Now we can cancel units of days, By studying the exact orbit of the planets and sun in the solar system, you can calculate all of the masses of the planets. where MSMS is the mass of the Sun and a is the semi-major axis. We also need the Constant of Proportionality in the Law of Universal Gravitation, G. This value was experimentally determined Manage Settings According to Newtons 2nd law of motion: Thus to maintain the orbital path the gravitational force acting by the planet and the centripetal force acting by the moon should be equal. 2023 Physics Forums, All Rights Reserved, Angular Velocity from KE, radius, and mass, Determining Radius from Magnetic Field of a Single-Wire Loop, Significant digits rule when determining radius from diameter, Need help with spring mass oscillator and its period, Period of spring-mass system and a pendulum inside a lift, Estimating the Bohr radius from the uncertainty principle, How would one estimate the rotation period of a star from its spectrum, Which statement is true? Can I use the spell Immovable Object to create a castle which floats above the clouds. Use a value of 6.67 10 m/kg s for the universal gravitational constant and 1.50 10 m for the length of 1 AU. 5. Because other methods give approximation mass values and sometimes incorrect values. $$ These are the two main pieces of information scientists use to measure the mass of a planet. The velocity boost required is simply the difference between the circular orbit velocity and the elliptical orbit velocity at each point. The transfer ellipse has its perihelion at Earths orbit and aphelion at Mars orbit. Mass of Jupiter = 314.756 Earth-masses. Does the order of validations and MAC with clear text matter? I need to calculate the mass given only the moon's (of this specific system) orbital period and semimajor axis. The formula = 4/ can be used to calculate the mass, , of a planet or star given the orbital period, , and orbital radius, , of an object that is moving along a circular orbit around it. I think I'm meant to assume the moon's mass is negligible because otherwise that's impossible as far as I'm aware. To calculate the mass of a planet, we need to know two pieces of information regarding the planet. So in this type of case, scientists use the, The most accurate way to measure the mass of a planet is to determine the planets gravitational force on its nearby objects. But how can we best do this? Creative Commons Attribution License Since we know the potential energy from Equation 13.4, we can find the kinetic energy and hence the velocity needed for each point on the ellipse. You can view an animated version of Figure 13.20, and many other interesting animations as well, at the School of Physics (University of New South Wales) site. We can find the circular orbital velocities from Equation 13.7. [You can see from Equation 13.10 that for e=0e=0, r=r=, and hence the radius is constant.] Learn more about Stack Overflow the company, and our products.
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