21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 11, Problem 40QP
To determine
The orbital time period of the outer edge of the Saturn’s Ring A.
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While looking through the Mt. Palomar telescope, you discover a large planetary object orbited by a single moon. The moon orbits the planet every 7.35 hours with the centers of the two objects separated by a distance roughly 2.25 times the radius of the planet. Fellow scientists speculate that the planet is made of mostly iron. In fact, the media has dubbed it the ''Iron Planet'' and NASA has even named it Planet Hephaestus after the Greek god of iron. But you have your doubts. Assuming the planet is spherical and the orbit circular, calculate the density of Planet Hephaestus.
A)At what altitude would a geostationary sattelite need to be above the surface of Mars? Assume the mass of Mars is 6.39 x 1023 kg, the length of a martian solar day is 24 hours 39minutes 35seconds, the length of the sidereal day is 24hours 37minutes 22seconds, and the equatorial radius is 3396 km. The answer can be calculated using Newton's verison of Kepler's third law.
Chapter 11 Solutions
21st Century Astronomy
Ch. 11.1 - Prob. 11.1CYUCh. 11.2 - Prob. 11.2ACYUCh. 11.2 - Prob. 11.2BCYUCh. 11.3 - Prob. 11.3CYUCh. 11.4 - Prob. 11.4CYUCh. 11 - Prob. 1QPCh. 11 - Prob. 2QPCh. 11 - Prob. 3QPCh. 11 - Prob. 4QPCh. 11 - Prob. 5QP
Ch. 11 - Prob. 6QPCh. 11 - Prob. 7QPCh. 11 - Prob. 8QPCh. 11 - Prob. 9QPCh. 11 - Prob. 10QPCh. 11 - Prob. 11QPCh. 11 - Prob. 12QPCh. 11 - Prob. 13QPCh. 11 - Prob. 14QPCh. 11 - Prob. 15QPCh. 11 - Prob. 16QPCh. 11 - Prob. 17QPCh. 11 - Prob. 18QPCh. 11 - Prob. 19QPCh. 11 - Prob. 20QPCh. 11 - Prob. 21QPCh. 11 - Prob. 22QPCh. 11 - Prob. 23QPCh. 11 - Prob. 24QPCh. 11 - Prob. 25QPCh. 11 - Prob. 26QPCh. 11 - Prob. 27QPCh. 11 - Prob. 28QPCh. 11 - Prob. 29QPCh. 11 - Prob. 31QPCh. 11 - Prob. 32QPCh. 11 - Prob. 33QPCh. 11 - Prob. 34QPCh. 11 - Prob. 35QPCh. 11 - Prob. 36QPCh. 11 - Prob. 37QPCh. 11 - Prob. 38QPCh. 11 - Prob. 40QPCh. 11 - Prob. 41QPCh. 11 - Prob. 42QPCh. 11 - Prob. 43QPCh. 11 - Prob. 44QPCh. 11 - Prob. 45QP
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- Io orbits Jupiter at an average distance of 4.22 105 km with an orbital period of 0.00485 yr. The Moon, which is one of the satellites of the Earth, orbits its parent at an average distance of 3.84 105 km with an orbital period of 0.07481 yr. (a) Use the above information to find the orbital speeds of Io around Jupiter and of the Moon around the Earth. vMoon = m/s vIo = m/s (b) What is the expression for the mass M of the parent in terms of the orbital speed v of the satellite, the orbital radius R of the satellite and the gravitational constant G? (Do not substitute numerical values; use variables only.)M = (c) Now use your answers from parts (a) and (b) to find the ratio of the mass of the Earth to that of Jupiter. ME MJarrow_forwardOrbital Radius and orbital period data for the four biggest moons of Jupiter are listed in the table below. The mass of the planet Jupiter is 1.9 × 1027 kg. Jupiter's Moon Period (s) Radius (m) T2/r3 Io 1.53×105 4.2×108 ? Europa 3.07×105 6.7×108 ? Ganymede 6.18×105 1.1×109 ? Callisto 1.44×106 1.9×109 ? What pattern do you observe in the last column of data? Which law of Kepler's does this seem to support?arrow_forwardWhat is the radial acceleration (m/s) of mercury if orbital period is 88 days and orbit radius is 5.79x10^7arrow_forward
- Given the following information on Jupiter's Galilean moons, (a) determine the average mass of Jupiter and (b) compare to the known value of 1.898 × 1027 kg. Jupiter's diameter is 1.40 × 105 km. Assume the diameter of Jupiter is 139,820 km. Period in Orbital Diameter in Name Days Jupiter Diameters lo 1.77 6.03 Europa 3.55 9.60 anymede 7.16 15.3 Callisto 16.7 26.9arrow_forwardJupiter has a mass of 1.9×10^27 kg, a radius of 7.1×10^4 km and one day lasts 9 hours and 55 minutes. How many times is the force of gravity bigger on Jupiters equator comared to Earth?arrow_forwardThe Great Red Patch is the name given to Jupiter's large red spot.Is it possible to forecast how long it will take for the planet to complete its rotation?arrow_forward
- To model a moon in the solar system, consider a sphere with radius R and uniform mass density p. Let gm = the acceleration due to gravity on the surface of the sphere. Calculate gm for these values of R and p: R = 2.0×106 m; p= 2.7x103 kg/m^3; (in m/s^2) OA: OB: 1.509 2.007 OC: 2.669 OD: 3.549 OE: OF: 4.721 6.279 OG: 8.351 OH: 1.111x101arrow_forwardNeptune's largest moon Triton has an orbit with a semimajor axis of 3.55 x 105 km. Considering that the mass of Neptune is 1.02 x 1026 kg, calculate the orbital period of Triton around Neptune, giving your answer in days.arrow_forwardIf the radius of Mercury is ~2,440 km, what is the required tangential orbital velocity needed to maintain a 100 kg satellite 1,500 km from the planet’s surface? (The mass of Mercury is Mm = 3.3 x 1023 kg)arrow_forward
- Assume these are the mass and radius of Venus. Myenus = 5 x 1024 kg, Ryenus = 6,000,000 meters. What is the velocity required to put a satellite into stable orbit around Venus starting from the surface of Venus so that it orbits once every 24 hours? [ignore the rotational velocity of Venus and gravity of the Sun] 10.23 km/s 9.95 km/s 10.35 km/s O 10.14 km/s 10.06 km/sarrow_forwardComet Halley (Fig. P11.21) approaches the Sun to within 0.570 AU, and its orbital period is 75.6 yr. (AU is the symbol for astronomical unit, where 1 AU = 1.50 1011 m is the mean EarthSun distance.) How far from the Sun will Halleys comet travel before it starts its return journey?arrow_forwardThe Great Red Patch is the term given to the enormous red area on Jupiter's surface. Are there any predictions on how long it will take the planet to complete its rotation?arrow_forward
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