A satellite of mass (m) revolves around the earth of radius (R) at a height (h) from its surface. If (g) is the acceleration due to gravity on the surface of the earth, the orbital speed of the satellite is : (a) gh (c) gR² R+h (b) (d) gR R-h gR² R+h 1/2
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A: Please see the answer in step 2
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- Two planets P, and P, orbit around a star S in circular orbits with speeds v, = 44.4 km/s, and v, = 59.6 km/s respectively. (a) If the period of the first planet P, is 7.80 years, what is the mass of the star it orbits around? kg (b) Determine the orbital period of P,. yrA communications satellite is launched into circular orbit around the Earth, at an altitude h. The satellite's mass is m, and it was launched from Earth's surface. (Use the following as necessary: Refor the radius of the Earth, Me for the mass of the Earth, G for the gravitational constant, m, and h.) (a) How long does the satellite take to complete one circular orbit? T= (b) What is the satellite's speed? V satellite (c) What is the minimum energy input necessary to place this satellite in orbit? Ignore air resistance but include the effect of the planet's daily rotation. (Use the following as necessary: RE, ME, G, m, h, and Te for the period of Earth's rotation.) AE minA geosynchronous satellite moves in a circular orbit around the Earth and completes one circle in the same time T during which the Earth completes one revolution around its own axis. The satellite has mass m and the Earth has mass M and radius R. In order to be geosynchronous, the satellite must be at a certain height h above the Earth’s surface. Part (a) Derive an expression for h in terms of m, M, R, T and constants. Part (b) Calculate the numerical value for h in meters.
- One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M = 4.07 × 1024 kg and R = 5.79 x 106 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet? (a) Number i Units (b) Number i Units(a) Evaluate the gravitational potential energy (in J) between two 6.00 kg spherical steel balls separated by a center-to-center distance of 19.0 cm. (b) Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast (in m/s) will they each be traveling upon impact. Each sphere has a radius of 5.20 cm. m/s(a) Evaluate the gravitational potential energy (in J) between two 4.00 kg spherical steel balls separated by a center-to-center distance of 19.0 cm. (b) Assuming that they are both initially at rest relative to each other in deep space, use conservation of energy to find how fast (in m/s) will they each be traveling upon impact. Each sphere has a radius of 5.50 cm. m/s
- On the ground level, the weight of a satellite is W N. The satellite is launched and stays in an orbit that is R/47 above the ground level, where R is radius of the Earth. If the gravitational force on the satellite is xW at this location, determine x.A satellite of Mars, called Phobos, has an orbital radius of 9.4 ✕ 106 m and a period of 2.8 ✕ 104 s. Assuming the orbit is circular, determine the mass of Mars. (ans kg)Current Attempt in Progress One model for a certain planet has a core of radius R and mass M surrounded by an outer shell of inner radius R, outer radius 2R, and mass 4M. If M-2.97 x 1024 kg and R-8.31 x 10 m, what is the gravitational acceleration of a particle at points (a) R and (b) 3R from the center of the planet? (a) Number (b) Number Units Units
- An asteroid, whose mass is 2.0 × 10-4 times the mass of Earth, revolves in a circular orbit around the Sun at a distance that is 2.7 times the Earth's distance from the Sun. (a) Calculate the period of revolution of the asteroid in years. (b) What is the ratio of the kinetic energy of the asteroid to the kinetic energy of Earth? (a) Number i Units (b) Number i UnitsAssuming that the Earth has a uniform density, ρ=5540.0 kg/m3, what is the value of the gravitational acceleration gd at a distance d=4900.0 km from the Earth's center?A planet requires 340 (Earth) days to complete its circular orbit around its sun, which has a mass of 7.5 x 1030 kg. What are the planet's (a) orbital radius and (b) orbital speed?