Show that the radius r of the orbit of a moon of a given planet can be determined from the radius R of the planet, the acceleration of gravity at the surface of the planet, and the time τ required by the moon to complete one full revolution about the planet. Determine the acceleration of gravity at the surface of the planet Jupiter knowing that R = 71 492 km and that τ = 3.551 days and r= 670.9 × 103 km for its moon Europa.

Q: The international space station is orbiting at an altitude of about 370km above the earth's surface.…

A: Given: Altitude h : 370 km Mass of Earth ME : 5.976×1024 kg Radius of Earth RE : 6.378 ×106 m

Q: Kepler’s First Law states that planetary orbits are ellipses with thesun at one focus. The orbit of…

A: The relation is  perihelion = a (1 - e)  aphelion  = a ( 1+e)

Q: We sent a probe out to orbit the planet Kerbal at a distance of 5.5x107m from the middle of the…

A: d = 5.5 *107m T = 3.5 * 105 sec using formula, V = 2πd/T V = 2π*5.5 * 107/3.5*105V = 987.36 m/s

Q: A satellite orbits a planet in a circular orbit at an altitude (distance above the surface) of…

A: distance above the surface (h) = 1000 km = 106 m radius of planet (R) = 8000 km = 8×106 m mass of…

Q: Two earth satellites are in parallel orbits with radii 6900 km and 6901 km . One day they pass each…

A:

Q: Given the acceleration of gravity at a surface of Planet K is ⅛ of what it is on Earth and that K…

A: Acceleration due to gravity at planet K = one - eight of the acceleration due to gravity on earth…

Q: The gas-giant planet Rom (mass 5.7⨯1026 kg) goes around the star Galla (mass 2.0⨯1030 kg) in a…

A:

Q: Given: Distance of Venus to sun is 1.08×1011 m and the distance of mars to sun is 2.3x1011 m (688…

A: Solution:-

Q: Suppose that a planet were discovered between the Sun and Mercury, with a circular radius equal to…

A:

Q: In fact, the actual orbit that the GS entered was slightly elliptical, with its closest approach to…

A:

Q: Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 x 10…

A:

Q: A planet of mass ?=6.65×1024 kg orbits a star of mass ?=1.55×1029 kg in a circular path. The radius…

A:

Q: A crew capsule is returning from the ISS, whose orbit is circular with radius Re + 400 km. Prior to…

A: The capsule is coming to the smaller parking orbit from the ISS orbit. Hence, the energy of the…

Q: A satellite used in a cellular telephone network has a mass of 2060 kg and is in a circular orbit at…

A: Given,mass of the satellite m = 2060 kgheight of the satellite from surface of the earth mass of the…

Q: A spacecraft is in orbit around Jupiter. The radius of the orbit is 3.0 times the radius of Jupiter…

A:

Q: Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon.…

A: The Moon's radius is, R=1.7×106 m The acceleration due to gravity on the Moon is, gm=1.33 m/s2 The…

Q: To find some of the parameters characterizing an object moving in a circular orbit. The motivation…

A: Gravity is one of the fundamental forces of nature. It is the weakest of them all and is always…

Q: A planet with a mass of 7.5 × 1025 kg moves around a 9.5 × 1031 kg star in a perfectly  circular…

A:

Q: A 100 kg person and a 75 kg person are sitting on a bench. Estimate the magnitude of the…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8.0 • 1011…

A: Given: M= 8 x 1011 solar mass r=6 x 104 light years T= 6 x 107 years

Q: You know the gravitational acceleration at the earth's surface.  The radius of the earth is 6400 km.…

A:

Q: Suppose an asteroid named Sparty has been discovered revolving around the Sun on a circular orbit…

A: Here, the gravitational force acts as centripetal force So: mv2R=GMmR2i.e.v=GMRAnd also as v=2πRT…

Q: When a falling meteoroid is at a distance above the Earth's surface of 3.30 times the Earth's…

A: Given data:  A meteoroid is falling above the Earth's surface Altitude (h) = 3.30R Required: The…

Q: The escape speed from a distant planet is 33 km/s. If the acceleration of gravity on the planet…

A: Let us consider the escape velocity to be vesc. The required  velocity to cross a distance equal to…

Q: Two planets of equal mass orbit a certain star. The planet Iang (m1) describes a circular orbit of…

A:

Q: The distance between the Earth and Mars when the two planets are at opposition varies greatly…

A: In astronomy opposition is defined as a configuration when two astronomicl objects are located at…

Q: A remote sensing satellite of the Earth in a circular orbit at a height of 400 km above the surface…

A:

Q: the velocity and orbital period of the spacecraft?

A:

Q: Calculate the period of a satellite orbiting a planet with the mass 8.7 x 1022 kg given the height…

A: Mass of the planet, M=8.7×1022kg Height to the satellite's orbit, h=300km=300×103m Radius of the…

Q: The mass of a sun is 3.36 x 1030 kg. The radius of the circular orbit of a planet around this sun is…

A:

Q: The orbital speeds of the planets Mercury and Mars are v(Mercury) = 50 km / s and V(Mars) = 24.2 km…

A:

Q: The ratio of the radius of the earth to that of the moon is 10. The ratio of acceleration due to…

A: To find-(Ve)Earth(Ve)MoonGiven-(r)Earth(r)Moon=10(g)Earth(g)Moon=6

Q: (a) A planet is in an elliptical orbit around a distant star. At its closest approach, the planet is…

A:

Q: One of the moors of Jupiter, named an orbital radius of 10 4.22 * 10 ^ 8 a period of 1.77 days.…

A:

Q: Whenever two Apollo astronauts were on the surface of the Moon, a third astronaut orbited the Moon.…

A:

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.