A 3390-kg spacecraft is in a circular orbit 1990 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 3990 km above the surface? Express your answer to three significant figures. Please find deltaE The answer is not 6.336*10^9,
0.407 *10^10 ,
7.05*10^9 ,
1.56*10^10
It is something different, all of the above are wrong.
total E = KE + GPE = ½mv² - GmM/r
and that for orbit, centripetal acceleration = gravitational
acceleration, or
v²/r = GM/r², which rearranges to v² = GM/r
So TE = ½m(GM/r) - GmM/r = -½GmM/r
where G = Newton's gravitational constant = 6.674e−11
N·m²/kg²
and M = mass of Mars = 6.42e23 kg
and m = 3390kg
and the radius of Mars R = 3.4e6m
first orbit: TE = -½ * 6.674e-11N·m²/kg² * 3390kg * 6.42e23kg /
(3.4e6m + 1.99e6m)
TE = -13. 452J
second orbit: TE = -½ * 6.674e-11N·m²/kg² * 3390kg * 6.42e23kg /
(3.4e6m + 3.99e6m)
TE = - 9.8J
Required Work = 3.64gJ
Note that the higher orbit is LESS NEGATIVE and therefore has
GREATER ENERGY (hence the negative sign for GPE).
A 3390-kg spacecraft is in a circular orbit 1990 km above the surface of Mars. How...
A 3000-kg spacecraft is in a circular orbit 2420 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4030 km above the surface?
A 3330-kg spacecraft is in a circular orbit 2770 km above the surface of Mars. How much work must the spacecraft engines perform to move the spacecraft to a circular orbit that is 4960 km above the surf
A spacecraft with mass 1500 kg is in a circular orbit at an altitude 200 km above the surface of Earth. A) Use the Law of Universal Gravitation and Newton's 2nd law for circular motion to derive and find the speed of the spacecraft in this orbit. B) How much mechanical energy does the spacecraft have in this orbit? C) How much work must the spacecraft engines perform to get it into the above circular orbit from the surface of...
80.A spacecraft is approaching Mars after a long trip from the Earth. Its velocity is such that it is traveling along a parabolic trajectory under the influence of the gravitational force from Mars. The distance of closest approach will be 300 km above the Martian surface. At this point of closest approach, the engines will be fired to slow down the spacecraft and place it in a circular orbit 300 km above the surface. (a) By what percentage must the...
(13% ) Problem 5: A 4500-kg spaceship is in a circular orbit 170 km above the surface of Earth. It needs to be moved into a higher circular orbit of 390 km to link up with the space station at that altitude a How much work, in joules, do the spaceship's engines have to perform to move to the higher orbit? Ignore any change of mass due to fuel consumption. Grade Summary 0%
A spacecraft is in circular orbit 200 km above Earth's surface. What minimum velocity kick must be applied to let the spacccraft cscapc from Earth's influcncc? What is the spacecraft's escape trajectory with respect to Earth?
A 5000 kg lunar lander is in orbit 10 km above the surface of the moon. It needs to move out to a 200 km -high orbit in order to link up with the mother ship that will take the astronauts home. How much work must the thrusters do? Express your answer with the appropriate units. I got 1568.5*10^6 J but it is incorrect
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...
A satellite is in circular orbit at an altitude of 4600 km above the surface of a nonrotating asteroid with an orbital speed of 11.8 km/s. The minimum speed needed to escape from the surface of the asteroid is 29.2 km/s. The mass of the asteroid is closest to Question 6 (1 point) A satellite is in circular orbit at an altitude of 4600 km above the surface of a nonrotating asteroid with an orbital speed of 11.8 km/s. The...
A 270 kg satellite is orbiting on a circular orbit 6180 km above the Earth's surface. Determine the speed of the satellite. (The mass of the Earth is 5.97×1024 kg, and the radius of the Earth is 6370 km.)