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?

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter13: Gravitation

Section: Chapter Questions

Problem 13.10CYU: Check Your Understanding Earth exerts a tidal force on the Moon. Is it greater than, the same as, or...

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Check Your Understanding Earth exerts a tidal force on the Moon. Is it greater than, the same as, or less than that of the Moon on Earth? Be careful in your response, as tidal forces arise from the difference in gravitational forces between one side and the other. Look at the calculations we performed for the tidal force on Earth and consider the values that would change significantly for the Moon. The diameter of the Moon is one-fourth that of Earth. Tidal forces on the Moon are not easy to detect, since there is no liquid on the surface.
asap do all steps please An asteroid in our Solar System has an eccentricity of 0.550 and a perihelion (closest to Sun) distance of 0.800 AU (Astronomical Units). a)What is its semimajor axis in AU? b)What is its orbital period in Earth years? (Hint: use the simpler form of Kepler’s law for orbitsaround our Sun. You do not need to know 1AU in m). c)What is the ratio of its maximum to minimum speedduring its orbit, vmax/vmin (3 sig figs)? (Hint: use a conservation law) d)Choose one: The asteroid’s total mechanical energy is: i) positive, ii) zero iii) negative, iv) any of theaboveare possible. e) The Earth’s orbit is very close to circular and draw it as acircle of radius 1AU (OK to trace sometime at least the size of a quarter or draw by hand). Label an “S” where the Sunis. Carefully mark theperihelion of the asteroid to the left of the Sun with a “P” and aphelion with an “A” to the right of the Sunto scale (use your ruler to measure it). Show the extent of the asteroid’s semimajor…
Write down an expression for the gravitational filed strength of a planet of radius R and density ρ. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate without the quotes). For Greek letters such as ?ρ and ?π use rho and pi. Please use the "Display response" button to check you entered the answer you expect
How can Kepler's laws of planetary motion and Netwon's Law of universal gravitation be used to describe planetary motion?
A minimum-energy orbit to an outer planet consists ofputting a spacecraft on an elliptical trajectory with the departureplanet corresponding to the perihelion of the ellipse, orclosest point to the Sun, and the arrival planet correspondingto the aphelion of the ellipse, or farthest point from the Sun.(a) Use Kepler’s third law to calculate how long it would taketo go from Earth to Mars on such an orbit. (Answer in years.)(b) Can such an orbit be undertaken at any time? Explain.
You are participating in a NASA traineeship, working with a group planning a new landing on Mars. Your supervisor has come up with an idea for putting a synchronous satellite over the landing spot near the Martian equator, so that radio communication between Earth and the lander is improved. She asks you to report to her on the required height above the Martian surface of a synchronous satellite. Note: The rotation period of Mars is 1.026 d. (Enter your answer in m.)
what is The gravitational constant? (I need Long answer plz)?
Please answer the question and subquestions entirely. This is one single question. According to the official guideline, I can ask two subquestions! Thank you! 1) The radius of Planet Z is 3 times the radius of the Earth. It has the same density as the Earth. What is the gravitational acceleration at the surface of the planet? 29 m/s2 88 m/s2 270 m/s2 3.3 m/s2 a) Use Kepler's Law to find the time (in Earth’s years) for Mars to orbit the Sun if the radius of Mars’ orbit is 1.5 times the radius of Earth's orbit. 1.8 2.8 3.4 4.2 b) The mass of Mars is about 1/10 the mass of Earth. Its diameter is about 1/2 the diameter of Earth. What is the gravitational acceleration at the surface of Mars? 9.8 m/s2 2.0 m/s2 3.9 m/s2 4.9 m/s2 none of these
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?
The motivation for Isaac Newton to discover his laws of motion was to explain the properties of planetary orbits that were observed by Tycho Brahe and analyzed by Johannes Kepler. A good starting point for understanding this (as well as the speed of the space shuttle and the height of geostationary satellites) is the simplest orbit--a circular one. This problem concerns the properties of circular orbits for a satellite orbiting a planet of mass M. For all parts of this problem, where appropriate, use G for the universal gravitational constant. Find L, the magnitude of the angular momentum of the satellite with respect to the center of the planet. Express your answer in terms of m, M, G, and R. The quantities v, K, U, and Lall represent physical quantities characterizing the orbit that depend on radius R. Indicate the exponent (power) of the radial dependence of the absolute value of each. Express your answer as a comma-separated list of exponents corresponding to v, K, U, and L,…
What is the average gravitational force between the moon (MM=7.38 x 1022 kg) and the earth (ME=5.98 x 1024 kg) if the average center-to-center distance of the two is 384,467 km?Solve the problem with GAFSA (Given, Asked, Formula, Solution, and Answer) Format
Using planetary motion, prove that the planet always being bound to the attracting solar center and never escapes from it. (explain with equation)