6. Use Kepler's laws to calculate the mass of the Sun based on data for average Earth's orbit and compare the value obtained with the Sun's commonly listed value of 1.989 × 1030 kg.
Q: of Kepler's third law to
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A: Given Mass of earth Me = 5.97 x 1024 Kg Mass of Sun Ms = 1.99 x 1030 Kg The radius of the earths…
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- 11) Newton's Law of Gravity says that the force of gravity between any two objects is G d2 where the m's are the masses of the objects and, d is the distance between them, and G is a constant that depends on your choice of units. This includes big things like planets and small things like you and your pets. We don't need to know the values of the masses to think about what happens as two objects approach each other! lim G d--0+ d? If you think too long about your answer, it may be a bit troubling. What does it say about the force of gravity when you actually touch your pets?6. A synchronous orbit is an orbit about a planet's equator that always remains above the same spot of the planet because the synchronous orbit matches the planet's rotational period. The pilot of the Mars spacecraft (which was named Cheetah 1 and had a 9556 kg mass) asked Tarzan to calculate the altitude of a synchronous orbit so they could remain over a particular geological feature on the Martian equator. Calculate the altitude above the Martian equator using the data above and Johannes Kepler's genius.12. Escape Velocity To escape Earth's gravitational field, a rocket must be launched with an initial velocity called the escape velocity. A rocket launched from the surface of Earth has velocity v (in miles per second) given by V = 2GM Tº + v² - 2GM R where vo is the initial velocity, r is the distance from the rocket to the center of Earth, G is the gravitational constant, M is the mass of Earth, and R is the radius of Earth (approximately 4000 miles). V= a. Find the value of vo for which you obtain an infinite limit for r as v approaches zero. This value of vo is the escape velocity for Earth. 192,000 T b. A rocket launched from the surface of the moon has velocity v (in miles per second) given by V = 1920 T +v-48 + - 2.17. Find the escape velocity for the moon. c. A rocket launched from the surface of a planet has velocity v (in miles per second) given by 10,600 T + v² - 6.99. Find the escape velocity for this planet. Is the mass of this planet larger or smaller than that of Earth?…
- According to Lunar Laser Ranging experiments the average distance LM from the Earth to the Moon is approximately 3.85 × 10° km. The Moon orbits the Earth and completes one revolution in approximately 27.5 days (a sidereal month). How can the mass of the Earth be calculated using the information above? Select the correct statements. Select one or more: O a. Use Newton's third law. O b. Use Newton's first law. c. Use Coulombs law. O d. Use Newton's second law.5. The acceleration of gravity on the Moon's surface is known to be about 1/6 the acceleration of gravity on the Earth. Given that the radius of the Moon is roughly 1/4 that of the Earth, find the mass of the Moon in terms of the mass of the Earth. (answer = 1/96 ME)3. A moon's orbital angular velocity and orbital velocity about a planet are 6.28x10-8 rad/sec and 12.56 m/s respectively. Calculate this moon's distance from the planet and the planet's mass.