You are a scientist exploring a mysterious planet. You have performed measurements and know the following things: The planet has radius d. It is orbiting his star in a circular orbit of radius b. it takes time T to complete one orbit around the star. the free-fall acceleration on the surface of the planet is a.  Derive an expression for the mass and of the star in terms of b,T, and G the universal gravitational constant.

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: A satellite is launched from the Kennedy Space Center in Florida, USA. The satellite is designed to…

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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: 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: In the figure, a square of edge length 16.0 cm is formed by four spheres of masses m1 = 4.80 g, m2 =…

A: Net gravitational force is  F = 10.56*10-15 i + 10.56*10-15 j  Newton

Q: Two planets  P1 and P2 orbit around a star S in circular orbits with speeds v1 = 44.0 km/s, and v2 =…

A:

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

A: Given that, Mass of the milky way galaxy, M=8×1011 Ms (Ms is the mass of Sun) M=8×1011×1.989 ×1030…

Q: An intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of T.…

A: Write the given values of the problem- T=26 hours R=2.1×108 m

Q: The center of a moon of mass m = 8 × 1023 kg is a distance D = 97 × 105 km from the center of a…

A: (a) Analyze the diagram of the given situation. Here, m, M, mo, D, x, and (D-x) represent the mass…

Q: 1. A planet with a mass of 7.5 x 1025 kg moves around a 9.5 x 1031 kg star in a perfectly circular…

A: Given Data, Mass of the planet (m)=7.5×1025 kg Mass of the star (M)=9.5×1031 kg Radius of the…

Q: a ship is orbiting a planet (M = 3.0 x 10^24 kg with a radius R = 3,600 km) roughly 10,000 km from…

A:

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

A:

Q: 1.) Assume that a satellite orbits Earth 225 km above its surface. Given that the  mass of Earth is…

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

Q: One of your summer lunar space camp activities is to launch a 1170 kg rocket from the surface of the…

A: The expression for the required gravitational potential energy,

Q: Planet Z-1 has a mass equal to one-third that of the Earth and a radius equal to one- third that of…

A: Given data: Mass of earth = M Mass of planet Z-1 (M1) = (1/3)M Radius of earth = R Radius of planet…

Q: A meteoroid is traveling with a velocity of 10.0 km/s directly toward the Earth when it is located 5…

A: v = 10 km/sec= 10000 m/s initial position = 5 R final position = R

Q: A minimum-energy transfer orbit to an outer planet consists of putting a spacecraft on an elliptical…

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Q: distant planet that rotates on its axis with a period of T. The spaceship enters a geosynchronous…

A:

Q: Some of the most spectacular objects in the universe are fairly small: neutron stars are spheres…

A: we have g=GMearthRearth2

Q: At what altitude above Earth's surface would the gravitational acceleration be 4.10 m/s?? (Take the…

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Q: Problem 1. A planet with a mass of 7.00x10-" kg is in a circular orbit around a star with a mass of…

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: The gravitational acceleration (gravitational field) at the surface of a Planet A is 9 m/s?. The…

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Q: Sketch the earth and mars, showing the center of the planets being separated by a distance d = 3 x…

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Q: (a) At what position in its elliptical orbit is the speed of a planet a maximum? O when it is…

A: Kepler's planetary law states that the areal velocity of a planet is constant that is a planet…

Q: The planet Pluto has an equatorial diameter of 1,188.3 km and its mass is 1.30900 * 1022 kilograms.…

A:

Q: A meteoroid is traveling with a velocity of 10.0 km/s directly toward the Earth when it is located 5…

A: We will use conservation of mechanical energy to solve this.

Q: One model for a certain planet has a core of radius Rand mass M surrounded by an outer shell of…

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

A: The gravitational force between two masses m1, and m2 seperated by a distance r is given…

Q: Two planets P, and P orbit around a star S in circular orbits with speeds v = 44.2 km/s, and v2 =…

A: According to Kepler's third law, in any planetary system, the third power of the orbital radius of 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,…

Q: When a falling meteoroid is at a distance above the Earth's surface of 2.4 times the Earth's radius,…

A:

Q: Problem 1 ysterious new planet has a radius of R = 6750 kilometers (km) and a mass of M = 2.75×1024…

A: Given, R = 6750 km M = 2.75 x 1024 kg h = 850 km G = 6.67 x 10-11 Nm2kg-2   (a) Speed of orbit , v =…

Q: Two planets P, and P, orbit around a star S in circular orbits with speeds v, = 46.8 km/s, and v, =…

A: Given: The speed of first planet is v1=46.8 km/s. The speed of second planet is v2=59.6 km/s. The…

Q: The eccentricity e of the Moon's orbit is 0.0549 and the mean orbital radius r, = (ab)l2 is 384,100…

A: a) Given:- e= √(1-(b/a)2) = 0.0549 => b =a√(1-0.0549^2).     (I) rL= √(ab) = 384100 km    =>…

Q: An object has a weight W when it is on the surface of a planet of radius R. What will be the…

A: Recall F=GMm/R2Where M mass of planet, m is mass of object and R is radius of the planet.

Q: Three objects of equal mass (m) are located at three corners of a square of edge length ℓ, as shown…

A: Given variable : mass -m edge of square -l

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

A:

Q: Assume a planet is a uniform sphere of radius R that (somehow) has a narrow radial tunnel through…

A: I this question we have to assume a planet is a uniform sphere of radius R that (somehow) has a…

Q: A satellite used in a cellular telephone network has a mass of 2410 kg and is in a circular orbit at…

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Q: An object of mass m is released from rest a distance R above the surface of a planet of mass M and…

A: According to the principle of conservation of energy, the total energy of the object must be…

Q: An object of mass is released from rest a distance 3.2R above the surface of a planet, which has no…

A:

Q: The magnitude of the gravitational field on the surface of a particular planet is 1/2g. The planet’s…

A: strength of gravitational field, g=GMR2where, G-gravitational constant           M-mass of planet…