10. Using the idea that the force of gravity is equal to the centripetal force of an object in orbit, show the derivation of the Law of Periods using Newton's Law of Gravitation. (Hint: set these two equations equal to one another, the velocity of an object in nearly circular orbit is distance (the circumference of the circular orbit) over time (the period of orbit). 4 points Gm,m2 Fgravity r2 mv² Fcentripetal

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.

c) Draw the expected tidal record (tidal height relative to mean sea level versus time) for the month illustrated above. Annotate the four points of time represented in the figure below. How are these tides called? Moon Moon Sun Sun Moon Moon Sun Sun

A planet and moon pictured above have identical densities. Identify the magnitude of the value that is identical to both cosmic bodies assuming that the only force they experience is their gravitational attraction for each other. O A. Kinetic energy O B. Velocity O C. Acceleration O D. Displacement from the center of mass O E. Gravitational force

1. On a planet whose radius is 1.5 × 107 m, the acceleration due to gravity is 20 m/s². An astronaut with a mass of 60 kg is standing on its surface.

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.

Leave the moon's amplitude (semi-major axis) constant. How does the changing of the moon's orbital period change the calculated value of the planet's mass? a. Increasing the orbital period results in a higher calculated value for the mass of the planet. Decreasing the orbital period results in a lower calculated value for the mass of the planet. b. Increasing the orbital period results in a lower calculated value for the mass of the planet. Decreasing the orbital period results in a higher calculated value for the mass of the planet. c. Increasing the orbital period results in a higher calculates value for the mass of the planet. Decreasing the orbital period results in a higher calculated value for the mass of the planet.

Part A The value of Gmdre", where me is the mass of the earth, r, is the radius of the earth, and G is the universal gravitational constant is (enter your answer with three significant figures) ΑΣΦ IXI X•10n -11 6.67 101 m/? Submit Previous Answers Request Answer X Incorrect; Try Again; 4 attempts remaining

3. The gravitational acceleration at Earth's surface (ge) is about 10 m/s? and ge = GM/R?. What is gp at the surface of a planet with 2X Earth's mass and 3X Earth's radius?