Earth's orbit is (on average) 1 Astronomical Unit from the Sun. For reference, 1 Astronomical Unit is about 93 million miles. Jupiter's orbit is about 5 Astronomical Units from the Sun. Suppose that the gravitational force between the Earth and the Sun is equal to 50,000 N (it's way more than that but we are just pretending here). If we move Earth to Jupiter's orbit, what will be the new value of the gravitational force between the Earth and the Sun?  Remember to include units of force (Newtons or N) in your answer.

We would like to be able to make meaningful interpretations of variations in the acceleration due to gravity, g, as small as 0.1 mgal. How accurate must our knowledge of the latitude of our gravity stations be? (A “gravity station" is just a location at which you make a gravity measurement.) You can assume your latitude is 45°.

Kepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion. Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU. Does this make physical sense? Explain why or why not.

Two masses are attracted by a gravitational force of 8.6 N. What will the force of attraction be if the distance between the two masses is quadrupled? (Round the final answer to four decimal places.) The force of attraction will be ____  N.

The unit of gravitational field strength g is newtons per kilogram. Explain how the unit of gravitational field strength relates to the unit of force.

Assume you are the lead Physicist at SpaceX and you are asked to calculate the gravitational force that will be acting on a new satellite they plan to launch into space to orbit Mars. Calculate the force between Mars, which has a mass of 6.39*1023 kg, and the satellite, which has a mass of 425 kilograms. Assume that NASA wants the satellite to orbit Mars at a distance of 20,827 meters. G = 6.67 x 10-11 N\cdot⋅m2/kg2 Answer in scientific notation ( #*10^#) Answer with 3 significant figures Do NOT include units in your response

Many people mistakenly believe that the astronauts who orbit Earth are "above gravity." Earth's mass is 6×1024kg, and its radius is 6.38×106m(6380 kmkm).   Use the inverse-square law to find a height above Earth's surface at that the force of gravity on a shuttle is about 96 %% that at Earth's surface.

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