A space shuttle is travelling between the Earth and Mars. Considering only the gravitational forces of the Earth and Mars, find the distance x from the Earth at which the space shuttle is subjected to Earth gravitational force equal to the twice gravitational force of Mars. (Given: mass of Mars, MM = 6.39 * 10 kg; distance between the centers of the Earth and Mars, r = 54.6 * 10° m) ?

(a) Find the magnitude of the gravitational force (in N) between a planet with mass 8.00 ✕ 1024 kg and its moon, with mass 2.50 ✕ 1022 kg, if the average distance between their centers is 2.90 ✕ 108 m. (Answer in N)   (b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) Answer in m/s2 (c) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.) Answer in m/s2

(a) Find the magnitude of the gravitational force (in N) between a planet with mass 7.00 ✕ 1024 kg and its moon, with mass 2.20 ✕ 1022 kg, if the average distance between their centers is 2.50 ✕ 108 m. (b) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) (c) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.)

(A) Find the magnitude of the gravitational force (in N) between a planet with mass 7.75 ✕ 1024 kg and its moon, with mass 2.35 ✕ 1022 kg, if the average distance between their centers is 2.20 ✕ 108 m.     (B) What is the moon's acceleration (in m/s2) toward the planet? (Enter the magnitude.) m/s2     (C) What is the planet's acceleration (in m/s2) toward the moon? (Enter the magnitude.) m/s2

The equatorial radius of the Earth is 6378 km and gravity at the equator is 9.780 m s-2. Compute the ratio m of the centrifugal acceleration at the equator to the gravitational acceleration at the equator. If the ratio m is written as 1/k, what is the value of k?

(a) Find the magnitude of the gravitational force (in N) between a planet with mass 7.75 x 1024 kg and its moon, with mass 2.20 x 1022 kg, if the average distance between their centers is 2.90 x 10° m. (b) What is the moon's acceleration (in m/s?) toward the planet? (Enter the magnitude.) m/s2 (c) What is the planet's acceleration (in m/s²) toward the moon? (Enter the magnitude.) m/s?

A satellite of mass 53.6 kg in geosynchronous orbit at an altitude of 3.58 * 10^4 km above the Earths' surface remains above the same spot on the Earth. Assume its orbit is circular. Find the magnitude of the gravitational force exerted by the Earth on the satellite. Hint: The answer is not 526 N.

Problem 2:  An object with mass m1 = 42 kg is located at the origin. Another object with mass m2 = 86 kg is located at l2 = 0.105 m. Consider position la = 0.035 m between the two objects and along the axis connecting them. Refer to the diagram. The gravitational field of m1 is denoted by g1. Enter an expression for the gravitational field g1 at position la in terms of m1, la, and the gravitational constant G.  The gravitational field of m2 is denoted by g2. Enter an expression for the gravitational field of m2 at la in terms of m2, m1, la, l2 and the gravitational constant G.  Enter and expression for the total gravitational field at position la, g, in terms of the quantities defined in the problem.

The Moon has a mass 7.35 x 1022 kg of and a radius of 1740 km. Air resistance can be neglected on the Moon. G = 6.67 x 10-11 m3 kg-1 s-2 is the universal gravitational constant. (a) If a ball is launched upwards from the surface of the moon with an initial speed of 1.15 km/s, what height maximum height above the surface of the moon will it reach? Give your answer in kilometers. (b) What is the escape speed of the moon? Give your answer in km/s.

During a solar eclipse, the Moon is positioned directly between Earth and the Sun. The masses of the Sun, Earth, and the Moon are 1.99×10^30 kg, 5.98×10^24 kg, and 7.36×10^22 kg, respectively. The Moon's mean distance from Earth is 3.84×10^8 m, and Earth's mean distance from the Sun is 1.50×10^11 m. The gravitational constant is G=6.67×10^−11 N·m2/kg^2. Find the magnitude F of the net gravitational force acting on the Moon during the solar eclipse due to both Earth and the Sun.