A spaceship moving $0.80 \: \mathrm{c}$ direction away from Earth fires a missile that the spaceship measures to be moving at $0.80 \: \mathrm{c}$ perpendicular to the ship's direction of travel. Find the velocity components and speed of the missile as measured by Earth.

To escape Earth’s gravitational field, a rocket must be launched with an initial velocity called the escape velocity. A rocket launched from the surface of Earthhas velocity v (in miles per second) given by v = √2GM/r + v_0^2 - 2GM/R ≈ √192000/r + v_0^2 - 48 where v_0 is the initial velocity, r is the distance from the rocket to the center of Earth, G is the gravitational constant, M is the mass of Earth, and R is the radius of Earth (approximately 4000 miles). (c) A rocket launched from the surface of a planet has velocity v (in miles per second) given by v = √10600/r + v_0^2 - 6.99. Find the escape velocity for this planet. Is the mass of this planet larger or smaller than that of Earth? (Assume that the mean density of this planet is the same as that of Earth.)

Assume that because of in creasing $\mathrm{CO}_{2}$ concentration in the atmosphere, the net radiation energy transfer rate for Earth and its atmosphere is $+0.002 \times 1350 \mathrm{W} / \mathrm{m}^{2}$,corresponding to a 0.2% decrease in radiation leaving Earth. (a) Determine the extra thermal energy added to Earth and its atmosphere in 10 years. [Note:The radiation falls on an area approximately equal to $\pi r_{\text { Earth }}^{2}$ where $r_{\text { Earth }}=6.4 \times 10^{6} \mathrm{m.} ]$ (b) If 30% of this energy is used to melt the polar ice caps, how many kilograms of ice will melt in 10 years? (c) How many cubic meters of ice will melt? (d) By how much will the level of the oceans rise in 10 years?

The oldest rocks on Earth date from about $4.2$ billion years ago. What does this indicate about the interval between $4.6$ billion years ago, when the Earth started to form, and $4.2$ billion years ago?

The speed of light is 3 $\times$ 10$^8$ m/s and the distance from Earth to the sun is 1.5 $\times$ 10$^{11}$ m. How many seconds does it take for sunlight to reach Earth? Write your answer in scientific notation.

At the surface of a certain planet, the gravitational acceleration $g$ has a magnitude of $12.0$ m/s$^2$. A $2.10$-kg brass ball is transported to this planet. What is (a) the mass of the brass ball on the Earth and on the planet, and (b) the weight of the brass ball on the Earth and on the planet?

A certain star is 4.3 × 10^2 light years from Earth. One light year is about 5.9 × 10^12 miles. How far from Earth (in miles) is the star? Express your answer in scientific notation.

How would the gravitational field at Earth’s surface be affected if Earth shrank in size without any change in mass? What would be its relative strength at the new surface if Earth shrank to half size? To one-tenth size?

How do scientists study objects in space that are at vast distances from Earth?

A space traveler whose mass is $75.0$ kg leaves Earth. Com- pute his weight $(a)$ on Earth, $(b)$ on Mars, where $g=3.72$ m/s$^2$, and $(c)$ in interplanetary space. $(d)$ What is his mass at each of these locations?

If 3C273 is moving away from Earth at $0.16 c$, what speed be low is closest to the light speed we on Earth detect coming from 3C273? (a) $1.15 c$, (b) $c$, (c) $0.85 c$, (d) None of these is correct.

An astronaut on a spaceship traveling at 0.75c relative to Earth measures his ship to be 25 m long. On the ship, he eats his lunch in 23 min. How long does the astronaut's lunch take to eat according to observers on Earth?

The weight of an object on Saturn 's moon Titan is about 0.14 of its weight on Earth. a. Write and graph an equation that describes this relationship. b. Use your graph to estimate the weight on Titan of a space probe that weighs 703 pounds on Earth.

Suppose you leave the solar system and arrive at a planet that has the same mass-to-volume ratio as Earth but has 10 times Earth's radius. What would you weigh on this planet compared with what you weigh on Earth?