. Two spherical objects have masses of 3.1 x 10° kg and 6.5 x 10° kg. The gravitational attraction between them is 65 N. How far apart are their centers? G = 6.67 x 1011 Nm²/kg?
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- 1. Find the centroid. The disk has radius 2ft and the hole has radius 0.5ft. yD Gm₁m₂ Fg KE = mv², Ug = - 2πr , ac = =²₁, v = ²7₁ T Gm₁m₂ GM g = G, Vesc = 2GM R , E = KE + Ug, G = 6.674 x 10-¹1 Nm²/kg² Problem 1: You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its radius to be 9 x 106 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.2 x 10¹¹ m from its star with a period of 402 days (3.473 x 107 sec). Once on the surface you find that the free-fall acceleration is 12.2 m/sec². a) What is the mass of the planet? Answer: 1.5 x 1025 kg. b) What is the mass of the star? Answer: 5.2 x 1030 kg.A spacecraft reaches the SOI of a planet with V = 500 m/s, ø = -65°. Use rsoj = Obtain m³/s?. 5.781 × 108 m, m, Hplanet = 4.297e13 Tplanet = 3.393 × 106 b, d, E using (r.co = 0), H, e, a, rperiapsis, hperiapsis of the orbit. Place your answers in a table.
- 2. An earth-orbiting spacecraft is known to have the following orbital elements: a 15000 km 55 deg e = 0.3 @= = 130 deg 260 deg 35 deg Find the position and velocity vectors (expressed in ECI coordinates). = V = 3. Complete the LEO-to-GEO 'Hohmann Transfer with Split Plane Change problem defined in class. Specifically, define the optimal amounts of inclination that should be removed at perigee and apogee and the minimum AVT. Assume an initial circular orbit with altitude 300 km and inclination 28.5 deg.Can you please help w/ the question in the pic? This is the data I have so far: 1. Determine the mass M of the massive object at the center of the Milky Way galaxy. Take the distance of one light year to be 9.461x10^15: answer= 4.26*10^37 2.Express your answer in solar masses instead of kilograms, where one solar mass is equal to the mass of the sun, which is 1.99*10^30: answer=2.14*10^7 TIAS Skype O Launch M X A Meet - pc X + 2020 SEC X Zohdy - DX Course: 2 X college.com/course.html?courseld=16544025&OpenVellumHMAC=2edceb9788c2d7ed3b6b62e30e29d5d3#10001 M Inbox (97 X M Inbox (1) Course H X O Maps Марs O Web design tutori. W MATH180: HW08-. Update Problem 13.37 < 7 of 7 I Review I Constants Part A What is the total gravitational potential energy of the three masses in the figure(Figure 1)? Assume mi = 30kg. m2 = 5kg and m3 = 5kg. %3D Express your answer to two significant figures and include the appropriate units. HẢ ? U = Value Units Submit Request Answer 1 of 1 Provide Feedback Figure < Return to Assignment m2 20 cm m3 mi 10 cm P Pearson MacBook Pro F11 F10
- a. Find the acceleration due to gravity at the surface of a neutron star of mass 1.5 solar masses and having a radius of R = 10.0 km. b. Find the weight of a 0.120-kg baseball on the surface of this star. c. Assume the equation U = mgh applies, and calculate the energy that a 70.0-kg person would expend climbing a 1.00-cm-tall mountain on the neutron star. d. Find the speed needed by a small satellite to maintain a circular orbit with a radius of 2R around the neutron star.Black holes are difficult to observewith telescopes because they, bydefinition, don’t emit or reflect any light. They can be found by look-ing for other nearby objects orbit-ing them, however. Here is a dia-gram of a star in a circular orbit around a black hole. a. The period of the star’s orbit is 90 days, and its orbital radius around the black hole isobserved to be 3.6 : ×10^11 m. Find the orbital velocity of the star in units of m/s. (You need to convert 90 days to seconds, first). The circumference of a circle is 2πr. b. The mass of the star is known to be 4 × 10^30 kg. Find the centripetal acceleration of thestar and the strength of the gravitational force on the star. c. Find the mass of the black hole.The figure shows a 8-kg sphere attached to the light rigid rod, which rotates in the horizontal plane centered at O. (Figure 1). Figure 1 of 1 0.6 m M = (0.9) N-m %3D 35° F= 40 N
- 4. A spaceship moves radially away from Earth with acceleration 29.4 m/s². How much time does it take for the sodium streetlamps (1 = 589 nm) on Earth to be invisible (with a powerful telescope) to the human eye of the astronauts? The range of visible wavelengths is about 400 to 700 nm.Small differences in the wavelengths in the sun’s spectrum are detected when measurements are taken from different parts of the sun’s disk. Specifi cally, measurements of the 656-nm line in hydrogen taken from opposite sides on the sun’s equator—one side approaching Earth and the other receding—differ from each other by 0.0090 nm. Use this information to fi nd the rotational period of the sun’s equator. Express your answer in days. (The sun’s equatorial radius is 6.96 x 108 m.)The speed of light is exactly e = 299792458 m - s1. (Also written 299, 792, 458 m - s-1 or 2.99792458 × 10°m - s1. This is exact because it is the definition of the metre.) It takes light 8.3 minutes to get from the sun to the earth. Assuming that the earth's orbit is exactly circular (an approximation) and that its speed is constant, and using the data in this question, calculate the speed of the earth in its orbit around the sun in km · hr. Practise writing your conversions clearly using the 'multiply by 1' technique. Speed of the earth =_ km per hour. Write your answer in standard (not scientific) notation, i.e. without using exponents, and without using commas. However, remember to use the correct number of significant figures. (Hint: which is the least precise of the given data?) Do not include units.