Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 17, Problem 68Q
To determine

(a)

The distance to 70 Ophiuchi in parsecs.

Expert Solution
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Answer to Problem 68Q

5 Parsecs

Explanation of Solution

Given:

Parallax=0.2arcsec

Formula used:

P=1d

Calculation:

d=10.2 arcsecd= 5 pc

Conclusion:

The distance to 70 Ophiuchi in parsecs = 5 pc

To determine

(b)

The actual length of the semimajor axis in AU.

Expert Solution
Check Mark

Answer to Problem 68Q

Actual length of the semimajor axis in astronomical units = 22.5 au

Explanation of Solution

Given:

The distance to 70 Ophiuchi in parsecs = 5 Parsecs (calculated in Part a)

Apparent length of semimajor axis=4.5arcsec

Formula Used:

α=Dd×206265

1 pc = 206265 au

Calculation:

α=Dd×206265D=αd206265D=4.5×5206265 pcD=4.5×5206265×206265 auD=22.5 au

Conclusion:

Thus, semi major axis is 22.5 au

To determine

(c)

The sum of the mass of the two stars.

Expert Solution
Check Mark

Answer to Problem 68Q

The sum of masses of the 2 stars in 70 Ophiuchi = 1.495 M

Explanation of Solution

Given:

Period=87.7years

Formula Used:

T2=4π2G( M 1 + M 2 )a3M1+M2=4π2GT2a3

Where, M represents mass, G is the gravitational constant, T is the period and a is the semi-major axis.

1M=1.989×1030 kg

1 au = 1.496×108 km1 year = 365×24×60×60 s

Calculation:

M1+M2=4π2GT2a3M1+M2=4π26.67259 × 10- 11 Nm2 kg -2 ( 87.7×365×24×60×60 )2  s2(22.5×1.496×1011)3 m3M1+M2=2.9735×1030kgM1+M2=2.9735×1030kgM1+M2=2.9735× 10 301.989× 10 30MM1+M2=1.495 M

Conclusion:

The sum of masses of the 2 stars in 70 Ophiuchi = 1.495 M

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Students have asked these similar questions
The nearest star to our solar system is 4.29 light years away. How much is thisdistance in terms of parsecs? How much parallax would this star (named Alpha Centauri) show when viewed from two locations of the Earth six months apart in its orbit around the Sun ?
Use a diagram to explain what is meant by the parallax angle, p, for a star observed twice from Earth, with a 6-month interval between each observation. Hence define the parsec, and calculate its value in astronomical units and metres. The star Betelgeuse is observed to have a parallax angle p = 4.5 × 10−3 arcseconds. State the distance of Betelgeuse in units of parsecs and light years.
the parallax angle of a star to be 0.002 arc-seconds.  what would the  distance be to this star?

Chapter 17 Solutions

Universe: Stars And Galaxies

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