Satellite X of mass m orbits planet X of mass M at a center-to-center distance r. Satellite Y or mass 4m orbits planet Y of mass 8M at a center-to-center distance 2r. By what factor does the period of system X vary from system Y (a system consisting of the satellite and its host planet)?

A meteoroid is moving towards a planet. It has mass m = 0.22×109 kg and speed v1 = 3.5×107 m/s at distance R1 = 2.9×107 m from the center of the planet. The radius of the planet is R = 0.46×107 m. The mass of the planet is M = 3.2×1025 kg. There is no air around the. Calculate the value of v in meters per second.

Planet X is a sphere where a 0.5 kg block weighs 36 N when sitting on the surface. If an object is dropped from rest at a distance 9R from X's center it is observed to impact the surface at a speed of 16,000 m/s. Find a value for the radius of planet X.

A meteoroid is moving towards a planet. It has mass m = 0.54×109 kg and speed v1 = 4.7×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.78×107 m. The mass of the planet is M = 5.6×1025kg. There is no air around the planet.  a)Enter an expression for the total energy E of the meteoroid at R, the surface of the planet, in terms of defined quantities and v, the meteoroid’s speed when it reaches the planet’s surface. Select from the variables below to write your expression. Note that all variables may not be required.α, β, θ, d, g, G, h, m, M, P, R, R1, t, v, v1 b)Enter an expression for v, the meteoroid’s speed at the planet’s surface, in terms of G, M, v1, R1, and R. c)Calculate the value of v in meters per second.

Can you please help me with this question please? I appreciate your help!

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 1.50×107 m and its rotation period to be 22.3 hours. You have previously determined that the planet orbits 2.50×1011 m from its star with a period of 402 earth days. Once on the surface you find that the free-fall acceleration is 13.1m/s2. What is the mass of the planet? Express your answer with the appropriate units.   What is the mass of the star? Express your answer with the appropriate units.

A 20 kg sphere is at the origin and a 10 kg sphere is at (x, y) = (20 cm, 0 cm). At what point or points could you place a small mass such that the net gravitational force on it due to the spheres is zero?

1. A satellite of mass M moves around the Earth in a circular orbit of radius R. The orbital period of the satellite is T. A second satellite of mass 3M is also moving around the Earth in a circular orbit of radius R. The orbital period of the second satellite is (a) 3T (b) T/3 (c) T (d) 97 (e) T/9

A satellite has a mass of 6398 kg and is in a circular orbit 4.41 × 105 m above the surface of a planet. The period of the orbit is 1.5 hours. The radius of the planet is 4.58 × 106 m. What would be the true weight of the satellite if it were at rest on the planet’s surface?

Two newly discovered planets follow circular orbits around a star in a distant part of the galaxy. The orbital speeds of the planets are determined to be 36.2 km/s and 65.0 km/s. The slower planet's orbital period is 8.33 years. (a) What is the mass of the star? (b) What is the orbital period of the faster planet, in years? (a) Number (b) Number i Units Units