A spacecraft of mass m is in a clockwise circular orbit of radius R around Earth.. The mass of Earth is ME. Derive an equation for the orbital period T of the spacecraft in terms of m, ME, R, and physical constants, as appropriate.

Q: Determine the height habove the surface of a planet of radius R and mass M at which the…

A: The gravitational field will be 60% on its surface, gh=g×60100=35g Then, weight of a mass on the…

Q: 1.1 A thin uniform disk of radius a, mass m and A mass per unit length. Find the grav ring exerts on…

A: Given:- A thin uniform disk of radius a, mass m and ) mass per unit length. thering exerts on a…

Q: velocity of the proton in units of km/s

A: Given: Mass of proton is m=1.673×10-27 kg Charge on proton is q=1.6×10-19 C Radius of path is r=4.46…

Q: A satellite is orbiting around a planet in a circular orbit. The radius of the orbit, measured from…

A: R=1.8×107 mM=4.8×1024 kg From the conservation of energy, 12mv2=GMm2R, here G is gravitational…

Q: While standing on the surface of a spherical asteriod of mass M and radius R., and astronaut thows a…

A: Mass of asteroid=MRadius=RMaximum height=h

Q: According to Lunar Laser Ranging experiment the average distance Lm from the Earth to the Moon is…

A: The average distance from the Earth to the Moon is given as, LM = LL×105 km (or) LM = 3.85×105 km…

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: A solid copper sphere of mass M and radius R has a cavity of radius ½ R. Inside the cavity a…

A: The force due to first sphere is, The force due to second sphere is,

Q: a) A 95 kg astronaut stands on the surface of a spherical asteroid with a mass of 4.5 x 1015 kg and…

A: Please see the answer below.

Q: You have been assigned to a team charged with developing a plan to explore a new planetary body…

A: Given g=2.8 m/s2 specific gravity of oil=0.93 weight of oil=4 lbf

Q: An engineer wants a satellite to orbit the earth with a period of 28 hours. Hint: You need to find…

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: In most calculations, we use W 2 mg. But we know that, for large changes in altitude, we need to use…

A: Given: The radius of the earth is re = 6400 km

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 satellite in orbit around the earth is at an altitude of 41.5 percent of the earth's radius.…

A:

Q: A planet in an orbit around the planet Mars has a period of 7 hours, 39 minutes and an orbital…

A: We know that a planet in an orbit around the planet Mars has a period of 7 hours, 39 minutes and an…

Q: A satellite of earth has a speed of 5900 m/s. Find: a) the radius of the orbit b) the period of…

A:

Q: A star is observed to undergo circular orbit around the black hole located at the centre of the…

A: We have a star which is undergoing a circular orbit of radius R=1000 AU=1.469*1014m with a time…

Q: At what altitude h above the north pole is the weight of an object reduced to 27% of its…

A:

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: The value of g at any latitude o may be obtained from the formula g = 32.09(1+ 0.0053 sin' 4) ft/s…

A:

Q: Suppose a planet is discovered that has the same amount of mass in a given volume as the Earth, but…

A: Suppose a planet is discovered that has the same amount of mass in a given volume as the Earth, but…

Q: While visiting Planet Physics, you toss a rock straight up at 11 m/s and catch it 2.5 s later. Your…

A: The speed of the rock is 11 m/s. The time taken to catch the rock is 2.5 s. The time taken by the…

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

A:

Q: Four planets of equal mass m are rotating with speed v in a circular orbit of radius R. The four…

A: Gravitational force is given as F = Gm1m2/r2

Q: According to Lunar Laser Ranging experiment the average distance LM from the Earth to the Moon is…

A:

Q: Scientists are studying a planet in a faraway galaxy that has the potential to sustain life. It has…

A: Given: Mass of planet is 5.97 x 1024 kg. Mass of star is 1.99 x 1030 kg. Distance during perihelion…

Q: A spacecraft revolves around the Earth in an elliptical orbit at an average distance equal to 10…

A: Say radius of the earth be R km then the radius of the elliptical path of the spacecraft is 10R.

Q: the velocity and orbital period of the spacecraft?

A:

Q: Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 x 1011…

A: The time period of an astronomical object revolving around a central mass is given by Kepler's third…

Q: Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 x 1011…

A: Given data, Mass of the galaxy = 8x1011 solar mass Radius of the orbit = 5.8x104 light years Time…

Q: A woman whose weight is 680 N on the Earth’s surface is in a spacecraft at an altitude above the…

A: Weight, W = 680 N  Weight in the spacecraft, W' = ?

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: The mean radius of earth from the Sun is 0.67 times the mars mean distancxe of mars from the sun.…

A: given that, The mean radius of earth from the Sun is 0.67 times the mars mean distance of mars from…

Q: The free-fall acceleration on the surface of a fictional planet is about 1/2 that on the surface of…

A: Given On frictional planet acceleration is gp =gE /2 Or gp/gE=1/2 With gE =gravity on earth. Radius…

Q: Two planets P, and P, orbit around a star S in circular orbits with speeds v, = 44.4 km/s, and v,…

A:

Q: Tidal forces are gravitational forces exerted on different parts of a object by a second object.…

A: The acceleration experienced by unit mass located at the point on the Earth's surface.

Q: (a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an…

A: given,  Vi = 5.96x104 m/s from conservation of energy, the initial total energy of the object at the…

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: A mood of a mass m and raduis a is orbiting a planet of mass M and if radius b at a distance d…

A: in this case, the gravitational force between the two is equal to the centripetal force of the mood,…

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.