A comet has a period of 71.3 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.700 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units. HINT (a) the semimajor axis of the comet (in AU) 34.4 X AU (b) an estimate of the comet's maximum distance (in AU) from the Sun 33.67 Remember that the semimajor axis, a, is half the longest distance across an ellipse. For the special case of a circular orbit, the semimajor axis equals the orbital radius. AU

A comet has a period of 71.3 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.700 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units. HINT (a) the semimajor axis of the comet (in AU) 34.4 X AU (b) an estimate of the comet's maximum distance (in AU) from the Sun 33.67 Remember that the semimajor axis, a, is half the longest distance across an ellipse. For the special case of a circular orbit, the semimajor axis equals the orbital radius. AU

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 21P: Comet Halley (Fig. P11.21) approaches the Sun to within 0.570 AU, and its orbital period is 75.6 yr....

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(a) Jupiter's third-largest natural satellite, Io, follows an orbit with a semimajor axis of 422,000 km (4.22 ✕ 105 km) and a period of 1.77 Earth days (PIo = 1.77 d). To use Kepler's Third Law, we first must convert Io's orbital semimajor axis to astronomical units. One AU equals 150 million km (1 AU = 1.50 ✕ 108 km). Convert Io's a value to AU and record the result. aIo = AU (b) One Earth year is about 365 days. Convert Io's orbital period to Earth years and record the result. PIo = yr (c) Use the Kepler's Third Law Calculator to calculate Jupiter's mass in solar units. Record the result. MJup(Io) = MSun (d) Based on this result, Jupiter's mass is about that of the Sun. Jupiter has a similar fraction of the Sun's volume. The two objects therefore have rather similar density! In fact, Jupiter has a fairly similar composition as well: most of its mass is in the form of hydrogen and helium.
A comet has a period of 72.3 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.540 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units. HINT (a) the semimajor axis of the comet (in AU) AU (b) an estimate of the comet's maximum distance (in AU) from the Sun AU
A comet has a period of 81.8 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.540 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units. (a)the semimajor axis of the comet (in AU) AU (b)an estimate of the comet's maximum distance (in AU) from the Sun AU
A comet has a period of 75.3 years and moves in an elliptical orbit in which its perihelion (closest approach to the Sun) is 0.640 AU. Find the semimajor axis of the comet and an estimate of the comet's maximum distance from the Sun, both in astronomical units. (a) the semimajor axis of the comet (in AU) (b) an estimate of the comet's maximum distance (in AU) from the Sun
(a) Based on the observations, determine the total mass M of the planet. (b) Which moon and planet of our solar system is the team observing? (Use literature.)
A new planet is discovered orbiting a distant star. Observations have confirmed that the planet has a circular orbit with a radius of 12 AU and takes 117 days to orbit the star. Determine the mass of the star. State your answer with appropriate mks units. [NOTE: AU ..stands.for...astronomical unit". It is the average distance between Earth & the Sun. 1 AU≈ 1.496 x 1011 m.] Enter a number with units. I be quite large and your calculator will display the answer as a power of 10. If, as an example, your answer was 8.54 x 1056, you would type "8.54e56" into the answer box (remember to state your units with your answer).]
Using the m, = 1.99 x 1030 kg and the mę = 5.98 x 1024 kg and the distance between them as 1.00 AU (astronomical unit), what would be the orbital period of an object orbiting the sun at a distance of 2.12 AU? (please give answer in years) Number Units
(a) A reasonably accurate value for the AU is 1.50 × 101 m. If the year is a × 107 s, (2) (a good approximation, and one easy to remember) calculate Earth's speed in km/s assuming a circular orbit about the Sun. (b) The experimental determination (first attempted by Cavendish in 1797/98) yields G = 6.67×10-11 N-m²/kg?. Calculate the mass of the Sun. (c) On the other hand, when we measure distances in AU and speeds in km/s, the constant in the Vis-Viva Equation is GM = 900. Explain why this is the case. (d) Once we know the distance to the Sun, using its angular size one could determine that the radius of the Sun is approximately Rsun = 7 × 10* m. Calculate the ratio of the Sun's density to that of water.
A comet has a period of 76.3 years and moves in an ellipticalorbit in which its perihelion (closest approach to the Sun)is 0.610 AU. Find (a) the semimajor axis of the comet and(b) an estimate of the comet’s maximum distance from theSun, both in astronomical units.
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.
The average Earth-Moon distance is 3.84 X 10^5 km, while the Earth-Sun is 1.496 X 10^8 km. Since the radius of the Moon is 1.74 X 10^3 km and that of the Sun is 6.96 X 10^5 km. a) Calculate the angular radius of the Moon and the Sun, qmax, according to the following figure. D Bax R b) Calculate the solid angle of the Moon and the Sun as seen from Earth. (c) Interpret its results; Would this be enough to explain the occurrence of total solar eclipses?
3. The Moon has a period of 27.3 days and a mean distance of 3.90×105 km from the center of Earth. a. Use Kepler's laws to find the period of a satellite in orbit 6.70x103 km from the center of Earth. b. How far above Earth's surface is this satellite?