Let ΔgM represent the difference in the gravitational fields produced by the Moon at the points on the Earth’s surface nearest to and farthest from the Moon. Find the fraction ΔgM/g, where g is the Earth’s gravitational field. (This difference is responsible for the occurrence of the lunar tides on the Earth.)

A sphere of copper has a radius of 50.0 cm and a mass of 4690 kg.  A sphere of unknown metal has a radius of 30.0 cm.  The surfaces of the spheres are 20.0 cm apart.  The force of gravitational attraction between the two spheres is 0.372 mN.  What is the mass of the unknown metal?

A satellite in geostationary orbit (also called synchronous orbit) appears to remain stationary in the sky as seen from any particular location on the planet.  a.) In the future, there will be need for satellites in synchronous orbit around Mars to aid colonies. At what altitude would such a satellite need to be above the surface of Mars?Assume that the mass of Mars is 6.39 × 10^23 kg, the length of the Martian solar day (i.e., sol) is 24h 39m 35s, the length of the sidereal day is 24h 37m 22s, and the equatorial radius is 3396 km. (Hint: if you haven’t had a physics class before, you can find this by using the fact that the acceleration of an object in circular motion either as v2/r, where v and r are the velocity and radius of the orbit, or as 4Pi 2r/T2 , where T is the period. Use this second equation and Mathematical Insight 4.5 on p. 131 to find r for T=1 day. Make sure to use values for Mars nstead of Earth, as necessary. Alternatively, you can calculate the answer using Newton’s…

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Astronomers discover an exoplanet, a planet orbiting a star other than the Sun, that has an orbital period of 3.17 Earth years in a circular orbit around its star, which has a measured mass of 3.63×1030 kg. Find the radius r of the exoplanet's orbit.

The International Space Station (ISS) completes one orbit of Earth in 92 minutes.  What is the radius of the orbit in kilometers (km)?    You may assume the orbit is circular.  The mass of the ISS is 420 kg, and the mass of the Earth is 6.0×10246.0×1024kg.  Newton’s gravitational constant is 6.7×10−11N⋅m2kg26.7×10−11kg2N⋅m2​.

(a) Based on the observations, determine the total mass M of the planet. (b) Which moon and planet of our solar system is the team observing? (Use literature.)

The ratio of the gravitational field at an altitude 2 RF above the Earth's surface (R = the radius of the Earth) to the field at the Earth's surface is 1/9 1/3 9

A satellite is in circular polar orbit around Earth at an altitude of 450 km – meaning it passes directly overhead of the North and South Poles. What is the magnitude and direction of the displacement vector when it is directly over the North Pole to when it is at 40° latitude? Earth’s radius is 6,370 km.

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 × 10³0 kg, 5.98 × 1024 kg, and 7.36 × 1022 kg, respectively. The Moon's mean distance from Earth is 3.84 × 108 m, and Earth's mean distance from the Sun is 1.50 × 10¹¹ m. The gravitational constant is G = 6.67 × 10-¹1 N-m²/kg². Find the magnitude F of the net gravitational force acting on the Moon during the solar eclipse due to both Earth and the Sun. F = What is the direction of this force? toward Earth toward Venus toward the Sun elsewhere N