway between the two stars. Determine the minimum speed the space probe must be moving so that it can escape from the binary star-that is the space probe can just reach an infinite distance away from the stars. This speed is called the escape speed. We want to just reach infinity. This means we will have zero speed at infinity. Using conservation of energy, we have: U₁ + K₁ = U∞ + K c. Determine the escape speed for a object from the surface of the Earth. First give the answer symbolically in terms of the mass of the Earth My and the radius of the Earth Rg and then calculate the value numerically. Show work! Show the numbers you use. Do not just look up the answer! Again, conservation of energy we have: U₁ + K₁ = U∞ + K
2. In a binary star system, the two stars orbit the center of mass of the system. If both stars have the same mass M, the center of mass will be midway between the stars. Assume the orbital radius is R. Answer in terms of G, M and R. 0. Determine the orbital speed of the stars. (Your answer should not be the same as the answer for 1b.) Note that the Earth and moon also actually both orbit around the center of mass of the Earth-moon system. However, the Earth is so much more massive than the moon that the center of mass is very close to the center of the Earth and as an approximation we say the moon orbits around the Earth. * b. A space probe is exactly halfway between the two stars. Determine the minimum speed the space probe must be moving so that it can escape from the binary star-that is the space probe can just reach an infinite distance away from the stars. This speed is called the escape speed. We want to just reach infinity. This means we will have zero speed at infinity. Using conservation of energy, we have: U₁ + K₁ = U∞ + K c. Determine the escape speed for a object from the surface of the Earth. First give the answer symbolically in terms of the mass of the Earth My and the radius of the Earth Rg and then calculate the value numerically. Show work! Show the numbers you use. Do not just look up the answer! Again, conservation of energy we have: U₁ + K₁ = U∞ + K
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Transcribed Image Text:2. In a binary star system, the two stars orbit the center of mass of the system. If both stars have the same mass M, the
center of mass will be midway between the stars. Assume the orbital radius is R. Answer in terms of G, M and R.
a. Determine the orbital speed of the stars. (Your answer should
not be the same as the answer for 1b.)
Note that the Earth and moon also actually both orbit around the center of mass of the Earth-moon system.
However, the Earth is so much more massive than the moon that the center of mass is very close to the center of the
Earth and as an approximation we say the moon orbits around the Earth.
b. A space probe is exactly halfway between the two stars. Determine the minimum speed the space probe must
be moving so that it can escape from the binary star-that is the space probe can just reach an infinite distance
away from the stars. This speed is called the escape speed.
C.
*
We want to just reach infinity. This means we will have zero speed at infinity. Using conservation of energy, we
have:
U₁ + K₁=U + K
Determine the escape speed for a object from the surface of the Earth. First give the answer symbolically in
terms of the mass of the Earth Me and the radius of the Earth R. and then calculate the value numerically.
Show work! Show the numbers you use. Do not just look up the answer!
Again, conservation of energy we have:
U₁ + K₁=U + Ko
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