A satellite of mass m is traveling at speed vo in a circular orbit of radius...
2) A satellite of mass m is in circular orbit of radius ro in a potential of the form V(r) --kr-3/2 (a) Use the Viral Theorem to find the orbital speed of the satellite. (b) What is the value of the one-dimensional effective potential at ro, Vefr(ro), for this situation? (c) Sketch Velf as a function of r for this potential, labeling your axes carefully, The satellite is now given an impulse which increases its kinetic energy by 20%. (d)...
A satellite of mass m is in a circular orbit of radius r about a planet of mass M. The period of the satellite's orbit is T. A second satellite of mass 2m is in a circular orbit of radius 2r around the same planet. The period of orbit for the second satellite is 2T 8T O2T OT O 4T
A spacecraft of mass m = 1900 kg is moving on a circular orbit about the earth at a constant speed v = 5.12 km/s. [Given: Mass of the earth M = 5.98 times 10^24 kg, radius of the earth R = 6.37 times10^6 m, gravitational constant G = 6.67 times 10^-11 N.m^2/kg^2.] a. Determine the radius r of the circular orbit. b. What is the period T of the orbit? c. The satellite, by firing its engines, moves to...
Satellite A has mass MA 1997 kg and moves in a circular orbit of radius RA - 10.3x10 m around a planet (measured from its center). The mass of the planet is M - 6x10 kg and the universal gravitational constant is G = 6.67 x 10-11 NmⓇ/kg. 1) What is the speed V of the satellite ? OV - 7605 m/s OV- 13152 m/s OV - 6233 m/s OV-5109 m/s OV-8976 m/s Submit 2) Satellite B moves in a...
The planet shown has a mass of M, and the satellite is in a circular orbit of radius r. a) In terms of M, r, and the universal gravitational constant G, what is the period Tof the satellite? Derive the formula. b) By what factor would the period change if the mass of the planet doubled? c) By what factor would the period change if the radius of the orbit doubled?
Accidently uploaded the photo in a recent question and need help solving this one. 3. Earth's orbit. The Earth, with mass m and angular momentum L, moves around the Sun in arn elliptic orbit of eccentricity e. The equation of trajectory is given by, r=p1+ecoso 1+e where p is the distance of the closest approach to the Sun (perihelion) (a) Find the two components of the velocity as functions ofQie, v,(9) and vo(9). (8 marks) (b) Prove that the angle...
An object of mass m moves at a constant speed v in a circular path of radius r. The force required to produce the centripetal component of acceleration is called the centripetal force and is given by F=mv2/r. Newton's Law of Universal Gravitation is given by F=GMm/d2, where d is the distance between the centers of the two bodies of masses M and m, and G is a gravitational constant. The speed required for circular motion is v= √(GM/r). Use the...
A small satellite of mass m is in circular orbit of radius r around a planet of mass M and radius R, where M>>m. a) For full marks, derive the potential, kinetic, and total energy of the satellite in terms of G, M, m, and r assuming that the potential energy is zero at r=infinity. b) What is the minimum amount of energy that the booster rockets must provide for the satellite to escape? c) Now we take into accouny...
A satellite with mass 748 kg is in a circular orbit with an orbital speed of 9040 m/s around the earth. What is the new orbital speed after friction from the earth's upper atmosphere has done -7.5×109 J of work on the satellite? Express your answer with the appropriate units.
A satellite with mass 898 kg is in a circular orbit with an orbital speed of 5840 m/s around the earth. a) What is the new orbital speed after friction from the earth's upper atmosphere has done −7.5×10^9 J of work on the satellite? Express your answer with the appropriate units. b) Does the speed increase or decrease?