Question

Astonomers discover a new planet orbiting a fixed point in space, but for reasons unknown, they can't directly observe a star where one is expected. The radius of the orbit is measured to be 1.85 x 10^8 km, and the lone planet completes an orbit once every 530 days.
a.) Calculate the mass of the unseen star or other celestial object this planet is orbiting.
b.) For an orbit to be stable, the centripetal force must exactly equal the force of gravitational attraction between 2 bodies. If this planet orbited the object once every 580 days, would this be stable orbit? Explain. Assume this planet is about the same size as Earth, and use the mass of the hidden object found in part a.

Answer 1

you know the velocity of the planet(r*2PI/530days)...change that to m/s

Then set force of gravity equal to centripetal acceleration

GMm/r^2=mv^2/r and solve for M

Answer 2

After converting the radius to meters (1.85 x 10^11m) and the period of circular orbit into seconds (45,792,000s), solve for "M," and you'll get M=(v^2 x r)/G. Then plug-in your values and the answer you'll come up with will be approximately 1.65 x 10^30kg in mass.

Answer 3

Who still here in 2019