In the image below, the radius of the red orbit is 3.02 times bigger than the radius of the green orbit. The "energy boost" AЕ1 (from the green circular orbit to the yellow elliptical orbit) is % of the total "energy boost" AE1 +▲Е3.

Since 1995, hundreds of extrasolar planets have been discovered. There is the exciting possibility that there is life on one or more of these planets. To support life similar to that on the Earth, the planet must have liquid water. For an Earth-like planet orbiting a star like the Sun, this requirement means that the planet must be within a habitable zone of 0.9 AU to 1.4 AU from the star. The semimajor axis of an extrasolar planet is inferred from its period. What range in periods corresponds to the habitable zone for an Earth-like Planet orbiting a Sun-like star?

The distance between two stars of masses 3M² and 6M, is 9R. Here R is the mean distance between the centers of the Earth and the Sun, and Mã is the mass of the Sun. The two stars orbit around their common center of mass in circular orbits with period nT, where T is the period of Earth's revolution around the Sun. The value of n is

In recent years, scientists have discovered hundreds of planets orbiting other stars. Some of these planets are in orbits that are similar to that of earth, which orbits the sun (Msun = 1.99 x 1030 kg) at a distance of 1.50 x 1011 m, called 1 astronomical unit (1 au). Others have extreme orbits that are much different from anything in our solar system. The problem relates to some of these planets that follow circular orbits around other stars. HD 10180g orbits with a period of 600 days at a distance of 1.4 au from its star. What is the ratio of the star’s mass to our sun’s mass?

A star is observed to undergo circular orbit around the black hole located at the centre of the Milky Way galaxy. The orbital period is measured to be 16 years and the distance between the star and the black hole is determined to be 1000 Astronomical Units. Estimate the mass of the black hole in units of the Solar mass, and explain any approximations you make in your calculation.

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?

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.

XCM M A binary system is shown by the image above. It consists of two stars of equal mass. These stars revolve in a circular orbit about thgeir center of mass, which is midway between them. If the orbital speed of each star is 3,800 km/s and the orbital period of each is 15.3 days. Find the mass M of each star.

A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.02 × 104 m/s. The mass of the planet is M = 5.9 × 1024 kg. The mass of the satellite is m = 5.7 × 103 kg. a)Calculate the value of PE in joules. b)Enter an expression for the total energy E of the satellite in terms of m and v. c) Calculate the value of the total energy E in joules.

We sent a probe out to orbit the planet Kerbal at a distance of 5.5x107m from the middle of the planet. It took our probe 3.5x105s to orbit the planet. Which equation will be used to calculate the mass of planet Kerbal? Possible Formulas that can be used to answer the question: v=(2πr)/T ac=v2/r ac=(4π2r)/T2 Fc=mac Fg=mg F=(Gm1m2)/d2 g=Gm/r2 T2=(4π2/Gm)r3 v=√(Gm)/r g=9.80m/s2 G=6.67x10-11 (N∙m2)/kg2