Two 700-kg masses (1543 lb) are separated by a distance of 76 m. Using Newton's law of gravitation, find the magnitude of the gravitational force exerted by one mass on the other. (Use G = 6.67 x 10-11 N-m²/kg2.) Newton's Law of Gravitation The gravitational force between two objects is proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the masses: Gm F= where G is a constant. The direction of the force is attractive and lies along the line joining the centers of the two masses (fig. 5.19). F, 0:00/5:04 m₂ figure 5.19 The gravitational force is attractive and acts along the line joining the center of the two masses. It obeys Newton's third law of motion (F,-F.). 480p The magnitude of the gravitational force exerted by one mass on the other is x 10-9 N.

. The drawing represents two suspended spheres.   The force of gravity between the two spheres is 12 N (newtons). If the mass of each sphere is doubled (2x), and the distance between the spheres remains constant, what will happen to the force of gravity?

Use Kepler's Law, which states that the square of the time, T, required for a planet to orbit the Sun varies directly with the cube of the mean distance, a, that the planet is from the Sun.Using Earth's time of 1 year and a mean distance of 93 million miles, the equation relating T (in years) and a (in million miles) is 804375T2=a3.Use that relation equation to determine the time required for a planet with mean distance of 206 million miles to orbit the Sun. Round to 2 decimal places. years

Use Newton’s universal gravitation formula to determine the gravitational force of attraction between the earth and the moon given: mass (moon) m(moon)=7.35 x 10^22kg the mass of the earth is m(earth)=5.98 x 10^24kg the distance between centers of the earth and moon is r=3.92 x 10^8 m use Newton gravitation equation F=G(m(1) x m(2))/r^2

The gravitational force between two objects that are 2.2x10^-1m apart is 3.1x10^-6N. If the mass of one object is 45 kg what is the mass of the other object?

Newton's Law of Gravitation 2. The magnitude of the acceleration of an object under the pull of Earth's gravity is given by Newton's Universal Law of Gravitation МЕ a = G R? where G is the universal gravitational constant, ME is the mass of Earth, and R is the distance of the object from the center of Earth. Let x be the distance above Earth's surface. We can rewrite the formula for the acceleration as a function of x by noting that R = Rp + x, where Rp is the radius of Earth. Therefore, МЕ a(x) = G- (RE + x)2 d. (a) Show that dx 1 1 (1 – x)* - x. (b) Use the above fact, along with the power series of 1 to determine a power 1- x 1 series for (1+x)²* (c) What is the radius of convergence for the series in part (b)? (Hint: You do not need to calculate anything. What is the radius of convergence for the power series of 1 does not change the radius of convergence.) -? This series has the same radius of convergence since taking a derivative

A distant star has a single planet circling it in a circular orbit of radius 8.47 x 10¹1 m. The period of the planet's motion about the star is 668 days. What is the mass of the star? The