GM for the speed v of a satellite (of mass m) moving in a circular orbit of radius r r about a central body with mass M. (a) Derive the formula v = A satellite is in circular orbit above the earth at an orbital radius of 6.77 x 106 m. 7.67 i. Show that its orbital speed is 768 x 10³ ms¹¹ ii. Hence or otherwise, determine the value of the gravitational acceleration (g) at this satellite's orbital radius. (2 marke) KA

On the ground level, the weight of a satellite is W N. The satellite is launched and stays in an orbit that is R/47 above the ground level, where R is radius of the Earth. If the gravitational force on the satellite is xW at this location, determine x.

(a) Imagine that a space probe could be fired as a projectile from the Earth's surface with an initial speed of 5.96 x 10“ m/s relative to the Sun. What would its speed be when it is very far from the Earth (in m/s)? Ignore atmospheric friction, the effects of other planets, and the rotation of the Earth. (Consider the mass of the Sun in your calculations.) 354790 Your response differs from the correct answer by more than 100%. m/s (b) What If? The speed provided in part (a) is very difficult to achieve technologically. Often, Jupiter is used as a "gravitational slingshot" to increase the speed of a probe to the escape speed from the solar system, which is 1.85 x 10“ m/s from a point on Jupiter's orbit around the Sun (if Jupiter is not nearby). If the probe is launched from the Earth's surface at a speed of 4.10 × 10“ m/s relative to the Sun, what is the increase in speed needed from the gravitational slingshot at Jupiter for the space probe to escape the solar system (in m/s)? (Assume…

A mood of a mass m and raduis a is orbiting a planet of mass M and if radius b at a distance d (center to center) in a circular orbit.  Derive an expression for the speed of the mood v in terms of M,d and the gravitational constant G.

A satellite orbits Mars on a closed orbit with e=0.6 and rp= 4500 km. Calculate the flight path angle(s) y and velocity vectors v components in the rotating frame (v, and v₁) when r = 10000 km.

Please don't provide handwritten solution .....

The earth is 150 × 10^9 m from the Sun. Earth and Sun masses are 5.97 × 10)^24 ?? and 1.99 × 10^30 ??, respectively. (a) Find the gravitational attraction between the Earth and the Sun. (b) Find the orbital period of the Earth around the Sun based on these numbers.

In a geosynchronous orbit, a satellite stays above the same point on Earth because it takes exactly one day to go through one orbit of 2(pi) radians. If the radius of this orbit is 42,100 km, how fast is the satellite traveling around the Earth? pick the one equation and define the relevant knowns and single unknown.

An exotic planet Vogsphere is known to have a mass that is 1/81 that of the Earth and a radius 0.25 that of the Earth. Astrophysicist Trillian built a rocket and decided to leave the planet and never to return. Given that the escape speed from the Earth is 11.2 km/s, with what speed must Trillian achieve his goal?

Plaskett's binary system consists of two stars that revolve in a circular orbit about a center of mass midway between them. This statement implies that the masses of the two stars are equal (see figure below). Assume the orbital speed of each star is v| = 225 km/s and the orbital period of each is 11.6 days. Find the mass M of each star. (For comparison, the mass of our Sun is 1.99 x 1030 kg.) M XCM M Part 1 of 3 - Conceptualize From the given data, it is difficult to estimate a reasonable answer to this problem without working through the details and actually solving it. A reasonable guess might be that each star has a mass equal to or slightly larger than our Sun because fourteen days is short compared to the periods of all the Sun's planets. Part 2 of 3 - Categorize The only force acting on each star is the central gravitational force of attraction which results in a centripetal acceleration. When we solve Newton's second law, we can find the unknown mass in terms of the variables…