An extrasolar planet can be detected by observing the wobble it produces on the star around which it revolves. Suppose an extrasolar planet of mass m B revolves around its star of mass m A . If no external force acts on this simple two-object system, then its cm is stationary. Assume m A and m B are in circular orbits with radii r A and r B about the system’s CM. ( a ) Show that r A = m B m A r B . ( b ) Now consider a Sun-like star and a single planet with the same characteristics as Jupiter. That is, m B = 1.0 × 10 –3 m a and the planet has an orbital radius of 8.0 × 10 11 m. Determine the radius r A of the star’s orbit about the system’s cm. ( c ) When viewed from Earth, the distant system appears to wobble over a distance of 2 r A . If astronomers are able to detect angular displacements q of about 1 milliarcsec ( 1 arcsec = 1 3600 of a degree ) , from what distance d (in light-years) can the star’s wobble be detected (l ly = 9.46 × 10 15 m)? ( d ) The star nearest to our Sun is about 4 ly away. Assuming stars are uniformly distributed throughout our region of the Milky Way Galaxy, about how many stars can this technique be applied to in the search for extrasolar planetary systems?
An extrasolar planet can be detected by observing the wobble it produces on the star around which it revolves. Suppose an extrasolar planet of mass m B revolves around its star of mass m A . If no external force acts on this simple two-object system, then its cm is stationary. Assume m A and m B are in circular orbits with radii r A and r B about the system’s CM. ( a ) Show that r A = m B m A r B . ( b ) Now consider a Sun-like star and a single planet with the same characteristics as Jupiter. That is, m B = 1.0 × 10 –3 m a and the planet has an orbital radius of 8.0 × 10 11 m. Determine the radius r A of the star’s orbit about the system’s cm. ( c ) When viewed from Earth, the distant system appears to wobble over a distance of 2 r A . If astronomers are able to detect angular displacements q of about 1 milliarcsec ( 1 arcsec = 1 3600 of a degree ) , from what distance d (in light-years) can the star’s wobble be detected (l ly = 9.46 × 10 15 m)? ( d ) The star nearest to our Sun is about 4 ly away. Assuming stars are uniformly distributed throughout our region of the Milky Way Galaxy, about how many stars can this technique be applied to in the search for extrasolar planetary systems?
An extrasolar planet can be detected by observing the wobble it produces on the star around which it revolves. Suppose an extrasolar planet of mass mB revolves around its star of mass mA. If no external force acts on this simple two-object system, then its cm is stationary. Assume mA and mB are in circular orbits with radii rA and rB about the system’s CM. (a) Show that
r
A
=
m
B
m
A
r
B
.
(b) Now consider a Sun-like star and a single planet with the same characteristics as Jupiter. That is, mB= 1.0 × 10–3ma and the planet has an orbital radius of 8.0 × 1011 m. Determine the radius rA of the star’s orbit about the system’s cm. (c) When viewed from Earth, the distant system appears to wobble over a distance of 2rA. If astronomers are able to detect angular displacementsq of about 1 milliarcsec
(
1
arcsec
=
1
3600
of a degree
)
, from what distance d (in light-years) can the star’s wobble be detected (l ly = 9.46 × 1015m)? (d) The star nearest to our Sun is about 4 ly away. Assuming stars are uniformly distributed throughout our region of the Milky Way Galaxy, about how many stars can this technique be applied to in the search for extrasolar planetary systems?
Definition Definition Angle at which a point rotates around a specific axis or center in a given direction. Angular displacement is a vector quantity and has both magnitude and direction. The angle built by an object from its rest point to endpoint created by rotational motion is known as angular displacement. Angular displacement is denoted by θ, and the S.I. unit of angular displacement is radian or rad.
A space vehicle is traveling at 4450 km/h relative to the Earth when the exhausted rocket motor is disengaged and sent backward with a speed of 82 km/h relative to the command module. The mass of the motor is four times the mass of the module. What is the speed (km/h) of the command module relative to Earth after the separation? (Note: this answer requires slightly higher precision than normal.)
An average-sized asteroid located 5.0x107 km from the centre of the Earth with mass 2.0x1013 kg is detected headed directly toward Earth with a speed of 2.0 km/s. What will its speed before it hits the Earth's atmosphere (400 km above ground)?
Find the kinetic energy for two masses, m1=(64±3)Kg and m2=(136±4)Kg, traveling together at a velocity v=(5.0±1.5)m/s.
Hint: the equation for kinetic energy is E = 1/2mv^2, where m is the total mass (m1+m2).
Chapter 9 Solutions
Physics For Scientists & Engineers, Vols. 1 & 2, And Masteringphysics With E-book Student Access Kit (4th Edition)
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