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Exoplanet Mass Calculation A Doppler spectroscopy plot for a star (already interpreted in terms of speed of the star) is shown in Figure 11-25. Assume that the mass of the star is 1.06 times the mass of our Sun, as well as the assumptions we made in this chapter. What is the wavelength shift ratio compared to the original wavelength (i.e.,∆λ/λ_s ) suggested by the plotted velocity? If the original source wavelength emitted is 486.13320 nm, what is the observed range of wavelengths from the star? Calculate the mass of the exoplanet. Express your answer from (c) in terms of the mass of the planet Jupiter.
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Nuclear Physics
Finding g on an Asteroid (a) Find the value of g on the surface of an asteroid that has a density of 3200 kgym3 and a radius of 5.00 km. Assume that the asteroid is homogeneous and spherical. (b) How long would it take an object starting from rest to fall through a height of 1.0 m above the surface of the asteroid? Assume that g is constant during the fall. (c) Show that the assumption in part (b) is justified.
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Nuclear Physics
Finding the Acceleration Due to Gravity Show that the observed value of approximately 9.81 〖m/s〗^2 for the magnitude of the gravitational acceleration at Earth’s surface is consistent with Newton’s law of universal gravitation.
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Nuclear Physics
Gravitational Force Near Earth’s Surface Find the gravitational force near Earth’s surface where the potential energy function is given by U = mgy, where y is the height above the U = 0 point.
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Nuclear Physics
Gravity at the ISS (a) Calculate the gravitational force exerted by Earth on a 1.00 kg object at the ISS. Assume that the ISS is in a circular orbit at an altitude of 353 km above Earth’s surface. (b) What is the value of g at the ISS? (c) Calculate the centripetal acceleration required to keep an object in the circular orbit of the ISS, given that the orbital speed of the ISS is 7.70 km/s
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Nuclear Physics
Interplanetary Spacecraft Orbit An interplanetary spacecraft has a speed of 32.0 km/s when it is at a distance of 1.20 AU from the Sun. It is at this time moving in a direction perpendicular to the line between the spacecraft and the Sun, as shown in Figure 11-20. (a) What type of orbit is the spacecraft in? Justify your answer. (b) When it is at a distance of r = 2.00 AU from the Sun, what is the speed of the spacecraft? (c) What is the aphelion distance of the orbit (expressed in AU)? (d) What is the angle, 𝛷, between a line to the Sun and the velocity of the spacecraft (see Figure 11-20) when it is at a distance of 2.0 AU from the Sun?
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Nuclear Physics
Interstellar visitor A spacecraft is observed to be at a distance of 2.00 AU from the Sun and is moving at a speed of 38.0 km/s. (a) What type of orbit (relative to the gravitational field of the Sun) is the spacecraft following? (b) Could the spacecraft have come from interstellar space?
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Nuclear Physics
Kepler’s third Law Derive Kepler’s third law for a planet moving in a circular orbit around the Sun. Assume that the mass of the planet is negligible compared to the mass of the Sun.
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Nuclear Physics
