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- Newton’s version of Kepler’s third law is P2 = 4 π2 / [G (M1 + M2)] · a3, where G is the gravitational constant, which is equal to 6.67*10-11 m3 kg-1 s-2. NASA's New Horizons mission found that Pluto's moon Charon orbits Pluto every 5.3 days at an average distance of 20400.0 km. What is the combined mass (in kg) of Pluto and Charon?In the book 2010: Odyssey Two, Chinese astronauts land on Europa, one of Jupiters Moons. Suppose one of these astronauts on Europa drops a tool 2 m above the ground. How long will it take for it to hit the ground? MEuropa = 4.7998×1022 kg, REuropa = 1.561×106Planet X has four times the diameter and five times the mass of earth. What is the ratio gx:ge of gravitational acceleration at the surface of Planet X to the gravitational acceleration at the surface of the earth? Please put the ratio on decimal form not on fraction form.
- Weight refers to the force of gravity acting on a mass. We often calculate the weight of an object by multiplying its mass by the local acceleration due to gravity. The value of gravitational acceleration on the surface of Mars is 0.38 times that on Earth. Assume your mass is 81.00 kg. Then your weight on Earth is 793.80 newtons (793.80 N = m × g = 81.00 kg × 9.8 m/s2). What would be your mass on Mars? kg What would be your weight on Mars? NWhat percent of Earth's acceleration due to gravity is the acceleration on Mars? Take G = 6.67 x 10^-11 N m^2/kg^2 and the mass of Mars 6.42 x 10^23 kg and its radius as 3400 km. (Answer should look like '55.5 %'.)The gravitational acceleration constant gx on Planet X can be approximated by determining the acceleration of an object assuming Newton's Law of Universal Gravitation. If gx = 3.8 m/s^2 , G = 6.7 x 10^-11 Nm^2/kg^2, and Planet X's radius is 4000 km, what is the approximate mass of planet X? Give answer in kg.
- Europa orbits Jupiter at a distance of 6.7 x 108 m from Jupiter's cloudtops (the surface of the planet). If Jupiter's mass is 1.9 x 1027 kg and radius is 6.8 x 107 m, what is the speed of Europa as it orbits in m/s? Round to the nearest hundredth. Don't worry about putting units, just put the number.A new planet named Vulcan has been discovered. Vulcan is a rather large planet with a radius twice that of Earth and a mass three times that of Earth. An astronaut has a mass of 60.0 kg and weighs about 132 lbs. on Earth. If the astronaut is on the planet Vulcan, what is her weight? The following numerical values may be helpful in this question. G = 6.67 ∙10-11 N∙m2/ kg2 Earth’s mass = 5.98 · 1024 kilograms g = 9.80 m/sec2 1 kilometer = 1000 metersA newly discovered planet X has a mass of 36.7 × 1023 kg and radius 2.47 × 106 m. What is g on this planet's surface, in m/s2?
- A rocket lifts off the pad at Cape Canaveral. According to Newton's Law of Gravitation, the force of gravity on the rocket is given by F(x) = −GMm/x^2 where M is the mass of the earth, m is the mass of the rocket, G is a universal constant, and x is the distance (in miles) between the rocket and the center of the earth. Take the radius of the earth to be 4000 miles, so that x > 4000 miles.Find the work, W1, done against gravity when the rocket rises 1500 miles. W1=___GMm (mile-pounds) Next, find the limit of the work, W2 , as the rocket rises infinitely far from the earth. W2=___GMm (mile-pounds)The gravitational field strength of Venus is 8.9 N/kg. If its radius is 6.05 x 106 m, the mass of Venus, expressed in scientific notation, is a.b x 10cd kg. The values for a, b, c, and d are andThe mean diameters of Mars and Earth are 6.9×10^3km and1.3×10^4km, respectively. The mass of Mars is 0.11 timesEarth's mass [Mass of Earth = 5.98×10^24kg]. What is: a)The ratio of the mean density (mass per unit volume) of Mars to that of Earth? b)The value of the gravitational acceleration on Mars? c)The escape speed on Mars?