A satellite is traveling around a planet in a circular orbit with radius R. It moves in a constant speed of v = 1.1 × 104 m/s. The mass of the planet is M = 6.04 × 1024 kg. The mass of the satellite is m = 1.2 × 103 kg. a)Enter an expression for the radius R in terms of G, M and v.  b)Calculate the value of R in meters.  c)Enter an expression for the gravitational potential energy PE in terms of G, M, m, and R.

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

In the year 25 000 the Earth is 1.42x101 m away from the sun and in a circular orbit, but a year remains 365 days long. Part A Calculate the mass of the sun in the year 25 000. ΑΣΦ ? msun = kg

a) Calculate the magnitude of the gravitational force exerted by the Moon on a 65 kg human standing on the surface of the Moon. (The mass of the Moon is 7.4x1022 kg and its radius is 1.7x106 m.) b) Calculate the magnitude of the gravitational force exerted by the human on the Moon. c) For comparison, calculate the approximate magnitude of the gravitational force of this human on a similar human who is standing 4.5 meters away.

A new planet named Vulcan has been discovered. Vulcan is a rather large planet with a radius twice that of Earth and a mass three times that of Earth. An astronaut has a mass of 60.0 kg and weighs about 132 lbs. on Earth. If the astronaut is on the planet Vulcan, what is her weight? The following numerical values may be helpful in this question. G = 6.67 ∙10-11 N∙m2/ kg2 Earth’s mass = 5.98 · 1024 kilograms g = 9.80 m/sec2 1 kilometer = 1000 meters

Help me to solve this problem step by step and give answer as a 3 significant figures

Sphere A with mass 92 kg is located at the origin of an xy coordinate system; sphere B with mass 65 kg is located at coordinates (0.25 m, 0); sphere C with mass 0.50 kg is located at coordinates (0.19 m, 0.18 m). In unit-vector notation, what is the gravitational force on C due to A and B? Number i i+ i j Units eTextbook and Media

a) i. b) i. Define gravitational field strength at a point. Determine the mass of the Earth assuming that it is a uniform sphere of radius 6378 km and that the gravitational field strength at the Earth's surface is 9.81 N kg¹¹. Determine the average density of the Earth. iii. Use the mass of the Earth as calculated in part b)i to determine the gravitational field strength due to the Earth at a distance of 3.5 x 108 m from the centre of the Earth. ii. iv. Consider a point X a distance of 3.5 x 108 m from the centre of the Earth and which lies on the line joining the centre of the Earth to the centre of the Moon. c) i. ii. At X the gravitational field strength due to the Moon is equal but opposite to that of the Earth. The mass of the Moon is 7.4 x 10²2 kg. Determine the distance from the centre of the Moon to X and hence determine the distance between the centres of the Earth and Moon. Determine the time in Earth years for the planet Jupiter to complete one orbit of the Sun. Take 1…

Newton's law of universal gravitation can be expressed by the equation Mm F= G where F is the gravitational force, M and m are masses, and ris a length. Force has the SI units kg · m/s2. What are the SI units of the proportionality constant G? m2 kg ·s m2 kg · s2 m3 kg . s2 m3 kg - s3

The table below gives the masses of the Earth, the Moon, and the Sun. Name Mass (kg) Earth 5.97 x 1024 Moon 7.35 x 1022 Sun 1.99 x 1030 The average distance between the Earth and the Moon is 3.84 x 10° m. The average distance between the Earth and the Sun is 1.50 x 1011 m. Use this information to answer the following questions. Part F Part G Find the net gravitational force Fnet acting on the Earth in the Sun-Earth-Moon system during the full moon (when the Earth is located directly between the moon and the sun). Express your answer in newtons to three significant figures. ? Fnet = 3.54 • 1022 N