2 Earth TT John Glenn's orbit in Friendship 7

The Sun occupies an angle of approximately 0.5 degrees to us on Earth, at a distance of 150 million kilometers from the Sun. Given this information, calculate the Sun's radius.

Let's assume that the planet was originally orbiting around something with the mass of our Sun (and thus the mass of the planet is negligible). Now we will examine the case where the planet orbits a star with 8 times the mass of our Sun, but we will say that the dates listed in the diagram above are still accurate for indicating the planet's position as it orbits the new star. What is ratio of the size of the semimajor axis of the planet in this case compared to the original (aka how many times larger {ratio greater than 1} or smaller {ratio less than 1} is the new semimajor axis than the old one)?

Kepler'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.

Kepler's 3rd law is given as p2 = a3. If the orbital period of a space telescope at the second Sun-Earth Lagrange point (L2) is 1 year, is its orbit a violation of Kepler's 3rd law?

On February 28, 2010, Earth was equidistant from the spacecraft Dawn and the Sun, forming an isosceles triangle. The distance from Earth to Dawn and Earth to the Sun was 0.99 AU (astronomical units). The distance from Dawn to the Sun was 1.84 AU. a) Draw a diagram to show Dawn, Earth, and the Sun. b) Determine the angle between the sight lines from Earth to Dawn and the Sun.

Many people mistakenly believe that the astronauts who orbit Earth are "above gravity." Earth's mass is 6×1024kg, and its radius is 6.38×106m(6380 kmkm).   Use the inverse-square law to find a height above Earth's surface at that the force of gravity on a shuttle is about 96 %% that at Earth's surface.

What is the force of gravity between two keen physics students who are (3.30x10^0) m apart if one physics student has a mass of (1.250x10^2) kg and the other has a mass of (8.6x10^1) kg ? (Note: the red writing below just means to input your answer in proper scientific notation, with 2 significant digits) Note: Your answer is assumed to be reduced to the highest power possible.

The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the Sun. A light-year is the distance that light travels in one year (365 days). How far away, in kilometers, is Proxima Centauri from the Sun?Express your answer using two significant figures.

Use the 1967 International Gravity formula to calculate g at 0°, 45°, and 90° latitude. How big is the difference in g from that at the equator in an absolute sense (how many gal or mgal), at 45° and 90°? How big is the difference in a fractional sense?