For the following questions, start your analyses by considering at least Newton's Law of Gravitation, centripetal acceleration, Kepler's law or Energy Conservation. Take the Gravitational constant to be a. From Earth we can measure the radius of Mars using our telescopes. An estimate for it is 3.39 x 106 m. By sending an exploratory robot to Mars, we determined the acceleration due to gravity on its surface as 3.73 m/s?. Estimate the mass of Mars. b. The Earth revolves around the Sun once a year at a distance of 1.50 x 1011 m. Estimate the mass of the Sun. c. A rocket is launched straight up from Earth's surface at 2100 m/s. By ignoring air resistance, determine the maximum height it reaches?

For the following questions, start your analyses by considering at least Newton's Law of Gravitation, centripetal acceleration, Kepler's law or Energy Conservation. Take the Gravitational constant to be a. From Earth we can measure the radius of Mars using our telescopes. An estimate for it is 3.39 x 106 m. By sending an exploratory robot to Mars, we determined the acceleration due to gravity on its surface as 3.73 m/s?. Estimate the mass of Mars. b. The Earth revolves around the Sun once a year at a distance of 1.50 x 1011 m. Estimate the mass of the Sun. c. A rocket is launched straight up from Earth's surface at 2100 m/s. By ignoring air resistance, determine the maximum height it reaches?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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A) When one object is orbiting a much larger object, the period of the orbit (T) is related to the semi‐major axis (r) by the general form of Kepler’s 3rd Law. Write this general form in the space below: B) What units must the period be in if we want to calculate the semi-major radius in meters? Note that G = 6.67 x 10-11 N m2/kg2. Complete problems using Kepler’s 3rd law as you wrote it down above:
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
In 1993 the Galileo spacecraft sent home an image of asteroid "243 Ida" and a tiny moon "Dactyl" orbiting the asteroid. Assume that the small moon orbits in a circle with a radius of r = 100 km from the center of the asteroid with an orbital period of T = 27 hours. a. Show and explain how we derived Kepler's 3rd law using Newton's 2nd Law, the definition for centripetal acceleration, and the equation for gravitational force. b. Use your result for Kepler's 3rd Law to determine the mass of the asteroid. c. If the asteroid has a radius of about 16 km calculate the approximate value for the acceleration due to gravity, g, on its surface. d. What velocity would you need to achieve in order to lift off and leave this asteroid? e. Use Newton's 2nd Law, the definition for centripetal acceleration, and the equation for gravitational force to determine an expression for circular orbital velocity. f. What is the orbital velocity of the small moon if we assume it is in a circular orbit?
Congratulations! You just derived a version of Kepler's Third Law for Mars! Using the mass of Mars in kilograms and converting the 4.5 hours to seconds, calculate the distance from the center of the planet. GM kg 4π² ]s)² 3 = And then determine the distance (in km) from the surface. r = rm + rs rs km = km
. Solve the following problems. Use GFSA (Given, Find, Solution, and Answer) on the given space below. Encircle your final answer, write it in scientific notation with 2 decimal places (if possible). You’re involved in the design of a mission carrying humans to the surface of the planet Mars, which has a radius 3.37x106m and a mass of 6.42x1023 kg. The earth weight of the Mar’s lander is 39,200 N. Calculate its weight and the acceleration due to Mar’s gravity at 6.0 x 106 m above the surface of Mars. r= 3.37x106 m h = 6.0x106 m above the surface of Mars.
Gravitational Forces (A) Gravitational, Electrical, Magnetic, and Nuclear Forces Math Connections Gm The surface gravity, g, on a planet can be calculated using the formula: g = , where • G = Gravity = 6.673×10-11 N • m² kg • m = mass in kg • r= radius in m Characteristics of the Planets Planet Mass (kg) Radius (m) Surface Gravity (m/s?) Mercury 3.30 х 1023 2,440,000 3.70 Venus 4.87 x 1024 6,051,000 Earth 5.97 х 1024 9.79 Mars 6.42 x 1023 3,397,000 Jupiter 1.90 x 1027 71,492,000 Saturn 5.69 x 1026 10.45 Uranus 8.66 x 1025 25,559,000 8.84 Neptune 1.03 х 1026 24,764,000 Use the table above to answer the following questions. Insert your answers into the spaces in the table. 9. Calculate the surface gravity on the following planets: (6.673x10-")(4.87×10²4)_ a) Venus g= 6,051, 000 (6.673×10"")(1.90 ×10") 71, 492, 000 b) Jupiter g= %3D c) Neptune (6.673×10-")(1.03×10%) g= 24, 764, 000 (6.673×10 ")(6.42 ×10") g= d) Mars 3, 397,000 Gm 10. Calculate the radius of each of the following planets…
r r M M 1. What is the gravitational potential energy of the mass (m) in the picture? The mass is the same distance away r from the centers of both of the other masses, and both of the other masses have the same mass, M. Give your answer in Joules. r = 400 million meters m = 7x1022 kg м- 2х1027 kg 2. What is the net gravitational force for the mass m at this location? Give your answer in Newtons.
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(1) From the slope, determine gravitational acceleration g. How is slope related to gravity g. HINT: Write the kinematic equation that you plot and compare it to the equation of a line y=m x where m is slope. measured g (from slope) = _______________ write unit: (2) Calculate the percentage error with respect to the standard value of 9.80 m/s2 percentage error = |g (from slope)-9.80| x 100 / 9.80= a. Was the experiment accurate? YES NO Briefly explain your reasoning. b. Was the experiment precise? YES NO Briefly explain your reasoning.
the up mIbi, thla 2. In the future, we may encounter a civilization from another planet. They will not use the SI or AE systems of units. Suppose we meet aliens who use the Zerf as a unit of mass and the Spund as a unit of force. One Spund is the weight of a mass of one Zerf on the surface of Mars. The gravitational acceleration on Mars is 3.7 m/s?. a.) What is gc in the alien system of units? Be sure to include the numerical value and the units. b.) How much would a 350 Zerf object weigh on the surface of Mars, in Spunds? c.) How much would a 350 Zerf object weigh on the surface of the Earth, in Spunds? d.) To which system of units is the Zerf-Spund system most similar, Sl or AE?
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Neptune orbits the Sun with an orbital radius of 4.495 x 10^12 m. If the earth to sun distance 1A.U. = 1.5 x 10^11 m, a) Determine how many A.U.'s is Neptune's orbital radius (Round to the nearest tenth). b) Given the Sun's mass is 1.99 x10^30 kg, use Newton's modified version of Kepler's formula T^2 = (4pi^2/Gm(star)) x d^3 to find the period in seconds using scientific notation. (Round to the nearest thousandth). C) Convert the period in part b) to years (Round to the nearest tenth)