(a)
The gravitational force exerted by the moon on a 1 kg rock placed at the point on Earth’s surface that is closest to the moon.
Answer to Problem 58Q
The gravitational force exerted by the moon on a 1 kg rock at the closest point on the Earth’s surface is
Explanation of Solution
Given:
Distance from the moon to the center of the Earth,
The diameter of Earth,
The mass of rock,
Formula used:
The gravitational force between two objects is given by,
Where, G is the universal gravitation constant,
Calculation:
We take the formula for gravitational force,
Here,
First, we calculate the value of
This is given by,
Putting in all the values in the formula for gravitational force, we get,
Conclusion:
Thus, the gravitational force exerted by the moon on a 1 kg rock at the closest point on the Earth’s surface is
(b)
The gravitational force exerted by the moon on a 1 kg rock placed at the point on Earth’s surface that is farthest to the moon.
Answer to Problem 58Q
The gravitational force exerted by the moon on a 1 kg rock at the farthest point on the Earth’s surface is
Explanation of Solution
Given:
Distance from the moon to the center of the Earth,
The diameter of Earth,
Formula used:
Calculation:
Again, we have
Here,
Substituting all values in
Conclusion:
Thus, the gravitational force exerted by the moon on a 1 kg rock at the farthest point on the Earth’s surface is
(c)
The difference between the two forces
Answer to Problem 58Q
Difference between the two forces
Explanation of Solution
Given:
Formula used:
The difference between the two forces is calculated by
Calculation:
The difference between the two forces is,
The tidal force, i.e., the difference between the two forces
Conclusion:
Thus, the difference between the two forces
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Chapter 4 Solutions
UNIVERSE (LOOSELEAF):STARS+GALAXIES
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- A planet has two moons with identical mass. Moon 1 is in a circular orbit of radius r. Moon 2 is in a circular orbit of radius 2r. The magnitude of the gravitational force exerted by the planet on Moon 2 is (a) four times as large (b) twice as large (c) the same (d) half as large (e) one-fourth as large as the gravitational force exerted by the planet on Moon 1.arrow_forwardI0 orbits Jupiter with an average radius of 421,700 km and a period of 1.769 days. Based upon these data, what is tha mass of Jupiter?arrow_forwardCalculate the mass of the Sun based on data for average Earth’s orbit and compare the value obtained with the Sun’s commonly listed value of 1.9891030kg .arrow_forward
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- A planet has two moons of equal mass. Moon 1 is in a circular orbit of radius r. Moon 2 is in a circular orbit of radius 2r. What is the magnitude of the gravitational force exerted by the planet on Moon 2? (a) four times as large as that on Moon 1 (b) twice as large as that on Moon 1 (c) equal to that on Moon 1 (d) half as large as that on Moon 1 (e) one-fourth as large as that on Moon 1arrow_forwardOn a planet whose radius is 1.2107m , the acceleration due to gravity is 18m/s2 . What is the mass of the planet?arrow_forwardThe average distance separating Earth and the Moon (center to center) is 384,000 km. Use the data in the table to find the net gravitational force exerted by Earth and the Moon on a 3.00 x 104-kg spaceship located halfway between them. Useful Planetary Data Body Mass (kg) Mean Radius (m) Period (s) Distance from Sun (m) T2/r³(s²/m³) Mercury 3.18 x 1023 2.43 x 106 7.60 x 106 5.79 x 1010 2.97 x 10-19 Venus 4.88 x 1024 6.06 x 106 1.94 x 107 1.08 × 1011 2.99 x 10¬19 Earth 5.98 x 1024 6.37 x 106 3.16 x 107 1.50 x 1011 2.97 x 10¬19 Mars 6.42 x 1023 3.37 x 106 5.94 x 107 2.28 x 1011 2.98 x 10-19 Jupiter 1.90 x 1027 6.99 x 107 3.74 x 108 7.78 x 1011 2.97 x 10-19 Saturn 5.68 x 1026 5.85 x 107 9.35 x 108 1.43 x 1012 2.99 x 10-19 Uranus 8.68 x 1025 2.33 x 107 2.64 x 109 2.87 x 1012 10-19 א 2 Neptune 1.03 x 1026 2.21 x 107 5.22 x 109 4.50 x 1012 2.99 x 10-19 Pluto ~1.4 x 1022 ~1.5 x 106 7.82 x 109 5.91 x 1012 2.96 x 10-19 Moon 7.36 x 1022 1.74 x 106 Sun 1.991 x 1030 6.96 x 108arrow_forward
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