Use a distance of R = 1.48x10^11 meters for the distance between the earth and the sun.  Use a mass of 1.99x10^30 kg to be 1 solar mass. For each of the different sun masses (as values of solar mass, aka 0.5 solar masses = 1x10^30 kg), as outlined in the lecture, calculate the period of the earth's orbit in days using Kepler's law for circular orbits (I double-checked it with these values and it works) and also calculate the corresponding orbital velocity of the earth.  Questions: 1.) Using these values, and 6x10^24 kg for the mass of the earth, what is the strength of the gravitational force between the earth and the sun?  2.) If the earth were twice as far from the sun, what would be its period of orbit? 3.) Mars orbits the sun at a distance of 2.18x10^11 meters. How long is a Martian year, using Kepler's law for circular orbits

A satellite in orbit around the earth is at an altitude of 107 percent of the earth's radius. Rounding off our old friend "g" to ten meters per second squared, what is the acceleration due to earth's gravity at the satellite?  Your answer should be in meters per second squared, but do not put the unit, just the number.

I need help with this hw problem.

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.

A planet of mass ?=2.85×1024 kg orbits a star of mass ?=6.85×1029 kg in a circular path. The radius of the orbit is ?=7.45×107 km.. What is the orbital period ?planet of the planet in Earth days?Tplanet = ? days

You are planning a dream vacation to Mars. For the orbital dynamics part of the vacation planning assume that Earth is in a circular orbit 1.00 AU from the Sun and Mars is in a circular orbit 1.52 AU from the Sun. Assume the the orbits of Earth and Mars are coplanar and that they go around the Sun the same way. The orbit you plan to use for your trip is an ellipse with the Sun at one focus (Kepler's 1st Law). The perihelion of the ellipse is at Earth's orbit at 1.00 AU and the aphelion is at Mars' orbit at 1.52 AU. Your spacecraft will go around the Sun in the same sense as Earth and Mars. The orbit you have chosen is called a Hohmann Transfer Orbit.   A. What is the semi-major axis a of the spacecraft's orbit? What is the eccentricity of the spacecraft's orbit? B. What is the orbital period of the spacecraft? How long does it take to get to Mars? How long does it take to get back? C. When (at what Earth - Mars configuration) do you launch to go? In other words, where does Mars need to…

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

We sent a probe out to orbit the planet Kerbal at a distance of 5.5x107m from the middle of the planet. It took our probe 3.5x105s to orbit the planet. Calculate the mass of planet Kerbal. Possible Formulas that can be used to answer the question: v=(2πr)/T ac=v2/r ac=(4π2r)/T2 Fc=mac Fg=mg F=(Gm1m2)/d2 g=Gm/r2 T2=(4π2/Gm)r3 v=√(Gm)/r g=9.80m/s2 G=6.67x10-11 (N∙m2)/kg2

The supermassive black hole at the center or our galaxy (Sagittarius A*) has a mass equal to 4.3 million Suns (the mass of the Sun is 1.99 × 1030 kg). The distance from Sgr A* to Earth is 7,940 parsecs, where one parsec is equal to 3.09 × 1016 m. (a) What is the gravitational force that Sgr A* exerts on a 75 kg person on Earth, in units of Newtons? Hint: use Newton's law of universal gravitation. (b) Suppose the same person is sitting 1.0 meter away from a paperclip with a mass of 1.0 grams. What is the gravitational force that the paperclip exerts on the person? (c) Compare the forces from parts (a) and (b). Which is greater?