OrbitalMotionSE

Kepler's Third Law and Newton's Law of Universal Gravitation (a) Use Newton's Universal Law of Gravitation and what you know about centripetal acceleration/force to derive Kepler's Third Law for a planet in a circular orbit about the sun: T² = Kr³ K = constant = 4²/GM where T is the orbital period of the planet (the time for one complete orbit), r is the radius of the planet's orbit, M is the mass of the sun, and G is the universal gravitational constant. (b) Determine the metric system units of K and show that they make the units of T² – Kr³ work out correctly. (c) The earth orbits the sun once per year (365 days) and its average orbital radius is 1.50 x 10¹¹ m. Use this information and Kepler's Third Law to estimate the mass of the sun in kilograms. [answer: about 2 x 10³⁰ kg] (d) The radius of the sun is about 7 x 108 m. Use this radius and the mass of the sun estimated in part (c) to estimate the acceleration of an object near the surface of the sun. [answer: about 300 m/s²] F₂ =G…

The moon on Mars Phobos ( Fear) and Deimos ( Terror) are very close to the planet compared to Earth's Moon. Their orbital radii are 9,376 km and 23,463.2 km respectively. A) what is the orbital speed of Phobos to that of Deimos? B) If the period of Phobos orbits 7hr 39.2 min, what is the mass of Mars? C) Calculate the orbital period of Deimos.

Which of the following are, or follow directly from, Kepler's Laws of planetary motion?  Check all that apply. More distant planets move at slower speeds.   The force of attraction between any two objects decreases with the square of the distance between their centers.   The orbit of each planet about the Sun is an ellipse with the Sun at one focus.   A planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun.   As a planet moves around its orbit, it sweeps out equal areas in equal times.

Kepler's Law What does Kepler's third law predict for the period of an Asteroid's orbit around the Sun? Give your answer in Years G=6.67x10-11 Nm2/kg2 MAsteroid=8.8x1020 kg MEarth=5.97x1024 kg MSun= 2.00x1030 kg Distance from Sun to Asteroid = 5.50x1012 m %3D There are 3.15x107 seconds in 1 earth year. Years

Far into the future scientists are exploring a new planetary system in hopes of finding an Earth-like planet. In this system they find a planet with five moons, and they decide to study these moons in order to learn more about the planet. Here's what they find: • Moon A orbits the planet once every 2.3 days in a circular orbit with a radius of 7.87x107m. • Moon B has a highly elliptical orbit with an average orbital radius of 1.56x108m that takes 6.4 days. • Moon C has a speed of 1550 m/s in its circular orbit of radius 2.03x108 m. • Moon D has an orbital period of 10.9 days with an average orbital radius of 2.23x108 m. • And Moon E seems to get four times further than Moon B does at their furthest point from the planet. Scientists observed that half its orbit took 25.6 days. Use this data to make a linear plot such that you can use the slope of the line to find the mass of the planet. You may plot quantities such as distances, speeds, or periods, or any powers of those quantities, and…

Kepler's Law What does Kepler's third law predict for the period of Mars' orbit around the Sun? Give your answer in Days. G=6.67x10-11 Nm2/kg? MMars=6.4x1023 kg MEarth=5.97x1024 kg MSun= 2.00x1030 kg Distance from Sun to Mars = 2.28×1011 n m There are 86400 seconds in 1 day. Days

19. Saturn’s moon Mimas has an orbital period of T= 82,800 s at a distance of d= 1.87 × 10^8 m from Saturn. Using Kepler's 3rd law listed below for mass to determine Saturn’s mass. You must show your calculations for credit.

Please answer the following question(s): 1. You have been selected to be the first person to travel to Mars, you are curious how strong gravity is there. Given the radius of Mars is 3.39-106 m, the mass is 6.39-1023 kg and the gravitational constant of 6.67-10-11 calculate the acceleration due to gravity on the Nm² kg² surface of Mars to three significant figures. Enter to 3 significant figures agrav= s²

Explain Gravitation and Kepler’s Laws of Planetary Motion?

Question 24 Use the information and the equation in lab # 9 “The Relationship between Revolution and Distance” to answer the following problem.  If the moon of the hypothetical planet X has a distance of 0.2 AU (astronomical units) and has a period of revolution around Planet X = 0.3 years what is the mass of this planet in solar units.     a. 0.01   b. 0.5   c. 0.6   d. 0.089

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…

Kepler’s Law relates the period T ( in a sec) of a satellite to the distance from the center of the earth r (in m) to some physical constants as shown:                  T2 = (2π/ G ME) r3 Where G = Universal Constant of Gravitation and ME is the mass of the earth.  A stationary satellite is one that circles the earth in a circular orbit but stays exactly above the same spot on the earth. Calculate the distance above the earth in m for this “geo-synchronous satellite” to orbit, then convert that height to miles.

Differential Equation  "Rectilinear motion And Escape Velocity " (TOPIC) Please show solutions Thankyouu!

Two planets orbit a star. You can ignore the gravitational interactions between the planets. Planet 1 has orbital radius r₁, and planet 2 has r₂ = 4r₁ Planet 1 orbits with period T₁ Planet 2 orbits with period A. T₂ = -1/T₁ B. T₂=2T₁ C. T₂ = 4T₁ D. T₂=8T₁

An object is orbiting earth at a height of 100 km from the surface. What's the period? Gravitational Constant, G = 6.673 x 10 Newtons kg-2 m² Mass of the Earth, Me = 6 x 1024 kg Radius of the Earth, R = 6400 km %3D Note: Your answer should be in second. Round the answer to two decimal places.

Direction: Complete the table below. Calculate the problem using the Laws of Planetary Motion based on the given basic planetary data below. F Earth Mars Saturn Uranus Neptune Jupiter 1. 3. Mean Distance(r) Period of 1.496 x 108 44.97x108 2.28 x 108 14.27x108 2. 4. Revolution (T) 365.2 days 1.88 yrs. 11.86 yrs. 84 yrs. Using the Earth as reference, determine the mean distance(r) or the Period of revolution (T) of each planet. Here is the formula in the Law of Period. (T₁)² (r₁)² (T₂)² (r₂)² = 1. Find the Mean distance of Jupiter. 2. Find the Period of Saturn 3. Find the mean distance of Uranus. 4. Find the Period of Neptune.

4 Hello, I have questions about the physics, can you please help me with your diagram and explanation? I am highly appreciate it and thank you very much! In 1843, a comet passed extremely close to the sun, mass Ms: its distance from the perihelion was d = 6.1*10^3 * a0, where a0 is the radius of the Earth's orbit. Accurate measurements showed that the eccentricity of the comet was e=1-x with x = 9.4*10^-5. Given u = 30 km/s is the speed of revolution of the Earth around the Sun. (a) Express the product GMs as a function of u and a0. (b) Considering that the trajectory of the comet is quasi-parabolic, calculate its speed of passage vp at the perihelion. (c) Deduce the speed Va of transition to aphelion as a function of Vp and x. Do the digital application. (d) In what year will this comet return to the solar system?

What is the gravitational acceleration between two identical 5,000,000,000,000 kg asteroids whose centers of mass are separated by 1000 m? Represent your answer without using scientific notation. G = universal constant of gravitation = -11 6.67x10 N m2 / kg2

7. Kepler's Third Law relates the period (P) it takes a planet to go around the Sun in an orbit of a given semi-major axis (a). Assume that the mass of the Sun is much, much greater than any of the planets (which it is), and measure P in years and a in astronomical units. The simplified relationship (formula) is: P =a The following two orbits have the same value for a. How do their values of P compare?

What would Kepler’s third law be for circular orbits if an amendment to Newton’s law of gravitation made the gravitational force inversely proportional to r3? Would this change affect Kepler’s other two laws? Explain.