Loose Leaf For Explorations: Introduction To Astronomy
9th Edition
ISBN: 9781260432145
Author: Thomas T Arny, Stephen E Schneider Professor
Publisher: McGraw-Hill Education
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Chapter 3, Problem 7QFR
To determine
Estimating the mass of the planet using the motion of the moon.
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Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 1011 solar masses. A star orbiting near the galaxy's periphery is 5.6 x 104 light-years from its center.
(a) What should the orbital period (in y) of that star be?
y
(b) If its period is 5.3 x 107 years instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of other matter, such as a very massive black hole at the center of
the Milky Way.
solar masses
We sent a probe out to orbit the planet Kerbal at a distance of 5.5x107m from the middle of the planet. It took our probe 3.5x105s to orbit the planet.
Which formula will be used to solve this problem?
Possible Formulas that can be used to answer the question:
v=(2πr)/T
ac=v2/r
ac=(4π2r)/T2
Fc=mac
Fg=mg
F=(Gm1m2)/d2
g=Gm/r2
T2=(4π2/Gm)r3
v=√(Gm)/r
g=9.80m/s2
G=6.67x10-11 (N∙m2)/kg2
Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 6.0 ✕ 104 light years from its center.
(a)
What should the orbital period (in y) of that star be?
y
(b)
If its period is 6.9 ✕ 107 y instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.
solar masses
Chapter 3 Solutions
Loose Leaf For Explorations: Introduction To Astronomy
Ch. 3 - What is meant by inertia?Ch. 3 - (3.1) What does Newtons first law of motion tell...Ch. 3 - Explain how inertia and gravity are both involved...Ch. 3 - How does mass differ from weight?Ch. 3 - If your mass is 70 kg on Earth, what is it on the...Ch. 3 - What is Newtons law of gravity?Ch. 3 - Prob. 7QFRCh. 3 - (3.7) If you weigh 110 pounds on Earth, do you...Ch. 3 - Prob. 9QFRCh. 3 - Prob. 10QFR
Ch. 3 - Prob. 1TQCh. 3 - Prob. 2TQCh. 3 - (3.2) Is there a force of gravity between the...Ch. 3 - (3.3) Use Newtons second law of motion to explain...Ch. 3 - (3.4) How many times greater is Earths...Ch. 3 - Prob. 6TQCh. 3 - Prob. 7TQCh. 3 - Prob. 8TQCh. 3 - Prob. 9TQCh. 3 - Prob. 10TQCh. 3 - Prob. 11TQCh. 3 - (3.3) If you apply a force F to a mass m, it...Ch. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - (3.6) Gliese 581e is an exoplanet with a mass of...Ch. 3 - (3.7) Using the method of section 3.7, compare the...Ch. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - Prob. 12PCh. 3 - Prob. 13PCh. 3 - Prob. 1TYCh. 3 - Prob. 2TYCh. 3 - Prob. 3TYCh. 3 - Prob. 4TYCh. 3 - Prob. 5TYCh. 3 - Prob. 6TYCh. 3 - Prob. 7TYCh. 3 - Prob. 8TYCh. 3 - Prob. 9TY
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- Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 • 1011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0 • 104 light years from its center. a) What should the orbital period of that star be in years? b) If its period is 6.0 • 107 years instead, what is the mass of the galaxy in solar masses? Such calculations are used to imply the existence of “dark matter” in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.arrow_forwardTaking the age of Earth to be about 4 ✕ 109 years and assuming its orbital radius of 1.5 ✕ 1011 m has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun). ..............m Answer and simplifyarrow_forwardTaking the age of Earth to be about 4 ✕ 109 years and assuming its orbital radius of 1.5 ✕ 1011 m has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun). ..............marrow_forward
- Taking the age of Earth to be about 4 ✕ 109 years and assuming its orbital radius of 1.5 ✕ 1011 m has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun).............marrow_forwardAstronomical Datat Mass (kg) 1.99 × 1030 7.35 X 1022 3.30 × 1023 4.87 X 1024 5.97 X 1024 6.42 × 1023 1.90 × 10²7 5.68 × 1026 8.68 × 1025 1.02 × 1026 1.31 × 1022 Body Sun Moon Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto O 4.17 x 10^23 N O 5.16 x 10^31 N O 5.16 x 10^23 N Radius (m) 6.96 × 108 1.74 X 106 O 3.24 x 10^35 N 2.44 X 106 6.05 X 106 6.37 X 106 3.39 X 106 6.99 X 107 5.82 x 107 2.54 x 107 2.46 X 107 1.15 X 106 Orbit radius (m) What force maintains planet Jupiter's orbit around the Sun? 3.84 × 108 5.79 × 1010 1.08 × 10¹1 1.50 × 10¹1 2.28 × 10¹11 7.78 x 10¹1 1.43 × 10¹2 2.87 × 10¹2 4.50 × 1012 5.91 × 1012 Orbital period 27.3 d 88.0 d 224.7 d 365.3 d 687.0 d 11.86 y 29.45 y 84.02 y 164.8 y 247.9 yarrow_forwardOne of Saturn's moons is named Mimas. The mean orbital distance of Mimas is 1.87 x 108 m. The mean orbital period of Mimas is approximately 23 hours (8.28x104 s). Use this information to estimate a mass for the planet Saturn.arrow_forward
- Taking the age of Earth to be about 4 ✕ 109 years and assuming its orbital radius of 1.5 ✕ 1011 m has not changed and is circular, calculate the approximate total distance Earth has traveled since its birth (in a frame of reference stationary with respect to the Sun). ..............m Answer and simplfyarrow_forwardAstronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 6.0✕ 104 light years from its center. (a) What should the orbital period (in y) of that star be? y (b) If its period is 5.1✕ 107 y instead, what is the mass (in solar masses) of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies. solar massesarrow_forwardWe sent a probe out to orbit the planet Kerbal at a distance of 5.5x107m from the middle of the planet. It took our probe 3.5x105s to orbit the planet. Calculate the gravitational acceleration experienced, by our probe, at a distance of 5.5x107m from the center of planet Kerbal. Possible Formulas that can be used to solve the question: v=(2πr)/T ac=v2/r ac=(4π2r)/T2 Fc=mac Fg=mg F=(Gm1m2)/d2 g=Gm/r2 T2=(4π2/Gm)r3 v=√(Gm)/r g=9.80m/s2 G=6.67x10-11 (N∙m2)/kg2arrow_forward
- Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 6.0 ✕ 104 light years from its center. What should the orbital period (in y) of that star be?arrow_forwardAstronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 • 1011 solar masses. A star orbiting on the galaxy’s periphery is about 6.0 • 104 light years from its center. What should the orbital period of that star be in years? Part (b) If its period is 6.0 • 107 years instead, what is the mass of the galaxy in solar masses? Such calculations are used to imply the existence of “dark matter” in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies.arrow_forwardAstronomical Datat Mass (kg) 1.99 × 1030 7.35 × 1022 3.30 × 1023 4.87 X 1024 5.97 X 1024 6.42 × 1023 1.90 × 1027 5.68 X 1026 8.68 x 1025 1.02 × 1026 1.31 × 1022 Body Sun Moon Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Pluto 8.43 x 10^24 N 2.07 x 10^10 N O 843 N Radius (m) 6.96 × 108 1.74 X 106 2.44 X 106 6.05 × 106 6.37 X 106 3.39 X 106 6.99 X 107 5.82 X 107 2.54 x 107 2.46 X 107 1.15 X 106 What is the weight of a 75 kg astronaut on the surface of Neptune? O 2.07 x 10^5 N Orbit radius (m) 3.84 × 108 5.79 × 1010 1.08 × 10¹1 1.50 × 10¹1 2.28 × 10¹1 7.78 x 10¹1 1.43 × 10¹2 2.87 × 10¹2 4.50 × 1012 5.91 X 1012 Orbital period 27.3 d 88.0 d 224.7 d 365.3 d 687.0 d 11.86 y 29.45 y 84.02 y 164.8 y 247.9 yarrow_forward
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