Suppose you're in a circular orbit around Saturn (M = 5.683 × 1026 kg) with a semi-major axis of a = 237,948 km. a. What is your orbital velocity? b. Using the "Vis-viva" equation (which can be derived from the total energy) v = |GM What is the delta-V you would need to get from your current orbit, into an elliptical orbit that has an apoapsis near Titan (a = 1,221,870 km)? %3D
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- What is an orbital acceleration on an object? Explain it by giving an example.The figure below shows a planet traveling in a counterclockwise direction on an elliptical path around a star located at one focus of the ellipse. What can be said about the speed of the planet when itis at point A? STAR O its speed is a maximum O its speed is increasing O its speed is a minimum O its speed is decreasing O its speed is constant E MThe MAVEN orbiter orbits Mars with a period of 4.5 hours. How far (in km) above the surface of the planet is it? (The mass of Mars is 6.42 × 1023 kg, and the radius of Mars is 3.40 × 10³ km.) Part 1 of 3 The period of the orbiter's orbit can give us the speed at which the orbiter orbits the planet. We imagine the orbiter tracing a circle around the planet I a certain height, the speed is Part 2 of 3 V = 2πr P Next, we combine this with the circular velocity equation to determine the height above the planet's surface. 2πr P 202 = GM r GM r Squaring both sides and solving for r gives the following equation. What is the exponent for r? GM 4π² Submit Skip (you cannot come back)
- 2. The generalized Kepler orbit is given in polar coordinates r($)=c/(1+e cos()), where c is a constant and & is the eccentricity of the orbit. Rewrite this in Cartesian coordinates for -1 and show that the orbit is a parabola, y² = A + B x, where A and B are constants. Define constants A and B via constant c.1. using Newton’s Law of Universal Gravitation and some kinematics calculation we can calculate the mass of the planet. For this, use this equation in the image: Given: - vmax = 1.5 m/s - Pstar = 3.5 days - Mstar = 1.148 Msun, where Msun = 1.98847×1030 kg. This calculation is not shown.Question 1 (Total: 30 points) a. What is a repeat ground-track orbit? b. Explain why repeat ground-track and Sun-synchronous orbits are typically used for Earth observation missions. c. The constraint for a Sun-synchronous and repeat ground-track orbit is given by T = 286, 400, where I is the orbital period in seconds, m the number of days and k the number of revolutions. Explain why this is, in fact, a constraint on the semi-major axis of the orbit.
- Plant A orbits a star at a distance R from the center of the star. Planet B circles the same star with a period eight times that of Planet A. Planet B orbits the star at a distance of. a. 4R b. 1/8R c. 8R c. 1/4RKepler's 1st law says that our Solar System's planets orbit in ellipses around the Sun where the closest distance to the Sun is called perihelion. Suppose I tell you that there is a planet with a perihelion distance of 2 AU and a semi-major axis of 1.5 AU. Does this make physical sense? Explain why or why not.1. Moon is at the distance 384400 km from Earth and orbits the Earth every ~28 days. If the radius of the Moon is 1737 km (consider it to be spherical), what is the area of the moon as measured by the observer on Earth? (Hint: Length contraction)