
How close would an Earth-mass planet have to be to the star so that the planet’s radial velocity would exceed the natural 1 ms-1 radial velocity jitter by a factor of 2?
How long would the year be if the planet were this close to the Sun?
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How close would an Earth-mass planet have to be to the star so that the planet’s...
An exoplanet is observed to transit across a 0.1 solar mass star. (i) If it is in the middle of its habitable zone (Earth conditions), what value should be measured for its period, and mass if its velocity amplitude K is measured to be ~ 2 ms-1 (ii) The transit depth is measured to be ΔL / L = 10-3. What is the radius of the planet? (you’ll need to look up some stellar data). What is the planet’s density?...
A nearly Earth sized planet obits in the habitable zone of Proxima Centauri, the closest star to the solar system. If the orbit is elliptical use either conservation of mechanical energy or conservation of angular momentum to show where in the orbit the planet’s highest and lowest angular velocity occurs. Be sure to show how the rule you choose actually applies to this situation.
Suppose that you have a planet in a circular orbit about a star with the mass of the Sun. The orbital speed is 141 km/s. If you could increase the planet’s speed, what speed would you need to make it to escape the gravitational pull of its parent star?
Calculate how long it would take the Earth to fall into the Sun if its orbital motion were stopped. Then, instead of the Earth, imagine a second 1 solar mass star orbiting the Sun. Start with the equations of motion and calculate how long it would take for the two stars to crash into each other.
Over 500 planets have so far been detected beyond our solar system. This is accomplished by looking for the effect the planet has on the star. The star is not truly stationary; instead, it and its planets orbit around the center of mass of the system. Astronomers can measure this wobble in the position of a star. a.) For a star with the mass and size of our sun and having a planet with two times the mass of Jupiter,...
HD209458b was discovered in 1999, becoming the first exoplanet to be discovered using the transit method: this planet’s orbit is oriented just right, so that it regularly passes in front of its star, as seen from Earth. When this happens, it blocks out a portion of the star’s light. If astronomers notice the star’s brightness dipping for a short time over and over with a consistent period, it suggests a planet is responsible. Further observations of the star’s Doppler shift...
Suppose there is a planet orbiting close to a black hole, as Earth is to the Moon. There is an ocean on that planet. If you happen to be there, what would you notice? Select one: a. The ocean has tides, but only once per day, unlike Earth when we have them twice per day b. The ocean has tides, but they are way higher than on Earth c. The ocean has tides, but they are way smaller than on...
What would the mass of the Sun have to be if Pluto (the outermost planet most of the time) were to have the same orbital speed that Mercury (the innermost planet) has now? The orbital speeds of Mercury and Pluto are 47.9 km/s and 4.74 km/s respectively. Express your answer in terms of the Sun's current mass MS, and assume circular orbits.
2) Planet Velocities and Energy (10 pts) We talked about how planet formation involves the collisions of bodies (planetesimals, embryos) leading to the growth (and heating) of a planet. Let's think about the velocities and energies involved here. a) The speed of a body in its orbit around the Sun is given by the equation V2= GM.[(2/r) - (1/a)] Here Vis the speed of the body in m/s, G is the gravitational constant, M. is the mass of the Sun...
In recent years, scientists have discovered hundreds of planets orbiting other stars. Some of these planets are in orbits that are similar to that of earth, which orbits the sun (Msun = 1.99 × 1030 kg) at a distance of 1.50 × 1011 m, called 1 astronomical unit (1 au). Others have extreme orbits that are much different from anything in our solar system. The following problem relates to one of these planets that follows circular orbit around its star....