Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
The largest mass is 4.7 x 10³⁰ kg and the smallest mass is 5 x 10²⁹ kg.
The given parameters;
- distance between the two black holes, r = 10 AU = 1.5 x 10¹² m
- gravitational force between the two black holes, F = 6.9 x 10²⁵ N.
- combined mass of the two black holes = 5.20 x 10³⁰ kg
The product of the two masses is calculated from Newton's law of universal gravitational as follows;
[tex]F = \frac{Gm_1m_2}{r^2} \\\\m_1m_2 = \frac{Fr^2}{G} \\\\m_1m_2 = \frac{(6.9\times 10^{25}) \times (1.5\times 10^{12})^2}{6.67\times 10^{-11}} \\\\m_1m_2 = 2.328 \times 10^{60} \ kg^2[/tex]
The sum of the two masses is given as;
m₁ + m₂ = 5.2 x 10³⁰ kg
m₂ = 5.2 x 10³⁰ kg - m₁
The first mass is calculated as follows;
m₁(5.2 x 10³⁰ - m₁) = 2.328 x 10⁶⁰
5.2 x 10³⁰m₁ - m₁² = 2.328 x 10⁶⁰
m₁² - 5.2 x 10³⁰m₁ + 2.328 x 10⁶⁰ = 0
solve the quadratic equation using formula method;
a = 1, b =- 5.2 x 10³⁰, c = 2.328 x 10⁶⁰
[tex]m_1 = \frac{-b \ \ +/- \ \ \sqrt{b^2 - 4ac} }{2a} \\\\m_1 = \frac{-(-5.2\times 10^{20}) \ \ +/- \ \ \sqrt{(-5.2\times 10^{20})^2 - 4(1\times 2.328\times 10^{60})} }{2(1)} \\\\m_1 = 4.7 \times 10^{30} \ kg \ \ or \ \ 4.9 \times 10^{29} \ kg[/tex]
The second mass is calculated as follows;
m₂ = 5.2 x 10³⁰ kg - m₁
m₂ = 5.2 x 10³⁰ kg - 4.7 x 10³⁰ kg
m₂ = 5 x 10²⁹ kg
or
m₂ = 5.2 x 10³⁰ kg - 4.9 x 10²⁹ kg
m₂ = 4.7 x 10³⁰ kg
Thus, the largest mass is 4.7 x 10³⁰ kg and the smallest mass is 5 x 10²⁹ kg.
Learn more here:https://brainly.com/question/9373839
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.