# Go Figure

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### 1. Driving to Pluto

How long would it take you to reach Pluto if you drove non-stop for 24 hours a day? Give your answer in years.

Pluto's distance from the Sun is approximately 5,900,000,000 km

Your car travels at 100 km/h

Time = Distance/Speed

### 2. Your Weight on Pluto and Charon

Both Pluto and Charon have significantly weaker gravitational pull than Earth. As a result, your weight would decrease if you were to go to the surface of Pluto or Charon. On Pluto your weight would be 5.9% of your Earth weight, while on Charon you would weigh 3.1% of your Earth weight. Calculate your weight on Pluto and Charon.

A person with a mass of 75 kg has a weight of approximately 750 N (165 lbs) on Earth. Determine this person’s weight (in N and lbs) on Pluto and on Charon.

### 3. Escaping From Pluto or Charon

Escape velocity is defined as the velocity needed to escape the gravitational pull of a particular body.

Escape velocity (v) is determined by the equation:

G = Universal Gravitational Constant = 6.67 × 10

^{-11}m

^{3}/kg

^{-1}s

^{-2}

M = mass of the body (that you are escaping from)

R = radius of the body

Assume that you are on the surface of Pluto and later Charon. How fast would you have to run in order to run right off each celestial body (i.e. escape)?.

Mass and Radius of Pluto and CharonPluto

M_{Pluto} = 1.31 × 10^{22} kg

R_{Pluto} = 1.20 × 10^{6} m Charon

M_{Charon} = 1.62 × 10^{21} kg

R_{Charon} = 5.93 × 10^{5} m

**Sample Calculation:**

Determine how fast you would have to run in order to escape from the surface of our Moon.

M_{Moon}=7.34 x 10^{22} kg

R_{Moon}=1.73 x 10^{6} m

**Answer**: You would have to run at 2.38 km/s (1.48 miles/s) in order to escape from the surface of the Moon.

### Escape Velocity

Which planet has the fastest escape velocity? That particular distinction belongs to the largest planet in the solar system, Jupiter. Jupiter has an escape velocity of 59.6 km/s (37.0 miles/s). Earth has an escape velocity of 11.2 km/s (7.0 miles/s). The New Horizons spacecraft was launched with a speed of 16.26 km/s (10.10 miles/s) thus ensuring that it would be able to escape the Earth’s gravitational attraction.