Orbital radius of the earth r = 1.5 x 1011 m. Given mass of the sun M =1.9 X 1030 kg. Using Kepler's third law to calculate the time-period T of earth's rotation in year. Universal constant of gravity G = 6.67 X 10-11 Nm²/kg².

The earth takes 365.256 days to go around the sun and 23 hours 56 min and 4.0905 s to revolve about its axis. These give the earth an orbital speed of 29.8 km/s and a rotational speed of 465 m/s at the equator, a 64:1 ratio. If the moon orbits the earth in a period of 29 d 12 h 44 min 2.9 s, has a sidereal period of 27.321582 days, a radius of 1737 km, and a mean distance from the earth of 384,000 km, what is the similar velocity ratio for the moon?

33. If you are at the top of a tower of height h above the surface of the earth, show that the distance you can see along the surface of the earth is approximately s = v2Rh, where R is the radius of the earth. Hints: See figure. Show that h/R = sec 0 – 1; find two terms of the series for sec 0 = 1/ cos 0, and use s = RO. _Thus show that the distance in miles is approximately v3h/2 with h in feet. Rİ

The planet Pluto has an equatorial diameter of 1,188.3 km and its mass is 1.30900 * 1022 kilograms. If the planet is modeled as a homogeneous sphere, what is the acceleration due to gravity at its surface? (The universal gravitational constant is G = 6.67 x 10-11 N-m²/kg?.) Answer in 3 decimals and in m/s2

What is the radius of geosynchronous orbit around the earth? (where the period of orbit is the same as the earths rotational period) Using the mass of the earth as me = 5.98 x 1024 kg and the sidereal day as 23 hours 56 minutes and 4.0905 s. Number Units

A man is standing on the moon. His mass is 100 kg. The mass of the moon is 7x10^22 kg. The radius is 3.8x10^5 km. How much is the gravitational force between the man and the moon?

The International Space Station (ISS) is a space station orbiting the earth above the ground. If the radius of the earth is 3,958.8 miles, mass of earth is 5.972 x 10 24 kg,  the period of the ISS at the orbit around the earth is 9.16 hours, can you calculate what is the distance from the ISS to the surface of the earth, in unit of miles? Use G=6.674 x 10 -11 Nm2/kg2. Write your answer in pure numbers, for example, 4567.8. Please keep at least on digit after the decimal point.

The solar system has a planet with an orbital period T1b=1.51d and an orbital radius of R1b=1.6456x10^6km. Another planet in the system has an orbital radius of R1f=5.5352x10^6 km. Calculate its orbital period in days.

3. The gravitational acceleration at Earth's surface (ga) is about 10 m/s? and ge = GM/R2. What is g, at the surface of a planet with 2X Earth's mass and 3X Earth's radius?

19.   According to Isaac Newton, the value of the constant, k, in Kepler's Third Law (P2 = ka3) is dependent on which one of the following quantities for objects within the Solar System?   a. The distance between the Sun and its planet.   b. The mass of the planet.   c. The electric charge of the Sun.   d. The mass of the Sun.