A spacecraft of mass 1.00 × 10^3 kg orbits the sun (mass 1.99 * 1030 kg) in a circular orbit of radius 1.50 * 10^11 m (equal to the average distance from the sun to the earth). You wish to move the spacecraft into a smaller circular orbit around the sun of radius 1.08 * 10^11 m (equal to the average distance from the sun to Venus). In doing this, what will be the changes in (a) the spacecraft’s kinetic energy, (b) the gravitational potential energy of the sun–spacecraft system, and (c) the total mechanical energy of the sun–spacecraft system? Neglect the gravitational pulls of the planets on the spacecraft.

Q: A satellite is orbiting around a planet with a mass of 6.0 x 1024kg and a radius of 6.0 x 106m.  If…

A: Let G, M, m, r, and v denote the gravitational constant, planet’s mass, satellite’s mass, orbital…

Q: An artificial satellite is traveling 8.0 x 10 m/s in a circular orbit. Assuming g= 9.7 m/s at that…

A:

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: he International Space Station has a mass of 4.12 x 105 kg and is orbiting at an altitude of about…

A: In this question we have to find the speed of the International Space Station in its orbit. Please…

Q: The Earth is 149.6 billion meters from the sun, and the moon is 384.4 million meters from the Earth,…

A: Lagrange points are positions in space where objects sent there tend to stay put. At Lagrange…

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

A: (a) orbital period of the star T=2πr3GM=2π6.0×104 ly39.461×1015 m1 ly36.67×10-11…

Q: The International Space Station is in a 260-mile-high orbit. What is the station's orbital speed?…

A:

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: You wish to place a spacecraft in a circular orbit around the earth so that its orbital speed will…

A: Part-a Given: The orbital speed of the aircraft v = 4×103 m/s.

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: orbit, measured from the center of the planet is R = 2.2 x 10' m. The mass of the planet is M = 6.4…

A:

Q: A satellite of mass 175 kg is launched from a site on Earth's equator into an orbit at 180 km above…

A:

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

A:

Q: A planet has a mass of 5.98 x 10²4 kg. It has an average orbital speed of 2.978 x 104 m/s as it…

A:

Q: A spacecraft was launched to perform a mission to observe the moon in a circular orbit 120 km above…

A:

Q: Mars orbits the Sun at an average distance of 2.28 x 108 km with an orbital period of 1.881 yr. Io,…

A: Given The average distance of the mars orbit about the sun is R=2.28×108km=2.28×1011m And the…

Q: Two spherical objects have masses of 4.3*10^5 kg and 2.4*10^4 kg. The gravitational attraction…

A: mass of first object (m) = 430000 kg mass of second object (M) = 24000 kg Gravitational force (F) =…

Q: Scientists have discovered a distant planet with a mass of 6.0x1023 kg. The planet has a small moon…

A: Mass of the planet, M = 6 X 1023 kg Time period of moon of planet, T = 5 hours 40 minutes = 340…

Q: ets are in orbits that are similar to that of earth, which orbits the sun (MsunMsun = 1.99× 10^30kg)…

A:

Q: A rocket is launched off the surface of earth. If it has a speed of 2.62×103 m/s, what height above…

A: Consider the mass of the Earth be M, the rocket’s mass be m, the distance of the rocket, that is the…

Q: Two satellites are in circular orbits around a planet that has radius 9.00×106m9.00×106m. One…

A:

Q: A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant…

A: Given data: Speed of the satellite, v=1.1×104 m/s Mass of the planet, M=6.04×1024 kg Mass of the…

Q: A 3000-kg satellite orbits the Earth in a circular orbit 11797 km above the Earth's surface (Earth…

A: Given that,Mass of satellite : m = 3000 (kg)Radius : r = 6380+11797 = 18177×103Here we need to find…

Q: Newton's theory of gravity, together with the Cavendish experiment to measure the value of Newton's…

A: mass = M = 1.989 X 1030 Kg radius = R = 6.96 X 108 m

Q: Scientists want to place a 4 × 103 kg satellite in orbit around Mars. They plan to have the…

A:

Q: The Earth’s orbit around the Sun is slightly elliptical. At Earth's closest approach to the Sun…

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

A: mass of milky way (m) = 8×1011 solar masses = 8×1011×2×1030kg = 16×1041 kg distance (d) = 5.6×104…

Q: A meteoroid is heading directly to the Earth. The speed of the meteoroid is 2000 m/sec when it is at…

A: Given Data:  Speed of Meteoroid Sm=2000 msec Distance between Meteoroid and Earth is (d)=3.84×108 m…

Q: Two spherical objects have a combined mass of 160 kg . The gravitational attraction between them is…

A: Total Mass = 160 kgM+m = 160 kg ....(i)Force = 7.61 x 10-6 Ndistance (d) = 21 cm…

Q: An Earth satellite has an orbital period of 5.3 h. What is its orbital radius? (ME = 5.98 x 1024…

A: The orbital period of the satellite is 5.3 h.The mass of the earth is 5.98x1024 kg.

Q: The mass and radius of a planet are M and R, respectively. A satellite of mass m orbits the planet…

A: The angular momentum is given by  L = mv r

Q: Problem 6: Two satellites are in circular orbits around a planet that has radius 9 x 106 m. One…

A: Q6.  Since both satellites are orbiting around same planet, So  Using force balance on satellites:…

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

A:

Q: A satellite with a mass of 500 kg orbits at an altitude of 3.8 x 10^5 meters above Earth, which has…

A:

Q: The earth is 150 × 10^9 m from the Sun. Earth and Sun masses are 5.97 × 10)^24 ?? and 1.99 × 10^30…

A: Answer             a) 35.219 X 10^21N             b) 8800.85hr

Q: Astronomers discover an exoplanet, a planet orbiting a star other than the Sun, that has an orbital…

A: The orbital period of a planet is, The planet’s mass is,

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.