Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8 ✕ 1011 solar masses. A star orbiting near the galaxy's periphery is 6.0 ✕ 104 light years from its center. (a) What should the orbital period (in y) of that star be?  y (b) If its period is 6.9 ✕ 10

Moon is at the distance 384400 km from Earth and orbits the Earth every ∼28 days. Ifthe radius of the Moon is 1737 km (consider it to be spherical), what is the area of themoon as measured by the observer on Earth? (Hint: Length contraction)

The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun. (b) Is the ratio an upper limit estimate or a lower limit estimate?

Write down an expression for the gravitational filed strength of a planet of radius R and density ρ.

A planet of mass ?=5.45×10^24 kg is orbiting in a circular path a star of mass ?=4.45×10^29 k . The radius of the orbit is ?=8.35×107^7km. What is the orbital period (in Earth days) of the planet ?planet?

Idealize the Earth as a perfect sphere of radius R = 6371 km. If you could measure distances with an error of ±1 meter, how large a circle would you have to draw on the Earth’s surface to convince yourself that the Earth is spherical rather than flat?  Note that (or prove yourself) on the surface of a sphere, a circle of radius r will have a circumference of C = 2πR sin(r/R).    Round your answer to the nearest whole number. Hint: recall that you can approximate sin(x) with a Taylor series expansion: sin(x) \approx≈ x - x3/3! Answer value

a) Observations and trigonometry can be used to determine that Earth's moon has an orbital period of 27.32 days and a mean orbital radius of 384,400 km. Using this information, calculate the mass of the Earth. 2 M = 47² ² 2 C M= 4+1 (30214100000) 667 e

A planet with mass 9.69x1023 kg orbits a star with mass 9.21x1030 kg. The orbit is circular, and the distance from the planet to the sun is 225x106 km. What is the length of a year on this planet? Give your answer in earth years (1 earth year = 31,557,600 seconds).

Astronomical observations of our Milky Way galaxy indicate that it has a mass of about 8  1011 solar masses. A star orbiting near the galaxy's periphery is 5.6  104 light years from its center. (For your calculations, assume that the galaxy's mass is concentrated near its center.) (a) What should the orbital period of that star be?_________yr (b) If its period is 6.0x107 years instead, what is the mass of the galaxy? Such calculations are used to imply the existence of "dark matter" in the universe and have indicated, for example, the existence of very massive black holes at the centers of some galaxies._________ Solar Masses

Let À = 3.92i + 4.41j and B = -3.02i + -2.43j. What is the angle between À and B measured in degrees. Note that the angle may be greater than 90 degrees. (I understand the basic steps of the question but I keep getting 115.432. My last step was Cos^-1(2.9/22.588)