A comet moves in an elliptical orbit around a star. When it is closest to the star at a distance of 7.75 ✕ 1010 m, the comet's speed is 70.0 km/s. How far is it from the star when its speed is 66.0 km/s? Take the mass of the star to be 1.99 ✕ 1030 kg, the same as that of our Sun.

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.

A satellite of Mars, called Phobos, has an orbital radius of 9.4 ✕ 106 m and a period of 2.8 ✕ 104 s. Assuming the orbit is circular, determine the mass of Mars. (ans kg)

Sally and Sam are in a spaceship that comes to within 14,000 km of the asteroid Ceres. Determine the force Sally experiences due to the presence of the asteroid. The mass of the asteroid is 8.7 x 1020 kg and the mass of Sally is 79 kg. For calculation purposes assume the two objects to be point masses. N

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.

Two planets P, and P, orbit around a star S in circular orbits with speeds v, = 46.4 km/s, and v, = 57.4 km/s respectivel (a) If the period of the first planet P, is 710 years what is the mass, in kg, of the star it orbits around? kg (b) Determine the orbital period, in years, of P2. yr

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Two satellitess, and S, orbit around a planet P in circular orbits of radil r, = 5.15 x 106 m, and r, = 8.40 x 106 m respectively. If the speed of the first satellite S, is 1.65 x 10 m/s, what is the speed of the second satellite S,? m/s

A meteoroid is moving towards a planet. It has mass m = 0.18×109 kg and speed v1 = 3.8×107 m/s at distance R1 = 1.6×107 m from the center of the planet. The radius of the planet is R = 0.26×107 m. The mass of the planet is M = 10×1025 kg. 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.  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.

Our solar system is roughly 2.2 x 1020 m away from the center of the Milky Way galaxy, and the system is moving at roughly 231.4 km/s around the galaxy's center. Since most of the galaxy's mass is near its center (and we are on an outer arm of this spiral galaxy), let's model the galaxy has a spherical mass distribution (like a single, giant star that our system is orbiting around).  What is the mass of the galaxy (according to our rough, spherical model)? Obviously, this will be a VERY big answer, and so enter in your answer to the order of 1040 kg. In other words, calculate the answer, and then divide by 1040 and then enter in the result.  BTW - by assuming that all mass in the galaxy is made up of stars that are about the same mass as our sun, it isn't too hard to then estimate how many stars are in the galaxy!). As an another aside, some measurements and observations that we have taken in Astronomy suggests that in reality, stars only make up a fraction of the total mass