You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be and its rotation period to be You have previously determined that the planet orbits from its star with a period of . Once on the surface you find that the free-fall acceleration is What is the mass of (a) the planet and (b) the star?
a. The mass of the planet is
b. The mass of the star is
Radius of planet = , time period = , free-fall acceleration =
Using the formula of gravitational law we get :
Where, F is gravitational force, M is mass of planet and r is the radius between masses.
Solving for acceleration we get :
The mass of the planet is
Orbit distance = time period =
Using Kepler's third law of planetary motion, the time period is given by :
Where, T is the time period, R is the radius of orbit of star, G is universal gravitational constant, M is mass of star.
The mass of the star is
Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times. As a satellite spirals inward, does it speed up, slow down, or maintain the same speed? Explain.
shows a particle of mass m at distance from the center of a very thin cylinder of mass and length . The particle is outside the cylinder, so .
a. Calculate the gravitational potential energy of these two masses.
b. Use what you know about the relationship between force and potential energy to find the magnitude of the gravitational force on when it is at position
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